sampling/0000755000176200001440000000000013777557156012113 5ustar liggesuserssampling/NAMESPACE0000644000176200001440000000014513764355656013327 0ustar liggesusersuseDynLib(sampling) import(MASS,lpSolve,stats,graphics) # Export all names exportPattern(".") sampling/data/0000755000176200001440000000000013767174322013011 5ustar liggesuserssampling/data/MU284.rda0000644000176200001440000001240413777316644014267 0ustar liggesusersݛyeEu^^陞gaa^aQQA6AMPpAT4QApBD (1*A# {ΝO?nU:uίN]( Q%)Bb~Wx(J1xpt@Hea0F0d s<0@` K2`k`/{h@t@̀?6}`#lp x8lOp(8 l#(Tp4x8<< ǃvL,p"8 Ns p&8 |B/E"p1x x)xx9\ ^ ^^ .^^.o  W߀ww׀k{uzp0{p# || |||4| nς;?/_     ?OOCW7,c11111( c?&c?&c?&c?&c?^zuG^4c>%Vo6$Ek$^LW$zJ|PObZtE4@4CtKB4FtHtTN=ۘeVCtJ(hH|s]*B}'*XKbPFn?]KY6:wk\?ۈjeT*_S}7u =bX9$*'-:5{-6[u u͎Hm<'ss&FD9ic˯џQ9;ȍsqH֟syU]rݻuvcD5Ϛj˰@+_չj[U{pn~,~<=ozu,Xtl9V V8c8] 9Vsv<ܜdm-r劖б hqݷpY.ݯ }6)9A[촯p}?9v2+,g9UVۉIN0 F;S:h5jUevK#ӝEf|u\5tgPxh*hdz4\w| ugPIz>3 m},[tj+>Fs9n,:-&кo c5;k?Ӷ>rϲuΔEFKsLJ9?HG >#sJmOwsm8cjO^ ~GM+Ŏ;V#1ܭhG,鎬{I61/}=>$ $IWɳDN]Y$r,99]L.ٺf"MͿ/#;͎׽dyrxbׇ3?ŗ,&E|w6ݿ'fvOĎr/|KrzXk2ߘq~Y6TgWoS69Fpڤ73T)s-ob#>JL}r/^ݒ{f|!kG>ZB7MFvyc:S3\rdk>E9Z~\9ކy}rYϡJ:{c)~N3h nѿ6M5$7QrRS!#Nbug^dsϚ>#xMZ";oϔOEv+sndwq/y:-.$c6?e ]>cs?>lB+#Ş~ 2Ff22 ^㌪<})7=fZ߾nB;ۨ"ir}"^2jyHtm+# I^#`7Q~]wLEB|6{1sk?{'NOF;∎9wߵl sst-smFmren߼Ǹ5O|,N뎿Oxl=7]VZIvOCkaڦÏܜ򾣿͑Z7\sX<}[6~{w>}]#qy}=smnF3FG#ՏDʫï3FOُXZKsʵɯw_}U:\_k[ϵϏg|_^Ý:{߻|;?a|XKwަ\>. oc՝2ǔ{k7H1r߄̡eRzsh~^z.2yu4qBݡQ0m=_9y c6>ebwpuӇhK8Oa ]O)4I6j_ߎ^|s?M|&u̧DnR{gߩr. o-r½9$O>H;1XQK r3"cm-}ys'NYWQ_Bou;~d#( Ϸ,JM=|x~yb!Y}W ,}6-{PpƔ9]*~vw阌_}wHߛWkhT.<1S_I{γD6أ_e Wb&ϤkN˕};(ۻ}Hx&L1\ Խ<Yb?vt}$~osP3~=̆(YsHXgbl7W'k-U}Qi7+O6` ֘>:[4'>[ٷJcUf$Vv*y`+8F\/lX| پNR.~302,%R|_C'S)n~<(S1KElN>ņc_,+^d 2-99⏥˩F^wψ29!)k;;ntd.ka ώreڏ\^K)m'QohK {q;־D?4(q_ ?ow_(e|pvyqKsH]$+hl,N fmK1iߣ >}Nm]&`-$FKD%N8U|H Wg"R@gWJn[/Vޗ>;rwاGh[-!m`9?Κ!|zUf5;1l:,qE| 1M,]֏c59D<+gzSl]x@K o|5;2,cU췘|,{1.W0ѣ(2G k L/62{ٗ$swE֖E|53@!q}>Y"l h6ޱ)~RĿ%jp*i/)z\ƞE2==fKm<1ovR:ӳ 2^̗G0.YƿW'eΚ{ ]UvVn4"6e{k1\)P홦>y05HC{>zimo%1,oSvc8d$KH(E9J,|z,x( hXc^\}0v>~}0g>`r'`>X ,}Q0K`NVʝ`U=`G]`];Ogn?$.Lٴm>Xv[ⶭG¦ûΗr޺ }7~6d=sr3D.q?G~+>sampling/data/swissmunicipalities.rda0000644000176200001440000037171510607636356017627 0ustar liggesusers dm^wϩ[w#2}FHPDӳˮ.jkzj&!JTA\LBHL ^6\!bCSO9ov\3~埗yy3_zbtb2mfӵ}n9ǽs~{j;'ص3~4d->G=wx;wϹqNvϏO{7~=#Qчܳjn~ڽqcOw_ |_dƴڎMn -]_M]:3cw﫯ŵFv+'n-nn<{ѽZWܩQn߉|:7Zwn.{YK=4{nNܻnf'|ƻWɬy y8gϼJl9rrjʍ=5fVg-Wd{Lfh+][20N;]y~:N,/lϼ;sXd0*|:~X[0*]psIwOw=#n^]3+?mojѵv)}3`ןq/۱KuɃ灹o*Yvhlu8dh`NvW镛7׍v6ܫ\˫| ?nnM.fLGk#_t/1+ry>5{uǽlWbMNN wF^%'sa{ɈWwv~nMVg܏'V6/vw+=YuƳd}?l[-חpG;o燞~3N垳46^eG/,Xkܚ<9q9ݽy;FUx?܍ieb{C3+\nɾGG+ѾWh-&؜KKn-&O枓9_kk'nSu4wx0;'˸99rrq:a;z8a& :5[޹-F8=|~w;7_KyGC~V#6 93}:w\][SoZӸgV.t8ϭϮbEF_fLM;|a5܏Ő<[7gvf\{w^'6a:2x5Y;buak:mݳv9omc;_ۧoqZc<9;OGx&ܻg'w.64?v1?dϼѧ{/i}V^>F36tq˨lsM&*8aKkg+Y;㟓{l7.4j,ٸɡ1hoɏ 9:yKןʚ֏}wn{JN-}beϮoھydv?6_feٟ]Khnw6p8ݶsio0)o+{&7㕦mMCCSoG󍜜7iegcZY< K+W6Gjd}'VOظ?ק߸bE^bCyaׇO،ܘ'2ϻodpf ߫jK-|mꑓUko>y$2hjʰ{ֶzҺIs˛Cмi]616)K[_Sa~M~CV}bIibcД eM;9ov;C>&răY?hFX]4lҬ;ʎ֮ZhiNӿw;Z>s94?+͵f!;hm[&ɉߴMmba`mƠV74sդۦκ,CSMc5`7ssh<|3v]V6:\;K8l"0ٜlҜ[ ߄vgښ8deuo3&sJϬX,![S7]ǮI&&Cru6ɇf~OoMM{МGVŝMl1MnY6G+0A㧉Kcǰ4skusmv ;& :>ɟ=Mw˞^Y6婙m]s;n}m8dynuPS)'lÇlݴ.Ml~1!z4e71Խߔ~54&^.5Nb 'W9y7Xl{>ݦ?M쐍hڎ&,M'O(i8MvMXM۔O솓\FoYӔȫ3xrClGw~akMܡ۵Y)'M{ĭ7aݣp~סy5ClLx!:ĻCe+5h7m!^xg5);liV٦mTx\![ڴv58:0~Sv(8$Co望>|St[Yl}޻zHGmq̦x4i&6q[!th̦&TsnoS|Zb~>6}Cx_״lt5p?759$vM|y/zM5x\/lt˗_ W$Mi@d;gw^MDޱ~snC~XS.xM:nC)MkgjƷMؤ]G|*<ģC7eVf}&u7}Ϛ\ \ͽf?v>$+I^˻&OsJ68Gs]u{i\ϢmxI~?幡~uQ^1mN]n;~/1 m??@+$?&˜KrM&<1kvbf_~~?7'~̭u3 si~/X9W#aj]Z5zgK|1As֖xBzmhyyr[yDs0)֌=WҶ?˳${|?EÜ2xw_3\kh14;y\sy9 %9w0|PΏ7|;s;'?M[{L@w/3o}ݬ9>Wod_3y gweݾxi]A> l_2/kׁ?? 5Џ3au/‡}-<s ygx3qio!ٿM;sXkCy~wј{)ΐY]jC۠| cZ=C>/+??Ydx -Τ4@@sżyiӃ&oa<7:+x!O<kc/?Y:_y \?!va<UƇ=h.k@ǣ>c'qZ \$p5F]nhCWz\xD;?B7X_}=+z:o&%g:OFKa9u#1+{-@~c!Ǩ5xo{Y!kulɘ ; :'#A>߼;(Y{g)C z>D~b9F>ً|?g=0 ~y |Rh}p[om5rB./o;:s X̱ƴз ?rM=00^}9F̷^e.c$}s=[w!{qo(:kK A 2'wcCpO KY_W#mlpCt+г3jx죃#lA_G: !է# =<~4͐l3N!8BV<g1V=8h&;spi=9G3xa-CՃV=g>1X2-Ler-d%;)t*]>ƾt ]0ķ቏B.x3dwCtv63a> ޵9Lrع#Б3|3FZ``-EGЫly̺N.Ͱ_{`OG@z팠St3!ςc,am=0,f\O x`~+V~Lu pBv31zA2d:=oтЭ 91 A I)k}|;oa{`O)9D[ػ>x?ο3E9}ѩZFQ +O&Od`\|fpʼح#Lh<bD~0`C~̵9b#WmFM?+g/3+1gZz7;b1-m?C|{~xyf` ۱>rCWB.ƵGjWϱC = )2{GO6 gnc0K_Cpdx;89aΡmN93)~s <s)If<)-0a=|F0`)4I>O#Yȿ\Ķ/-'BuNu{-Mg`T@q~䇢g!CŎ_x\Q\x}O9.<%#d6㎱7>qJ|0` ?θ=32_W5v[)9Щ601#1c!:c[r]dsS7G=֒}??6_%` s<3y<)X#7-E|>]d6A>uƯuL˗^]>v Е:6|0xsZ yJ3hS _1vtgLuuേ#m_aF<1 ctu0DFxB#C` B]+>rmۃ^G+]x>1 %]ŧá4iJ~샞GNrxǐ~bxBL ˚G9#|Ӟucm\S;=%n ۏ>ώ zLXO4ЬŜ3Z"kù<03tN3 gB1x#W>}#9wc_`j8}豦Xuntљ6GZ -N=;?HFg=p/EF<C痟D8WOYoG Ճ#6n)F_ @]pOз1:D;dп>~#c)=~3b.t>F #ر |!~Oyw$[ R, 0T6z<௞_2hAS"C[= '8N'CΡS>="cY gO1*'=H#s=dŌ'H>H<8bMycG1#vY)8gcm| \{䃵 z#g:`Sgؗs1Erv WI!9_=Gx6w|!6z3!Ja{BFN ]h+?w_"?=z|KSn𩏞txg`1Lmdg-C+%Im.н9 =h˟t!{-C/<6Nʁ='1B 8ߧ!zηڷ)6c}]*O&_ʁvX98 MM l +XyUg >r*ng>>D7zzrm|rvXg tϠU ?ߖיM+@0?:Xgqc| mɿoq]2fZNJQ  ']xCG~ L6#GLށCd|;WN~+OEYMO#UN]/#Ṷ~DqMOy0!_ Idk ST~dy?--گ\cz=a"4!~[ `N[~zBc>&<_>>>=`{Q ,a-GL!ޥ!dyȇA;S Y_ÚR|wk|ɯ0?"`0nnщsdKwyh{Kgke b=vl<?ڃln/SyO@ ;BBd Cr>ϧ.7we~Co+U寄oU/:C.៍%;A!:PG<C6Z?p,_YO 1>\%qx*@ڟ3ꄹwiK`9ci\d0U~Rr3gz! -=fl?; KCppXJW 9 ctW<>׼[p(20>r02"=ŇusSmBħIUG)|n#'c9u@؍/w|?SkWEB9g<>俢C1si ;"g!%?%_H~r+-H/e?C|;/gXaOzCqi$_%A7GȦQ#cy>ލ`;SO8^ ;]!xu&8cl\ Gz>W~/n79zǿh#C [sLyg(?i1n>#wnjqF|!3_{^+>rPuQccc|2NYP\Om'r[z? G_7>bg(=H?)k(gwzr.LIŞmЕ.tg^;)|e?R8::cGx),~..s𻃌 ;2p~fd'O} tG/Fm0ʵ-4 3%b]P` ѕ ֗':%#df)زQ:7J^S3@6d_5+CTNzc7`{0eu|䗀v׾,2&ƶwvbs}>'>Q<ЗbM;s(9ː=B:EF20~ξ0GR1r鱾D~$ %;Qdm0'{yiG{Ҟ j rc dC.c1T\/NY9r0F:ʷ  >H/c'=C{)s]e=< y&@`jL͜:)#^ O#i1V ㌴;r&nm]tn7:Bؗv,^ؾLm ^(u?8|.;.4>{j@v=_B:Lz=vR~ ="bGICVx#t|SdsL4~Ch,+"fg-0G#l^N]`}ɡ.c0vv/vgA 䩏 %zB p?<;w_9e]0|1V!t[_{#.6Gw [G$gWlY~Yɘw_z0ر6;n],ّ TcBw[>80Bf./?^l||l܅eUp[0?Q:A6ct~>Su:ŌipzBz؜d7.U3R̭#ϰ%t*|HS=C1 W)XASbTc>WTܣaG`@؈1cvO/ϗAsdh. B5\:L tz&; r '3O`U H5Uˈ, k).#}r 3cxu/TυrEN  >G,HaGؚ Brؕ!1@1 XowG:x} H>#d-ga[}ߡlbsj:~v#c1#=E }dXKu]CƎb%|yf\e14kϤ.ձ0 {k?UCVl~jU-@95=3r%SB:@Uڬ6/^4 k1e~/+f-s5l]x {<^^$ U. @ v3Q[N LwUz&i UT y{6/ӫUKrS֍jOS)>@o,hb[03}X¼+`GYk?T>gQBlY+V5dA6]i |Qe͛TӜA;sVi@uV g5(֒GxTqpZl`[͡a:֯/sO]fPj*bj:hɎtV#e{*P9KD>'ʺՓH5D*7~QD=)T/}̏$ʷ/نvΔ]ŇʚGt:o#'˽bZĺl$ڣ"C)?'{ 2Ƌ1TgsX$+Hle݌+wl؀| `7rO.E9Du?^ch8=SוtK_WYlșCse-bHaQ{ZUcPr6FɓrO[9N/+w+rSg<ufPm|KוI~g/t?|j<&[ 'jstJuJ{r~hĻ 8&i}vyvI{ zyD{d7IJ{nd(r9譚#61,uҾrʩ+*>Dt%Iy)5α\(YsU{s-:0D`/#&x ?i joYUj#IdL5;MQMj+FNT[vE`TF#Tjf:ؓDwt^gtJ{oV^g2(GfcƣW:rr!$E/Cl3H7UG;-VbT%WCce/DUITs.>(&a]-b"_O2B<'ʜw*st(f޵%əC $r?wv䗕{'WozD:+FE`cH~3YOw^sMgc(gDg|YA_د#^j\\ʮ#kdC6J'u79D1YU7(0Eg?c;sp9V p˽m}BgBG#zޒ]WUo:TΗߥ3~(?^'Uo5+CBՓ#d*t&dSg@q0C~܈l+BgMBQBfBd$;oj $[gNՂ :Sխ>?NlΩ1Η:O-Sݐ<0{#O=G|2lJ ;=QwQIyGɄ>)ItFUЂ:h?cdO߄*PgkCLn}}6Z{:s|:#3CơSd%_Ρ-sIENj@>?-#[?(=tR߸P @L @ciSĪPD#'Q%ܥr:$ ~acy&y1QS>]1t@УRS^Qy}H`?9Rm;}DF߂ɴf#Jc^k@Un TlR+nK9FբOMNo cɏb}/DC,:t}ȓfl$C`x ۭ!Q@gc'UO\g@d:G.CtFcW:c<=U#V(!3͋t69ނJwtnPz#WF=bcTwɖ }/BVtי)`gz+:Z|bCP#_[-@[ةP@Y圔$"R=:ϩҞ;_\ xk/s-6p.$^pS2DueP<0/eVPB1#77e _K_wRl%ޞ2Y pD -:|Gy6A?Mr&{NF:c"eɚԤe]΄nļs6< ?*|QM*8#ڳV|k@y2A\5 vԷOt!Ԟ@rCD|>[I=WUcȺ61ߠsm`aim@"k|jsW# xY댓6fE+d^g>&W\ P-ltN"?:@ @_Rd+֞+\Kv~C":S#TFz uF~a&9Q6T/Lad>==S\<.0'}",й KD[+OPnߡ_~bTw^=E#RM|)oEЭz# C5OQs1ȉg.:o[:=p#B3d:[i<#>~ Uhw|#}ǧ8K}V퉨.9n.ޙtS l^FztH57hEg}Tˍ3=$jx-ϲM.#J(y3uʓ!3 iiKg_x7 \5SH,劻ʗ"S~IH*jΠAr]y̠Wz g:tN$C[X6*)'EN@5RMv<E/WI w$)g ~@>bW>IXgCY{ tf G-C6t>~;Ax.+s0rŒK'բHߑYO2K̘IO? FWsْxG6EQߧԹ ՟y$$ۊt. }s,[7ހӹH{b:EyotF;m(R?:몽r:ӥof fw]"V>_9]#չ),ȊCۗ+z5]uM{ܬO>a-)ڋƁG,H";$Wx $ڷ&}ԹLy`董;Dy?RX3vKgftH@QI|>:oqĪR<;#A嚑xiUQ頓:K#:+n^:KOxV[z Ȣij3CO9Qn&?Eh3)uM 2lQܞ^EAiJYgݍWV!N{qTϱN/ĪsRr~q}Bu[S1|qG۱r##%w43彴oXEyF0bb}_+_g`oxNؔS0}wX~:Lp ʅ)GnCv.|LwTzZyOqj=* 7ZKҕ!-2ppYC8:ӮsH{mLHx)O+PtO}WgbT?(c[;P] #}9W(}⼭|2ޙ֢ܠsߑr @N_N{%'RzzMV"tuc/ˌˏM7ž'bz:?ܾw=z#Q;KDKssoz=]Npzo診6t[k-O;gimvqsv=o=5酷_̦i۱7w63Cf3sodutٳ|=m9LW- Lբ{7բf޻Y,WoVѽ|87[M'w?2csWܦ_iؾd2}o9,T,'[ }߬ E=z{<}n.7:7y{_|Us {dԍDxֻھoU3A0 l\?77Fz3lj?63k{9YL/'b:$HmpwM؈dz&{Fz:]jΔE~pmޘW^U=1vJi%t/^L/^v;OWh^{'].˻lpb̊kZAK%.dOa2ݍ6÷Ӫ3\ryGVlV^['n.chzвғ xov*r~B^oC;aQbcPK i{lj=ڶ_M^nfDҺU\cedec*]ڧ!>@JMGrۺXi*Ш^2r=y=3"r*hy:5:UČƙ=*j<)̢anq|*6z7Bdq'ݿs\9y}Z) Umq]Ѫiyd]Di=ޕEG ggn){dFoFƈ\di%(:p9e` {\r\} fu5lrV]h_oZ{]WTE5%2 Տkjgk$ j6.Jy-2ZtU~!"Kz|y]9jr|{[v'5_>}gc,v/kvgV痰%UՁ<_Vy~#5Ҥk\.P$|\o+".3se؋g˹ysVxhaVdV4BUK&IfKwYA}tybuj}a7u-^peYz{jXUO0\M_-V Zp:U!F+ͫ"TQm絹oKSV7w߆(3PʏlarkPfR`(ck#l;]dťq)\59WtqS>1f"`4N+ڹqWSccx=Ị"dkui@[Ar=&sRFgzZ^$ ,^㫯qԠݫrWHUͳ^Al5;Ɠ(ד{cqiE¥jKVA2mCJkmOn,w'bnnrw.gk-`vB4^ X,[gSU̲*R&8?}R~&4ϭ)tVO=/޵VP6 ɬ'V#\KZ~3_a"aX"luڠyoI|lg+YOylMrTWƒoUrnfUe[l, wM7^oo<^4Xڝ ;' nk䛙Gjk6UUUsD2ӹY uۦ ̺0fAE z$5ғ2j'^/&OM37>0?}^FO^}|yUo/s{mBnyϣjWvS [eش6rB!ϦP\Q"1Z=$&OT ( /fZbzhXAff@00?è->/$1|0gjy+>7.Wlt;͖{k2~{W mgҐ˹&+oR-^UY#]mo\W{CxLۮdjhIz'K|bYL"Z6{7fw?:UJ%7Y2!Z\4!Z$ ? ty5[&־`Tb"("tnn*8z nk{mɝ2}UYڭGf_9P* ᇧ&\:nACȁdXr tn1۽{lkVۉBuLmi1/!Kp| 7]K ymf6bVzV׫*??YY;~,Or=Uޡ ZQ)SfMF 0V^4p[/HrT; n&|XI ڵ{*9*Mn]>wxR7KL| հn4O̊a._h]/7S:|-6jj'e R+^>I7E[\V;?Y۔uhi\(.M9˛HPx93f-F~ sWyDU} nR<ܿ, ۧ* .ժ'{oaWS\k4 b_B4E%JTW]nvRx4zpw3^L ؇4G?Duzfa*%y1-n _^nnė/V^ *pi/4R([+7ZXߞ*U\,B .¡c ..٥ `́^ֳZʈvu kͦdl~] ]Zsܾ,=oqWz|-1UL᮱5lQ?l G{zO:ߔąLMEcd^MڽO6|N{]3m!TeÈ^?ĴX'V+roŵ]W&5?<_-麐}գɬ\z}\He’g1r?Hվ, qGӧGʊղ䑰rq8۵7w|ޙO{ tksZ8?.f t}{b0){$doЋ*A7@bBMCOTFu*~4(]fת/b6`]^iic{ѣYU@GXML|mP*p)wyQYMKWu U;‘h-3\:V-~]}4Mܚah>D{^ŭ)T-QQhVemn7U]#XB[’MVM y/G :/k!̮řZcK[sѪ88pe&*v9Tj,Zlyp+h5ՊDsi-/nMTyAiS95TV'f_)z_YY8xmY v^[LVjՎGiGl}*R9Vܭ ̽U:ʔjr]U%RL!o׹*wfՙF3(ɽZ%W(jCVLMvUG4hzUItpv8jzDjR LLqUq}yډji?W%h]UV^a&J21SZV;O&yM۽ݝf#ZU^[-lQ#瓫bz}&Wd *Ӕ\͞= Uoѕ*纂 j\ųnfԖ:WjW퓙p;{Wt`gr53Wki_Dv$ O%|YҰZ, j9~\^*߫Ɓk7Wj6ZQyЭm {\]]/{]ػ7v]0ȲTp휖k2d|V]r{QƇ Ս/2Es~a"]UʜgsE <ۘWO8{Op d @ YR/'Zfl(͵wUrVG駎k徢۵{H TdwOrj/а}dEdh*۔%pUb6\aV\̖kx<}heS]>% ƞX3q;1 3(.lQ0 o Wմ^「k4W2;W]S@],`p7ъ+񌯶X^WNuMV1jzN=m>zs;i`vqiqqnn+Y6ڮ-{-8 yc6t0}TDzsO?z\SړZx\3ڬ0 r-ff*:d, 6]8Lx&PO֦j0IcTEZ,S5Y=} SK0c%Vf+"Q;n 6U6jK]K͢-~өyaѲK4}{3w$k*VV5-А)3Ɲzye:a%7XgJI6 f{<{Wl?V~nDž|2YT3S(znag5Sh=sjg2._7}{󺮹2KƒG \Ӟ|̪~qle7@Sh&^53PBdgwjՉ 3ZrjbהFey4{Cf{+jf;)'ÄE>RG,W+#cU/T=ߒ?>M$}ض վ ݷ\nj~/?{8vxeu ~߳g*ʣ7WŜ'7wd5I[hRh %e.H3,P{$MXvA* " TAE6QY*3yO^|9yWGZ=:(xwzDcg:(ֶ7d1"5 wZs1awLAΝp|'PJICp3O=6w\&ԓżv. Ń|e9ؙmo,lc;Y:v'կ GmX9ո6i^ԯ*v0i3QCg//faIsMvtO-%k gf. %vXZ^I[2 pdr1XX0=Ѻ  D/cufAzϱ5 /e1ڻ1lbW`]kl]fRETn.IG/kꕄ eʞ]y˓]y;_otsW/]ѳm@S8ǡޔcp0ϩtM G'EKa׼tR紆 ~`Ҁe_x`Õd w!f=$Ɩw̱niY+]:kZo뗫vG ˳KK}6t:gˊhl'U$d MtJEuybбܕs?G k0꓂5<4,np_)q._ T 9UY|Nfǔ*/Сkc5.dߦ/Yh`A>Nĉ-ىi8jo73rF-:7~j*:8ϚSn0JwzP7e'uއt6FslGė7ހ&xdቒpo1C-U 5dT,$?߸e ˆ4fǃA +^tF%`^u8ט *mJ[tw^0M^ʸ8:M",gS== ̠ G%MIqH%jMp^!'|SNTrIٻM9Ii0GVFۯ2 :2զn=V|Xv聗IgGi}cz:?_ ZLl@{i 3ɥDå5䞋so~Zx7m uKWw8NŒXiYڱ K3l'-UeKSdz{yQ]IG)Q)2m>vH,oT ryr9R;31p>u| pRkw-$X,Y{)^8%@oq5K^^5Hҙmxd3 OA00+9m*&@^=iKgʭVwr=|mo\hXwN\w@7m:,gbvk} [f:i NiZ*ЩGLfd FFZ*"hGhI}{FVIF9yxxAZ$~s{,Yv`|^+8k泥Z0_uQ* rZ]t\5m8+<;gf;gR '9.YgKJ7ggҊdESהt,cM4 ˥+$8Utec'e8GVjJS@qIP'n*i?s KNLvxkNCnI-0ﯹ~gHz~ݺefˣW􏕷9}U9?d4fNw3Bo嫙 ;l*<$5jQ@+ukk n~%4>ökzq /@1K&Ӱ\έWVJrԩ,jtyݣ=`wݼrTcJ鬼ՑMIgPr[o\^JwwWns?f7[dBώ`q+lB؜}9phO۸[ fx~"ݽ#{G Q=[ZX- tܛk#t׶PXc̯ypN|l틏SM]S5/:>?J.뱞pl誸64v`MTϱY^gMmbڹd.l\ -BVLTo.'g5є)m#,WOw>e%N,lDY١`sSy4"awl2  rF[YRy @&dmnkD} <:u7NhLa,ڄ|_xF~=m6P=QCt@\3VxkZmis,-{>=2+LaDqO&kO)sYr'+ScaF!ݳߤwoܳtdXȈmD|RNG U>ؓ;{lBdNR5_ZAG@dXG"T)|f6 Osh/}sMz{mwM'(Yҩg9)޳nYg >t{Vqسr|3X.J٧ز> -vܸzrmαT, {;Hڹ A½C>m;#4]Kxv$&5Ddogy)[Zeǃ:lOw vVR{8{Ƀ+Mtrm챽.瀑l\W*}u06T2j@V٧t9ǫI{K Z{v6@Vhtrqa.K=֣)ϨoL:J=eߘQHyi^*^:<ͺg_/{|V'Þa'^0eE:>Z 2s'i^Za~]K-{gO:KYvO Lkōk:A&|D4 ٓ;2I Bre0LH4w?23(ciڞO%uN˙Hid [::CKW+:GE\0>ho3hO[ +QWRozV=Zۂ,u&ݬu q(#7 N[Q2kb/RJ~r?~aöAS;|} |wg2ѯq3CFhN&R6 ᱼLkﰗ5wo6YSC,|谷8 *Nv}vJ-ΒٚB)7N.$aj0I-Kd{ (NY3b%pr.TؘvFbA5TκK^R:%[˥igZK,mɃݕ~jl7)w%xb|V^*cnPl:\*UNh0<9fxjg VO驞lE9jO'J}JUH=c( 5 i=YAxmJIdkY5+aֱòU%6[pb jsbZ?;zlaNٍ8mjY;iyo(@Y]؜=f6g]ttt_,ܿyl`v`ZxѠ ^a۫'g{2SpDKrMH<ѱBLפ6DyI%3o Ji]`a`pUZiNdC%37_қgҺhrs1q }5N39-I̗Kލ>ڸ=+:?Sa'FK?6gRsNe Vn雚aAeqv@>}"9¶yp]t5{ZF8ۖ=Й^Yx ξUJt VsA.:yB'@,}{ZPfц @nQ 'JU>h%zٰOGV.739}2 Z-Om 0w; 9t2֤0j%o9T<#b`mv6<|)4)4XV>K RCɀQ%u ziA_k^i[XJ 5/{{0L% 3E #c dv4Y g15dʋD*`u9zTmp%k!k?OF'wiZ '*_X]KJr&5nKGMm#h- ݄mr:c sCS;Қ}n1wቔB[G£w^仢vZ?dnPz^; %OG eI'v:-u=91ZsKìeni`KjfRU ݷ%k<ξNJ֏m}l@|}1y&H4ijSXM_Y\=>Bn5V4]:Y̞m[t7h^I8NF#D<[$U|'S TLE^{KpFAHDϥƒBKWJ k!YcDnH]Z74˄1e 'FnI= i5 Q8-w3#X`GDs"0KO|YɧE{8NVl87Lߥk ڠ0k}n8j sFSRJOUٛ4`֎eq%Wn8X&X._>i\)ʩ2|,ܗNYc): qH:/Cؗ<y1TL}|m4jj|:TAްYf}֍=]?X}=0! <-s䜘6\ߗC7I~#響mq.s+ux2d:Hq89*mR@~nJo)mS? T޷w.p9Vt>uyr (a5xlܿ}}ܼ kLhƾ~bM 9l4kv7e ,J>RPuSvr!Nb' {0;t7mG7H=UWrx%;b㬁yTCeO%ZrԿMw Ez5`X2!?Ynۗ@ ݥK[R1<1%a $}G[u$w_H] ET `Vdqq_qQdwcjbFHV[+ >hf.w7d}?LL lFkdW3cc5A}CSuU.&|#ؘAr_~[]fCNtvh:?._7j*k>/g.$dƵێfߑoF9YgZI&`^Y#-$/;$!m r]G'ӝy?svZ]RbєteoN8r䅶*7;*$ |~N)nbH=|T\ qcr}@?|?|H}FjG, 8Iq1>x^~ű :2G1lvnJ>Еˌ]k6DZm@-viOΡ; 7l@/ge?-ѶLs(om>`[2!l2!Nb=Szj>@r^ZIv ׍@JZO rVnN'bgʇZm2%?3P R9KTu;c DG5iY{ļ*OTt,ƼG;G:ރ WK,hGX QV#O: A (Mk/ %aM/%ŵ'8J=A[OrF/(Q~m3v`O`AVkwTVNY>B,T'p6("]WvR׳8äϿdumE;$:9L8HG8ziR|d>kQ??UA+NG[ T}qo?x;oY݄={[(,?Hr4 ȿ/N'N q0ttFta?hkY&tV'S:ۤJԋB8~<8Q| _*3{oH>y24\Qg@QUO8',% 8Ny OZ1[d}cDULi^kR`bJ/ސy$ EV?  Y!e׃fK{ 9qsZӗmkc?:n』Zw)7BQh.>i?8ϚE{O:~ <})'O^9树8x2tȍmj`B'YS|⺎EH3A޺s*kD?v]Mu^n`~s@u$XY;C#uAT'!4Mn#zGZ1gԚŶ_g VǯQLްF?{}n.cv@Ҕ xkt&~_V_7LQ~<]8*t2m:kSϵ Jrzc\XA"P\p?S^"f12?LXǁ>ÒYfÌN\KFE7\\g?EiwGoj?Ԁ6EGz:[0GkUlJu~ߪT};qݬ g>YOoy/'z/ߤNhmhc3~xss+ѳz<:~xw/u tωg֋·=n:9WͷvJ]^ϐ~`ot|NZ6/yοLc՜ұ~AXc]i4t\[~ zWt[1pGSEq .=Rݬb)1ߺoxߢ?8;lJ^c6Ek^U~}@[t}u.뮮L^ ]]t*7~)Ƃ7t5ϻB瞤{5Oڟ!^~kL=%>Ǫ;^ZOb*ګ@wJ*:|J>sUo WD…y=$O5t6mHq?JsYwTE;w:j϶?׹s{ioј{MQn^Csc{UMJ|ΟkSw@IV?Ei[^kK 9&+kScz͚xo߸HrE~du[s{h) ͣ):on5h+NkWmK7N≉55&h&]C.E9uĆp;ҋ5ɮx5 g-ɝM'7f}&j 붞|FOe鮡9DKg+ߺtUU]0Z_弇|*Oiv.9Y8kn_>b U6ҤS-Te?r5uuۊt}7tPhZ˜׫y Ut\U.W,>mfMkZYv*,Ο@]n65͡}=cgUۛuaMk+% %Z)M,՗lzX]b{7kP! !yQ?`U{*XW_ۻȧ\bdCp:2{xlUNdgu=*~n6 ŋ[HSMSx _+i]^:|&ˊtBGnK*.Ǥ'g 6PАU]^?W|T6/ZmvK<\Yqښr =(s\714utlǏ3%&Yxals}},v?=+YU)JK겦)^w] Wy: .ݼm3K1xrE2;.u.=}?+dp[4TjnT>Zan˝/T*]?&9q_,еs>ɥ)?;_[@^qMT54n++X43l@> u8;o 6E2xSkNBXCN |$c1|Ͳyp ZlЂdyu[1o {M>b=4hCc/@N6꺯gTz.wk YƵOۢb~[EkT GM{;cu?1Ibz= qTV>~bELSywK4 .|vϘ+E%SH/sQs|G[kS|eHE:rwwƴ͵ucªhkLsnkT6U;~ǵ'+Or)&2z~#tacؐwMt@OAiJqg֐g+=Umb)TEhmT>3b5֒5<#kk- }} |.!&5&g|MK|mqs4w5" 441a_ܶaKM]~qcVm&>zӿIHW.sto*K~'1a$a%6RL 'fCba&#"|6͵"[@O ޻D4_?|**Gܖ( cғ'>AT^w^ѡWN[.^䴊oq\'-v l_p["y^|Yx]Huz'\ϣѺ~;A;ݎNE9V3 S흾ԕos[s~&!Ɇ֡2c|fqgl$/@e(Bk_| ~_;Nt^yۄ̝y#M,uO|Lƃ 5&'%-,_ruJl]s,,K~V~i|# kRN 2刺 ƍ;>{Z[_Dw{VP5+>\Voq=nso^aJqO~DN#f+|agFk[8'Y8yu§| ԑ TX:? %ϹV%u1 v {>{?i}Zmݯ.a֑6:&Y, \Ys\X,K/+A+u|ڊ~WsB6lr:~:~ύ{{N+^J\ޱ>O E'tݗ]>AFi >ˑW+ >%lDVA =}Ѕr^51C5 cC@ 1Ƽ<2q ɑ]Bb?Ȏ6o_j*lRr`w¦m5㹎csiՎߋM ;!k|e ;\:؋5Bgܐ-C:]ֈA?a!wj`~slUm.5w=^5@>m83BI~o/D_԰lǚlvNl̗ij2;-'zϭ 3ɽ aS›54KPc޼l*]Sp}`|Cވİ$'gN/6 /?Z?8N%-EUWt}Hΰ > ?B|8~Rƭ!lj b Hֵtۻ@K`[}J;| ? \Wm†r_OZE;Ѽ}\ZoK֝2B7N췁OT5nQ3ǡxk|6`S:tnN5uZ>8%.{(lx_[ |qyDɔIl/| GY o3uo3.'=?I˜lx]T^PKEnBbc~C:a~a{ q }yd?xA!mUԏ|Mi+Dwť.+;M:Q=#Ӛ~:f5C+ԯJ&4Y ru`lr~S>>ZRi_G\.'{%ԢPJ,1Dn׹oN'u5o#6A]F;b"+X5}qͧ1cgk$z {˖&1j\rr:.l}%5eMk /u}P=cc.SDE9q_[ _WF]Rqo){IwfF]8v3\Og0fCط>5&|ي 6p\'턍s0{fr Hoqx{36h&d|}{|+gG'l|)E2 r|#Q|DV/D-=zn[rw<זyY+6K&fP%N]GZD 8:&x}%rtmƏn9E_tW'B|b?g>_9ތD/V>4ao[YCAtw~zZZ¦']~,ǎ/l/C͝t,t|ϣoZ?tSˏ}N%vG>8Kl.s7§"vydM]cOخywh ۈrz0B |QǃXu6' &2![جF/pԕ`W1}o\rqecǥd AG 6x _@ȷ ;?ſ79u}ry^%'{IYz80}{sg|zjqI5:NMzG]o/<1mdw (gyCY~u+G4]fn^9]j,^ m3֛}-X -zA^HM1Ũ7݊́G~K^]o3G u.̞B6(1K˗fE[ \tWMq%{"OB^r:6Gm>|rZ.4lذGM\uByLdv˽g1~?Ϣv> 8O*?| &_2d<Şʷl.8v}^كj8d,V3 =V#L,cݙ_x}/[]sskxbWx6[< %ώ5_ufۑ]7ED/;Nq߉{*AG4P`Z>!rwz'~n~GFpgf[%Б}M!b17xu]~AS~]9P㡆MrMJkӚ٫ؼc 旰l[сlUw:Mw0C Y:G;˿贂4/m6 g.hNKm(b;$ /Acͷ.~} |$ƃ-1T.^|5)"],mG}w'4*:Svr6t${JG縳-ylvZfۜdBվ4K Oͧ:Xxһ"LyL^Uj͞?\cZ^MNO >V:<}?yOLB η^5bn y.9nc{4-Wc@kby'jnx,vG+({ptzX}nbYG}Бyag9]uUom{ohv1%㯡7/̆[#/7;>g=\BA׺nڞ[B`k c3L'6ķX'>»Ui<[{k.~W j sd!/_1{=5E[o ̯6_xA>Ox>m<6Ң+=>}b4lt_r{)f?f{4vbN3EA7 1q?|jN'U{ΈkbD!z|-,OubYb$+k">ϻ]Tę ;m ]/3\'M&YU?A ^zj<8*r&>.l[36v ]=bukî1{:1yx~`ԑEfc_+焭B].,Oo9'/:H|O1ҼZY߉z7G~ak׀~kf1Ƅzzmyt9StpkKK"*F=>9fq*p nsb|Gocx4e_6 rFj*hפ:C!okM&z1 UF>k\w1^Zt>Ǝ|FM,'<[Ō;E&\x|p0h~=Xl~ȫX!7O+#.5:ՄƐj$,gMcㆵ0슠#t#{YDž}#=A}.,ki>{%(9uܑ}OX, ۇL;>O=<kuLW;NzqR)u{jzj/;c=Ushj"Z,Xv˂*ru1<ӝ78wd ks[mg+AK %܋A#[sl8띂ǠK|ȊƗ;/DN"u>Vsx6_j;Xo/<6l'b_g\;^j^|3sȘ?ɠqόcX˜?Ӂ?=y @\lp~1;+;!wcߜv}C L~=rIc:r{+lpAn5c'?[7`gf=m _/8G 1a=^iIƚb3׋6bjyozVao'{[YWoHpk0 =yhg>F-|d 9n^k6s%p*?l1lh]e60 vtu&1'K>^fĥvХ3kz|oF=>1Mvd°QoDke&φ_ }~s MAk)Ƹn # ܐdo8_E+t -f?-F6փb1VǶX*K舆]ϣ3:~Duz!^#c$tSdy&jN]Cl O #4kf~eN3ԝ> ٮL^/LVϫ=?q/owW5x:UtS)_̘ aS=irAZ7fm4Z)Ӊ^/qO.q퉺ټ.snb{WC@?d4XSpM qf'cjͯEV㞼b}LeʰMNKoqܚp|ЙOM,N7ן՞~!h_K7qoy ͫ'[?Xz7;M6 ԯ5w_vZ7vV<4ZaYx+gOr^'>~Aݰ{Km$kj <,==eٟr|rN6W*zY1d#bϝ53B6G~oq5O.d*}Ϭ'6qPd*!ǺKnXN/2Bž&~kb1-o?ʘN%}=XG?++hQY ,m?]>^d{k;gOp|` Y |ܧK}x_g [niןt'-c??և/?ޫQ~7?|pǟxO:,?#c/qO{A9Ǫ^vq/ωL ( OqK.u3}Na96Bc 7;M[o,_ < v]}Dw!O~-{q{9Q#W!K8Vk>E2O:0d̸s¯?"r&_;_?&ھg8ҟt罷: XNf&7/Qˇf!v@#6x߻jo3ozZO}&N&DvBߊ} WaB /wOs?f l/,Kjf2^} >'FL|_zOMlVmd:e#ZA?r#i=0;w\Ez^u lq]67ďGyf|eY5$j5qz3+Otb>}$DO=? wT{vy(QoO8Ψ:7j~y5t 2}g:]YWG>gڳ]~Of#_i/_M ͯcF텧J[#EF}9!7^'zzR[ /f8u|Zx-o[  /_[;=Rs:3+7B1N~B7cڸu Fju:}ǜgMk\_5x"h2F2jС°}iE[F&j^dm=coPC 3~H'"B<@}ըy]V;G~Uό <Ė9'C?@kZw˿k@z+YΗk)zfob5¦<ߞ7Fh##Ki]R\[Oyhropo}myط}2M#7v[jߵ ͆V)ZrԒR| 0=˧K#'z1'/vހ_wX {mj$ω[gy\śoR_?/\ظo:/8esC666W/Σosv?;G87/{^iuqYΗ}gLӈU+pLLA4i#5+76!F]4^|dU.?lRvZ]nKd? \޲?ZzXᣀ?I MgަNG!$sk6od~=SlORdyĕև^V@|b{̺=j^+|AfSc}~"Ii1WK#iseŌ yUD ..g-^~eR7+%d[waq3||[`;yks^ -q9'k֐ww:C͓l8?rAԈi}mw5G/055֋U[,9Y&wM֢_ϡwOPֶK~Ŧw-. >ӐF+gCǚnC^N | ^춺2'43?D? G8~O]-Bg#{ =帶O Z-!^j~7E1.֞ƀ udq/7|<_ Xajv]e9lj\Xxl迂}l4:r;mas^t]b@~)w ? | eY|^'w|IltO pi|Yobut-m {%N Ic~e ZSw}_߹Bbknb\en݂q7d<<#V|n|Wf|&|G_ BiʾAf' جjr[\Ǒ}ߌzkjӕ٭pYhZXC} ~YO@?(&4OaN|,Ll~~X塪1Gs-7 ?z=;71YC %XCd+1ų.,&\?#͉ yكȽ9ܞhyU]vcZXO&g"Ƃw/xǹ<8BԡZ[g ?䈠qk!s|M;{MeC_K =]_ުڠ&}=E1#OZ==[}U_SG1%Է[RbG 59 ?;N;Ɨ!13}n{1*6(n#Ik&m势bO5 t6NSX;p cDž?]bBnO[7[ྎo})s1fMmxN寝+X.8CLR1>_c|f:'#x? [&use~G_4mxsӟ\~}D:<̵65'şcca7x,?ۻA4iA#t4_sd=yP#-|??܉u}pԇ-7~}? [ )6,ք2ꭡK# +q.۷򰿐ؑ5d<|OF 1kUEf}jn)Y~^ xzoc|5edog{kz>͓vEo=e'ѕ䡑vb4)i[ġ/٧>4vK3>x(k ~Zt~;}Mr>4V%3^{mJq»g:}HZ ]="ϲĪs;~yIż3 88蒹g ׿7p3A4H<o4'3U:qg9C`rB/$*4N8ߴ|]!k ?o2 ~SC2+V7_y{x:7Bz N^욠n/q6{N7|oc\ĵ[@`}Xˇ>ZǁwXlو9t>.q1\(;f.+Fyxx˃# K~jgm2 af72d9g.!Y_|qnz'+&|%O53!aO3;\Ƙ+ڛ<zmDbk 2oƛ'R}i\OG9R؍ #z: | >?|py2 ?c>!.wf_ `<ڜ'gW=o_u{A lmL{cMcfX{bf1띾 .p[>&[?_ > L|{Ǻ c^t'oG:D̗9=%78m|yn}5ޅ&] =xgYv󾱶[c]C%sh{cv7<,)ொu@N}7 E𳡷ͱ̥xC.?5}E<| |p敁g4v8șƜgxyOWo{#W-8*_fſ:a]~9~r"?O6;vٛhyks7l܎%7y>/lYt4CVEcnjm*Qנ~ꉹfi c~XY;s=^~;_ 97KX.O/G Wþ1}7N9_?c+Q,wC":=|/Gܧ ګ`whP^?~?X_]1ϩu5Ǯm1W)H+>]&'[W*|XL[v->ѹUncV@>WuGuO1&O8w8&G"6tvvoYDhߵ9\uKkT87|Tcr53[xXvg ~.|y=rhܚ84)7NQ!LEe3{5ԝ~ٵ vIiYrӣW>4;̵:"}Ə[~zklGsk}683͢U'32}{4d}~W+S?{!J75֧ѯ}tǧTO]T)!k}br?tKtBdYq:췑Wߎ?[#'pOt7<\Ǿj/yA'\cݘ Xh\MPbr.~sdy]yL 驍.>tf:0yg?v{7)g/>1?Re_ 1 rBB| 2gtM#o)m.K_iu?]/392xxIx<{3>hD8&ޔ2vpḨlMwm; u&__3>{}(s_%W G~7nxuk`RҹQKsga\GUƸF<.U1C6?̧¡DpuSAOdD zX:?g{@66D :ds{#gW6SyO'~߈2Ѹ!Řw_x|X1Y_ÇDZƞߦ=wy]4߹`V/FߔKtmsGg,υO |^&յV%U6ZZh>XQ$/ZsR0̏bOkcJZ.NeQYND+L+eoy6n_3^虝;Up KZ}XтQ1u1zewWplc[Dv*=uf??cg~aT05a+Lro;%ow57Zp>'7W' ~u47,?L#c^ϞNUd?cZQ )3*6Cg5-܃c:kɒ !x>)S0pgQ[DkNqDFA-n ٖϏ1~6Vv37F46I}bHg~hϤXCs}ڇL؎.S"|RΡ?cl83ٻq`ߡ9s/>ɱ%GHkz8Nep`:_Kpq8:29:b܇}D1'o$;kh_smz}0g9@?7˯W]sa͢yE?z Uqd\Jv?)ǟrIe`y? H_EH|i+ gPvXalO8;3Dg0.ܢ?ϥ:^e["ݮkq.އIEj["WU[S]x׻\K^3#H:_"vW}+׎|t_- k-[NJ~r vvSzgKg{0))#Cot{ Qvm%nZom'yWp8U:s9ǵE(.$ђikѧOsg^sjW+o屭6 }csgViwWH'{!jdQ*?A4Ic'5O\qM&=6٭vo&ƻE҉12ɵ/.qh5Tt6}sB>Uv/ ٖ9X*NUI:n$1;R^+7̥1h=,^ ߬v#Xץ5Y6iʟ#dњ(qbէIjk1եLT*ZӤq|g  wivȥ{"9Or:a%oE][. Q.t#h- K1J;K?DzL,oq'<gZ/yא e^:Rl:]IDgNE{GID<&84NyG:GGt}uOQ~٠Hgq W$; j9.+fӑ:_ [SY.+kI!?\eʷ?H|P[dtuteŃᒿt#)o0I(f%*% ^ut2]{`[CeGH.NxF:pе#U%ms?PTui$z{h/]I.%iݪ󡒷K]*Yx#@"}%3$Ourb6uKϥmDozSy?SKǑg}Ƽg{ťh St[푎fܢ{_}]U5ԥ13omBfIm虌=u":LM.}toKp/w-nڬCFr~OdqIut1=tթE`h{^-I]K- 6%k'7HJg rZ{[`X77Gm"]47#[im>\riҘ=PNnq|9aڪ[<ٲ5i>d{dmNv>֥~l}XjŠXExc][$OyՋaEnKcOEV͇͎͑#ݬZj%a*;4} Þ:ou6 Tml7Ia-{ʎ6 N_levqlmbժxW[k>/6[4N6ͽ]3mhlYUYth<=#:52FZ23:dۤ6EeLVf;W(FUk_N?4gv&HNf~DFGS7֡R7lXjqmgS6M]m~bLwCfWӅiK}-|hLuWKXLڢҾiٖQDtPuaMSDo[TeƓ~)c'ҳjڹ7L>1mQn.ֿJ.^?ڠh4 FW%O%ҙrZ+6&t:MO~CuU׹],&\]XK\K_lb6xb嬿X{6:?+}E4G>XuO[VjTKcR%oe ?gQfǠ"}uL/5b>lRp(RnmdNJQRī9]lVh[Ԣv=j8n5Gf$./+cz60mL6֎Ou֧RDXvhb<ѰOV"ަWyޥ~dm ZO{,ڶf>e.+?e-əLθMM^!`t*Mꑬq)Ft}bche-^dĥ%w>æH^qkdǸb[{v?216wd⡥8X|D#{1CVlUIijѶ9@.*o횋ucS {9%NP>P>"^ {">xb%|֜;.2:ӆ31.~=bNsMƫ~Ey9\g ^ޥґ]b<@NV*( 7|w ޞC8dؼ&==Og6cˎ{\<ў2r3x[ڻ.}OȮ$\>4RڻH{|{]YwϰP y=wTS]ǺKoˢ&Yʪ;F:\~3cEwH.}C6l5<_UY9G^]:g9skϩy辽g9zT/C]~y{qٞsqkO֞5Ѱ{t^>"hqٷ]Ng6ﶘgQ|չtf=7oRykKM={NΥ*[\|֦= k:ޟ\~Kg.7@[":9l)?c5sm$Wf׽+OϘlnsQ{gi%>3ιt]ckErD7^;$s-ʷ'.}voml=gFK} [7om󚥗Kli~<9sG칶kk>g;ΥqåkJT'uյM&w|6vY5mbv{`6v.Gel>O.e-[95v>jcvvi[5^ oK69Uչ=mS͟G\GgIDuLB!J 3~a 7Xx]{]-Eviֵ9A\EZ; limVY>uێI|ǥ18~7;L?Dr.-Vdw(tm~l}ldQ]5n\V.flB&l:2[{c3qX?v9seyakcYhX/~ec6&l\qg6{L]ṈF,)]$\9o|[|'X,4W8:8LgY[;=?o3ۘNLvΥ131VlI_K'gۏ1.lYYe+Y9ƾvK;E]o_e+gxam8r>dylˬg~Yx GzǼψ׹\8eMbom1.{-n';'x\:2emn--bW6^b='_/geʙef?ge}5(#+l ?.c2~qXbtnc?hdc=tMVܷfny>jW#hlټ.75k,c9ʳyEzq̌};vcڍuA[kc6jS^Auϒ=wV׸g6uVƻnW1b溫>dde̎_6Ƭl^}c1ﮮW'Ox5C/%_mP6\wvƞ8wEQ{ex:=;ogWv#~c41);lD>LLhH_#YVWQ|2+x|VL~܈}ZFk֮tm_vޙ6j$=ʑY];;hT+ݓ.J]{|%=ClfF46O?ϯ4]Ŗ~gu>ob祹_W:5ZϖmCWQG?K,*~fc?Ϗ<}1;gnT+?p_ S]mvVwſQLH3ghLs屺y|W25Zh]E|{kzWe/JZKzu]nܔs{ss۹N:F۹F:`8o f_ܗ;7͹i?Q*qۜ897lйQ;7΍~}OF87WH5:7 sp>pH|8oE\3qspn?HEȫ:.N {H"ay?N]OBs?EHq;H{ su'd ޽o+q4_vd; H(6ܿ5$أ/c{$m t;9C;u8 k? 4 y$ز}q:7!Y{'$GǑ8BǶ됶Gҹk9tm-!#xn?iź8^+ںu8^۴c$RG<]ԛ7 57[ЖХE$ةPп$[Hy%H5튄vkz [B4}m: MWpM 킴3R;TGM.!Mۦ#D~a|߬rȫC:|HuܫAV8G:Zviwg÷Ujk#jlU{H' tx z5m >PHtFqT/ԯ GOUqm 琵*!_-UюUSm\E[T O$*@u܃ߩފt9ʡOVA |#d@j_$\:W>Uاvn)ʠoWخ VUy}خr߆z;W'+ثߨ G} t*; \@ deOA̩ 5~VT*9M2MZ v,W@2lXF߭Be2t)#U`2\d8/} ʷ~_o#2G?eؽ a2l\F_)_,e2lUFw)Wv,-2(tP2[x a^Hh|ܦ:e%aZh~#bA qt31e c](veewˈ%rwѦeĪkH>QXS? ƧZ _::Bj$D }tJW0~"!6з-yOr".J%ei}n(Z,U?0^MZHC :J |݊%ع~^^Dw{Jy-aPDal[D|*AB)1NAEEq\D)E*q1wEحxPD("&8_|RexoErs"*bl,">ϊ=sy ׊_}ر]6+n,/_sUT\~_-`U/EB1&EYō?CeP/MKhb^Yh"6`b(".pLP>ySt |&' 9G&hq,A_Nl;힬&>#^%7y^kmM=_}'A{ =9T;XtY8`J06% ,9\ }D ,6M0v'kު-//91&o%hdKku~W9*BE[%y =~>`KQ>(w2C]W_J)18d@b^&eR@?M0/H0?+ 07/<q{9_#o'da^]} l_8g}r)( {7!VS_c *Gt ۅ'U1?.mĩ.|KwwyХ(R1o*DQ}\"= R8I10,#/ʁ8TxQxYoRɵ{IX^OF( [lXS@+L ց*ooCķ ds_c.Yser Wēq,#ٿuhZ?`AiBGP[? yN9:@M<<5hoWOy]~+Sy{?6U^Ph2&ʣF_z{X;yݭ1^hk(gyyE*LA<7o0{c%C?ՙTќ.r#_0S=%sU<s{12ߡkƲ%dC1^ 9ErX#sW.ueLC{UoT(~ùC!0gaa~C!VoFr6EA!;A~O1Dc彠xzޔ,/A/dy]!~01-ȚCL=&ynRO9wF l~N6@!n~zsWksl~7֒ƢmXzOյѤm'GƋI=0y_Z_0I7U6)i=]Tbʛ/^5eסJsrkK湪:3VljsVd!GG%w2:_ssda5ZyMz3`Q?ZuF>d~3'PɄqcbOuc(PY[Uftc^Qi ]+swte1p {J[o_@&YzboP2 ExO*z+SR_Um{S<:<·"zW*z]|MD<~w_T߉sCe-{=!>,yߋ1üi]0guDI=V'ґ<^zH7HoՒ շrW=ދ#ZWʿ^׊o(]22ݻ$uE*URrM\((c:Kj#Dl]_gKKt~grG_$Z(]#W˜tg3Ths+{3a]Xb3~}s 3)OjTl2NJQ;R'DT4=6keU:*:Zš5Nay1?X:V}ywRwtwɏqAw?:[|f߬=H{((s.|+rKewopww+{޾.N΢2^۶z̶oOѠs{&{D绫J;)-S9ZxEtmew/KHKtdl-Tξ/8UߝNϹў2]-?ۥIf^*V>kE2uD{PE{7g(t_;o}$'[3:ӔR{S$7Z1URIT~kDpy:kF.]i﹎swǸ;㣲X$Ga.{#\\Qob`훒}#Z]MA..`7ĥewtK^{Y?$u-p>^='۵GlS6}xmb9F] R8ǻ܁S\nke0G!lucȾ+\o>֐3A{̵aw*0 I/XFc;,1; ea5 mPCp>c LCu [ ACAG!^ z y׃D35W0~1k̓9i~4}w`[|zF}0NE {? ^ kޠ ^СDG=1r=f'}ǫcu{`u}wC|u=uq7ت;0vØ 늎"amہ[OrWsK||!_;w_;ڠ=Am1i|~֎yU;Q;h6ATmVشsVoZqn][9|ozHǶF[G[-k[+lB5o[Hзfj[][.ͨߌ9U3tlڱ6m^-hfأ44Ѷ{4a-ӌӌviB[7o4M6 m wVSma!CSnMgvi$ba/@Z[֡W-}ryX/ֿ#׋`~*]-ЯC:l^C=a:|$K P-A fکvj ?[ܵ$:} >Y ڿP=WV@z V=8Ǻ8R}/"=ykgU?U̓X{V1Ggk+H'rU=з9C*|!XT)ƺ*ƶ U#NW>U̍Ąoġ*뀯b*ԡ-[MXkFP9_Z_+ue6l*5d` ++h 5XpOe.#^T3fa? lb+1 ?(#U` /׆|FaH21Ng#Xh2_1pۗueh_ C= }u`nG)2|O'bV>RFە) GX8mľlV O}p3%L9 _ v) J>;X:PiشR%lV˜X^Ж%ąRi/a~(a XB,-,4QB))A^7M9%y Yj^kK tiIO&V4LP _^"<6jpxjG|nvۅyFmo HmmO 7M:"vT+N'"|xD]"ڲLa"ڧ6,"B͋ }p[ ?X]|\Dz6q^O}/\J>*cLf hO!yIGQYb ] 7>{&k-[}'bZo'{L fTX]2#8km?v-`- CUfdI5ۘhąGMb ^~ϼ&fgoUuw<>@_^_2>1;MB4V>KZ!x1L<)*ひE,EX}Ul⣉w&ْ<ƘBlx=%g!nxUL3q#Gϊ zzYS9}Pr>LͥhbE ӕqcYx@|/bz_2rRtyRI6RtX?SQc\~{t(y.'?|(32S'hbmO&װP->Ĥ߼GH8jX|kYi*C6GOl:"De6h=b‰%zVrlwkPߺʛ#NjUgh=򜧼9M6uD3[l_(9Q#:<`1 Dhݙa 1b;Y4g(z_GuͶ zÔxN?VR%KNJTњ+`|JCT _,OrԽafR|4:7,t_K mA϶:cyC*w=fɭe{sUy,[%=ߥd<.|I(cAK@kU&iy@Rq)^KrmDPXUץa%۴}l8xc?Vt伄8(#o(:[~[uD5};1ȼ~5DJvY)ކ~_ohG2qL+*GyKe_Uq_TԈys_g2,K\^)g0+UDAEtW4Ow)T[Ri*R׆6g,p֖NQtM|?>*sh~ݥ8Ut9QVcume>Zǩ1>IuKqYcT6:\_QD'>JQ:*>9:J_u)(ʓ6qǡeCp_M|᧙zOes;[9RzHC%מcf=dUi^?$6LawQ\>Pe ϼkDw׽m]{^q)yxRF hrL;GtU~[ɻ l4 _ʘ lMc+lX ăs)^zs)Nz moFcCbzs"ϴn&덤|u)nK<+e ?KGuHbb}y*%g٩oefg=]FczTZzQ95Y'ɵKrNx>u'|譩;I]$Zt=^iM5ڣEpּ:#Tg%H&G0Fc aJFDgK1Ѓ]-x TC= * XEX @XwaЫ'mXw`ц9Z ʶO;Zm}m6fe-X#@&[n5iyraMm ~҄y+50ߨcN_x\m &::ƣfOMU-0ƌ"[e؇{sަε5\9`@)G]$]'VްOoYswfV1V0"Vo |k eЩNՋ.{{'U`*1cuHce|nZvпW2b==W/>A"ejN _ bis$w-u< m\e *W<UzZ{ iCGHov 8J>¢=%ޱB(ſz^RɽvIL9I# (c}/jֹ)+5u#".CKqt-w>|cUZ"9^eb_GqVW+Eb 39!W]oI 0W{N 2y}?Cna?ҙchfa0W!ޑ"5;4n v0nE[8Q85b:# _K'wEmWVh~Ub HbfE>/{֡£m+v  3`ވ!{ׇyI ؽB9"$g=`_q"vEY/Jo>$%w|ܚ` +bz>ɽ/qĭ.X;┈y簫OxĊ]0vb%yp891w3z%xۃ< v~+҄, wǕPWl/bu;>ई2b(Dx6⪈#zχ>J$1#?Gv7Joژ#Ľ/ELbq0./HfbI#^^N\:,6{K+uŏ4! ԅ&l @hh|A|UW;:dMg;K,,MU7D bxڌXbq0y cvKlG[},mʇ/q:[|hK*, =Fm̶}#%-}(ҹwcz:ߖcBhKo>ďx[.33ټpߛCǟfϱ &fcvf7xm.rU|=ؤ7Uy#=*ag|xxw>GƥX!l7|ILZ#sOt`~li+FZhwso?q?><&NG]sgW.#x,^`_y>'q^?A, {y{R.b^o?RAՃ-1 w?xFtC:Ēإ8'.m!0{|н+jԮ)_.]lߕrh&+[B?-ost~4/x>l|Gz6A:?ե{F:Cuk8eIdOW̊ж N'Y/> KNe)yUJ2rlyhʆuk{K.^"^&;^!S.ӵQ[Rs*߷Ň{'}@G#d]=7V=b裘y ?b9Ɗ\%'r).~G2^- rڕ8K|g6g)r龜;%\ѹDRa?Kt,#۬}XU Tق{ґs ua85Hե8.?@ؿo}8_[]}gzQ,yKӢd; vvVeSt}\ ^u[!>;J=s/vK1O+TpMI tNU'۱}HvPݽEɺlyK1l6%Ow)vQ=@Yf.ijϓg~YðpaR;- .W3\7;ڥ'٘اPqi8]!:F9BQMOP0oc}v.ŌV.Ū6D2*ݖHVîbV{}9w+R`K\!y g8MTf/9Z3VlR2ŵ~*0 Nֹa ÷d:R6I!>˥J;(t-%*Gy-߽$afb]Άa\K 6Ez.S.mvZR\["+o]Nrl].< Ňt{ ɷK1tNۺt/mBً4]o[ٝ6;\zmuΒyL;K/ӅgH]_2an3Ek7њHv`ޗ"c=#^ڒX9b樞qnԞtke믯d2-qioR<֪gJ7]e/I.oulY۳H.I/ɶka h˭"= @i- v368˲TCJd-u)K?3G.0JN.*u)qRtKqf3қ/ #YyLP}սY=ߥygQ$\=aL>6D2rlKq1Q<'e`5utOuM7R8ҧ궹t^:wE<{I6ɲ|ɥx]ں,Z#tݦ:\ױڦkķ__[Nԣ9p-2v^+?>7oo]TGDUygݺtldmn|Xv@GۯkmDp|tw0oGi=eF#h6M0jC\k۰>o9-#[{ \[a`۰k=[@u[ hSHX6^8wp$yMX7M?}a4 ԯC:݄U#Qyew ڌB}Vؗ|SCDoЮ]Z5ط8ZՏIlþB*dBڷU {s/*qoh߫ckQ]{>ֺګos*vea<+m+h8b]]=PxqVz TnD=~1ת FB'mKзR-uB=?}ːkG_CI QR{bn]…z>=枴Ӵ}8:L 7ֈ%ўZ{W{j؃q?Ko>?GB>EA1" %ؽ1t>,ERNj=WF{ՀY&~tƖqa_֗ } k^EħҴp m\B!WZ!{p'g{(E\*"$'"~V?K'={|NF,ǫ}bf{[v{as8?\=pb!MFB6 }U;Ǽ"!}{aHG~tbݯ1夌O7Aׂ;Va`#J2F{k^lrs_ }uKK@ޡ޾ wvjb( Ġ;J7fq 6r?=U(O=<cZ~OΛd3QOT}=}~c+OKqd!tozxDJ,'Ă8A:g]kˆq@Dg1oh-s)~{'hcbd]by$.u7b &&uhO҉WLݜ%I\B黙l}do+@m#[ td9^`jdk1׳0dG=xJ0Fw|3a?Me1^^)|.c^@ [Zw3{I^B'H姈 $#ݟFy89+}-"eƁ9~ ^i? J؊=_I/B-.?~1A#1̟r!cod]ڢ'"n$ŽG)S/W|]}l,w`W#^Kl dg]E@9}?EVn!?0d*>NzE߉oi:C!׼ '^E۰=x?ESd{yq|-nf.? G+%`'`G8=nq.L4^?Dop%nª]r47ǜ;%d9tn {nE+w/4nt}69`vR3PǐE3U{j >hG28NRU[.t82x^r]Qx|r;/i{-2KSsߝ,?; 䓜4_Mt]q>GВ/q?)ڢB*Zv]5V[ L|u%4#諱sf G}*V[lc@ϣ:B< zy# _ ֱ@aGDd_CC{zGs3}NN]rNE!cIX;Mjw-dG"}OFNl`t8亜"8O {h5:k9_#Vc !c7\St 2-NnsRqWȸk:焐1DzRZ5ݛY0t<{?|v+B'`ts:x}Ʈ~=tNa9w3ÐOVI}֣)KQaw..~!cñs}%^U=wGC8_EeiE8wQ;Nc1^r-Уk;|c.qSh[D۽d1'#N!`e?v> /fS<]kVȵB{ː`s8zH.";[.c_2|! <ϥ"IǨ. Ʃ4ΠOEifKqa.|qSe*tq38xMB߱sq?\IdB:|fAp tѕ|3yb5]'ooMF2{w <8gq]y5AOۧ}f|{ڹMm6F~eӇo ~ a{7k}ͧ}^/kz]gWB w,侴ٱ=OL͞] 7[zg,loGsmO{Fi6~llgmL\nvΞm==sm[l{ڱ6O7{A;ξػ|jvlomxiۛ-Z_mb1w+?k>&kމۺ}ߵjl7o}'6nl36.4ێiPBAgsPKiqt7@K[{l@]eޣ[ڜlr--ZM[~Koozh04ػXKӭtq` ۷_i0nLifmfPoYgodq]w-jwӶb} ՙZ:훰x֞egv,ol{6[ ]c6:k.kڶ)ѩy6ﲽmJ5일99ʰ=z[JJ[GvL:ĺ+Kda `{X\_DItca#^\\.W@7Y`ƈXq';DLv_%#fݒd]؜ݢcxU}X]X#kG,|&+h؜´ olk۸y{[5c -̽`atdۈwza?tHX9_.duɥpݞ3%oĜw<H:ľz8ekwnOEx#hXyaCE済mmq/+݋Wj7oW[}gWx/iހ}vWͤXZSňrB>?GNn0Œ .,bGy˓ުs:N75{mk ފ]6*,uKT"]q*vNE{af+[V\]XuHyAgYXXRhK<g\l1kmv%W_Xw=Z|l1knK/;i IE ۼqʕZYi %1$Lr&V ճw[+6%bn[I8shd$ޚdz w.1t}bZ 0ϟ Pxb aku 3}~[,c;[ -~{2}?="w l {S5>l>`8<OGVxtNg@o˗x?Ν%,F+'w 9OgyVmg_"yO6Osȴ:(@@aLj Ma| dY+C]+&a3hP -sgKv'=CZcc=4lf{ v!rڄ 9z&gc?J{zvg7==`uC vxD\ZcNqp% m{-+{0 j4j?wB>{FLxkΧ{2%y#N|6:3 lG̻|0}kk|'ZoгNc'?C^IZx7'9~-wE>9 ւ~=D~ [麰# Uxߵ=3#Vk-ߣӧ;bCX\&Xoa|3ۤk~ۯP7^'O6~${E,o"o/>?+t @S, pۉo.|%<0.s-mgEޅh/!_Fۉ 6~wwx#;' 9G"?OqqJ<7`<6x6QqB_ q?K{G 2l˹« w+ܮ0ci{g EL%;LwKc%Ǘ竼]x۱u!ɾ;ʏܱ.Ӹw;vx C>-DNaw qm_x ] |~aU<*;8]Ʋv=+5M|~% uzaXw\ǽd7C^N/{^F_x*p*uٔgp7 >vn>WaK'0'ӹ!\Bǯ=QCcAG"|t.7sp 4h^6AsWxmA-tȱvaC{sm rI38_YC0B(mm;gl%m(z2T(-ln9<@Zllx ˼ :-A3C}ڻsvwrf춎{'qMqc"0YR(%Ⱦ.zKB#~|uW1$/^^ =Ox_xo@ .ˑSx#*d]6@S2{Gװ;]WPt> <~#Ghs: c8eАs@Gka dYpXr]|{.~]\Y:5sVtqۻbC6 =w2-Gy!^2z,h.//p߱ճCu>C߽ TK]Wǚoy?9|1w;6w !c*mwБ&l/] ܞ5 gCewL C #?ڣi{#sv ??:s<1ӎwcC;نsm XdͱdDZ16{cCIC]0x,vB={h?7@g@8A!sr]!uލv#B>&=hwֻPw|'Ꭹ !c>}ѧg{q rpׯwx!c{ Kon,r=rB[mZϐ!޻6j5wt7ن6rmnښoOm;&GAf;OhU8n2:-DŽ;Hqvu#7.d\x9yGڶ4:\?M놐1N1M!n^ch=h*uJh}eª( ZUcsCq\~YI8Zp"!p13&Ka)//^)Ljڤ&:!l֊EN/F,I~ak}M:w 5ggOS;~:uKlH'4քkqk'47&Ld5E\3>9{ģi uI$!$bB-w` uY)~F[sp1.{|1*6؈셻>КpnҸX/ȶ YO1֪RLF~B1'_E?h}]Gs#/,d^Kx]#1ZG??x;ױNP /a? %'i؂)n"Ll'i~YLǃi5+΄M1kIw?hl aqvc&Ygn14T(iA*qhEs-rmx6q]GDŧ~?z!a*з&02ٜ1+t^Rj-\ktdQL pX\I-W)~"UkQZԺkvQ~~s_dh7*=#4WBߎ[#] :##W~?lk~%|t* zfwH2)τW kSb%ei|k=8b]]{t!^*F)W'<ȯ}ZI׸F qߩF&@CtF|Hh,kZkK~qdG:@z>vz@.X:'Y+sIJ}=گn1&,u-IO#ƨրl%܄"q)W+ztq8ڥ Z}#o 1-1*)kaddslIM"C] )V!jljMMsVr߇n}xA}hMs/lbaF&cܞt25G +z]sqh֎{B\-O!cKNgB_>O4> ?r{mƷxhNy^B@g ~Թ/A0Ͻ6r.< o1D.'"Cz\|'c4MȯZS )F4Λt;9#Z`=F璐kJˑ_qBH:B=F&ɢ@M~m%=׮ڞe/|m19WȤ!#|Hv?I7%v4{5__ |q{DڬEɢq2aQRBE9Ǧt~ϙv:`ۛCڮy#tl+|Rt\Csu7 zL_whx;LsR`sB0*f8e#؞a! F [7q\;Ŭ0焌=) ~[ cG帋5cmD2;{472ikȲA$zyo33;9g.ȸv熌/ 9A0ḚUh퍎'Q1-9x5umR5$5Xָ/S6?6ZxlNJNFǃԐ1My"4t;&k"v_ɹڎwb_b=e{9k (֎ >!䚒#qƄ\{q62c"~8/w|8l3Ef̵}h d܂e ;, >VCE!c!xx!r/@uH2Nh{l<-KÎ!tU).vS4=d\d.dҮ!ތƆI96Bs'Kz>LCmBȼOǶBw ڎS۝%!zsSxA!d~!cy.'9@8rѴU,p(75wtr۱bcBl1,d\ l:v3'rO\vc~GO`duF} :L6]r Dz9.i tDS߮qv?NG~ i댌 ~o,:Z;>Ӡ <[qBxغGȵK ywL݄kïz7ȵ)!b6dd>̱Q> 纏WhOG7}wx!•BON ߭;8Dɠ9q5`!׬Pk]0P{qO1m*6ّhcǚM_?8O3s9CƳu#Cy?b7SQ_/q?=ǪuCy G8;dL\ߐnu,Yׂ,?DN}-伙kaGǔ9{WK~7dxl98yksȐkDؾKcgȸ@_ǐ1cy[x|m1?䚭QIl2r< muW@x֮Z\W}DŽߗGȘB:\Opx؟>v9v  nt2~1}}otkE_{xo6IN!?'{ 9z\nGAOE)dhGlP;\79dߏ t18Lmiߊ=Bbv N!~McBoƐk. 9񺎷l#B7C3*Մ^iے}3рMoq6y6mrbǪzڂMkFĎjW2Cȸ5 Y]:v7e֋wm[ct6jmUu ~5umCȘ.!ڮ9/\ۺ}:-8^.ؤ]]M=kC#7h9n)._[mnV!cK!c8b~lr<\mn \FhU !׈nqp:Ԏ.C!Dg;9_y5]7v U\[ׇ\]ʐԥPQ[nh1oТʞ/_ڼq!.c7gga2Moik{}bW{z }{S]mSa{Wh{m?.p= f.ۮ77L==nǣv<w1]{fa~m'f|3zk{mGw܆f;7ٻn6#ddM6Y&kmJ8֧؞,;̝L۝lMR]fo흩 ۿckMvOEj[؝km_sU[{w~n&{k}m&ov9-Zo1lcͿMg5ӷom߭?kfǦ?fwM&_Mee+qo7}|Z۷sh-vll4ݚ0}خn-Gڵ')1]{ö+.4hi,nOcogun77ȮmԶ5X51l;k:$;o&.Tkj|W;bީq[}Mҫz]wնج3ՀVٴ⼦oj[mfMbTK|=\''6S[llUkzdK^mP%>JU\ٸcmƎ],jy[lVd;g$Wv|;y措mt^u`j[U׶7RjUϦު<ӲWRțC^6_VYT)dlNL^v.YUQ~6W5+KT<^eIrH$OTOTܚRlFoSmsG$jWMLtcmUe{25ȍW k[e|8*zݒ)l/bt:~7p擲C_SFWQ]I5y%lk>e%qyv[)sIu6mNQXcʃ97ՅV=k6FdײrSf{嚬N} IFd'Sx*}hl $k_y)7EK=cJlUyJ#,[cmWmn%cMVc6,=r|;\ R?/Zch+)rtL9^mߥܔͳ^cr5/,eUmk,6BPKQn%I=;FuK룏^fd>uևǞ[Nuc^ƛbOS-NU+dtitQ rՓ6M95q_%%cn1"WзبKʳ5MRͿ'VNr*dGuoS*clkS~O<7boR)ɞrC)/Mcm1MX[RP~=cfb~ƶ1GPs1͉r!rc'_326yezl\%|5x k/|Wۯz${ZPn#ac5TNlʝQߒ1OvP?h1I&۶grmc-ta-_Hz|F2Pc{CNsCom1L/W]<=B\~\gvy^o\ucd".^_C]I. \Mzl,*lmsYR>XYl%|X";}z˰f`wޘ+e1U9]ޟ}s5? Td51p22\cMڈݕ{]MQr?g7Z[P{9UG9+<_roOdpKZd(wlT4h,=?F,EF] _GVȱu)wcS9fl'5koGkzV$YlZW1sO mk6q KrŜNim3OjXKP20uЪ+tCyB\#]Itbl~:?Rۘ'75=$_}LCCknB/-+`V;NgϘ/h!)eo|]>!*wOnHn/\a*G1*_w\ՏBq59{q<#GQ܋oCxJctyI|u= y[ƅr~LiFȵť?G_}ٛ3B|aknl߆q+ihNۧ<4"^ohi\3Wcos(Q#sۼ_Ѿ>7,"C6=rMuσ??M[}jw$2݃>#bF9Uw;"r<]>slE'ۡ mC~\#%~O@WnusǏs,7=r^Ois(O*h^۸$2.js"tFo3<ˡ!"?k@o#nȭ| 9s|z>΢srynr^):_*d8Nf;;'a5\?~WWCwtuO{鸂6Nk :p@oB5lgP\}/fNA܋E_C#}ba[]Kv_A =\c6:_̓i?Oh2*ΔwcЂsmohL%MƦs]ȵ<`/Ay]X\_ C>{&N|= 2.dgjȵ=fvK!ר=sȵѝ&1>~}:&\0n<'.О 7㽠=):3gKi!L 9g'{.P?~S8M 9gB!yݨvx@o9- 30zޮO{.àzy~8\\Ir>穩Mw;!~BM! Ϋs1vw m[u\krH[tͱٞx1ݧ}ȸz]iyo˾eȹ kw|[8ƽ&6i;L;6]omG{2ԚZ ;}ovN6ovV[ ckޝ{[;VvѸ.WZ=?흲FK{Ogͷu%n]n-_ sכ ۖѵ۱PgǾL5k޶F'Ioi3jU0ع}S{op '<`yԢo YcYT]Wevꃄw-۳cfa mn^0kU6/T ]]VށmOS_uiJuU#Z[~߂z$Ě® ~Ml0h ?]U6_|j>]bc1 ?63a&`܄I8=^,aK rɾoJcbrUM&FK,=0fkJ .&]&J'6%(MKmJ¶Ja.xmTLJ,,| 6w랄8agyl)}$W?Y60vodBb kq.L+0TT[X$"  #&_ 1PׅuV$ QH4OuĚ_a*m8,񳄹WN+eX["|0G–rtjޝl$_LHDLayu L8h]q3NR U.=,LpDNk_OvFk=o"Gk(€xPe6jĽܞ<&OZVȾ*&w|0OOg>ME>a7W?7$[DS*mlnfkkZue{ psU\ךž'q^ke¤h=KA@"l5F5Q ` ᪴ΩzHa.*~ZhߕI?LZOҚ1;9XdX[ZR\[պxt{d߈onkqxZ8{u6(~%0nZ^9MX#{`+XsYa:LHר_H:E<ӹ-=7$s\T|- q4@֤5689k+GZ5.k^㽄%eѺZw W-Кޅ]8NnSuֆ6r Z'Dح-ل\֓7ESq0.S D~1Ţ~Gzڐk=Ť(רd*=p[F!9Z{ܟuݓ"b״VN<'.NkA=ӽ_ZkҺ>-#d_+a)ׄ~z~G?Kdǡ~Ka]5ԞqM\}k ^u)~:?W+iD+֥_͸=hk$Wu5!9Akz W#OF㼌=Z{{D+bd3MaZ_\W οnDSO8`ovy'[A=G$9iZg9]nĖok^NZ'9ܲgN"| I&?^@/{ݛ|-ÐmNa(G<kCx{>;=f/ǏcK$Hc.亊4N>w-~/NCOnȴF|0rzM3+<.sA)6!kL[k9_b{]; Jgi/chq߈$2L->*d5rm-4t 6ZN7 gDׅ4~OFWɯyBWVܞ cckgGG!KM1ht ly_O-U4>B^\.ڿg&M|ùw)9=OgCCs!eBV_eAsRګjڊr|C ȱzL 1w"m߯k:̱~.}:!vנ~ךМdИAu&;q17DӠ)=ǡzfY+k}.$V<%%d6a[B{2CjzQ׽G\V׷C%\r}u{\GN+._L~? Fg@?MGΉ!Faq̐1HϢ\d^S\NB! _бW=u v ^1'G~o 8tƇz<[Wn+o_q0v@=\z>LEa!ׯ2F׺\u>mPCơd2c}:\k;N!ׇ̱Q lXSu yNwΘkА+C~.C>x\3kCD6O:@`;҇~Bu8nMȵ\/K{uw NiCB/<#wD.y;;r<#=76ù?$؎="d,Iϐ61eq;Sׇ6ѩQ`rOY3};wP?C]ә^-1 9o{ 9u! kjy8=}dj-Cֹ_zkAOwcDW!׸ Vp!c؁v~Bzt s:z lnsI[tiyM}ۄ\cn\k2vpq- u>;4\_/h(ұ`ӎЭ9w.hvm'Շ3MT÷ǭv۶yRru m[Jrȸ̦Bb媃^{BZׇ\?և<'CVab;i=CVtwUз*|q9:M!"vy_SwCȱTХr纐k ])\'cZCyJhք\eqYG}Lj+wk87pE;?wyk |s~BJנϙ\TRȵ+B3KsUYц- t~cOr&~6,W}Z{|“BXnmw?DkڣM7?6wiof6vwܦcOLg۵oxs0vLcn}7TϷT۟fyv}e[ضev|mNYݳoWckjVjzޓjMѷo'EvmZ[|XVj&s&OL꽞jVfTor$W 3lжv~՛:ZYjVTKl~2eflo:ڑeӡfX: u4/e{w/jV?,0ԦölZf+IX~΅7K#}PCUGUu )!Ҵ|'3{NƚfX;lRX^-Za<֠,ۄVD+/SOXi>ڑߧ5 zʟ%\fŧ S]~[3~6"Vr Xl/o+zߕL? %pͯl|VZLĺfXU3˄!=X_3⪇cߐSfc9X'riV [q%X㻓m*IVg7hoG #&ĺF՚5mΨW hpWܜ5-a-+bm>),fR a"Gޞ NݣLRcژT]h%㽿?͞Ηp7%la&x-JŇea~OVR#b]cA9!-"gbVS3b7o]b8+_CnĀbc8=&>;6 [Q.5:^$#k7B}rGoDsy ʿ.̕ps?ЖR.AH:GlyG)W|)#; -[c+5y>' ?+et?<'_~2,⁾LG1%g}boğ-nu*3>|뱭d.э>}O6|yoFd‚ 8<qO2ntdi^>X'ޗÿGD7q)r7Nx nA?O;M[a\~(<ʭ'dl3s.~bO#6RV"0+B2d=_'pSA9&d%>~6~{!zX8 \¢ ' calAnoM4NX44>7a!K.F.I9 ;]NfM?9s./q"ތ-&d1Mt.d=݊MHKA;W?n;! oߙ,jt /߆Yv8KCߵe!ƒgeg!EǑ-݆=bPd9- |s 6'OHq(tjd݌/Fw!mA?_0`xx^DcCИ<%܂-W#g[n<* ɋ1銵C-~>=N1NP _w]Gy}ԎDzf{z@_=?{r-uԎB }adzcƗckCp_3O͏7ӰR(4q.Ew WK}"בrc[5e6+ g[]l@ȭOu~8՗>{\kN4Eǃo-8ױv #]t*w,^/2lq$:ν=*69ȱ&!~&<ۘrN}9\nWlhLdr~%dY2wNa[ w$Yk!Dh/Dk>!fx(tr>AoGѧOȵ1]_-;nT q{{N2AN\2Nw5DK:0d<9'_XZ;>۱=;n7= [k:ױ]h=h?9wosxT8mB#wzWm 9G+> +}]Ě;W;&d:q莧o*(b]?)}Z6l 4l~+kձΎ nYЫ[.hvlc9q﵅ne |g=ǎuvnm^@uq//]UQQh_۔KBߚ]Y+ KvϯUx8ίEzhyڿvfz+žՏU mWجWvUw&n汵-mSm IxƐ7/~?n r!5vՐK޾+nf*g5+ #^U:<9'g_&G=҄5K~hS]˷m:a$+-57$c_mqo WTcxKs׆k [8v}I7HN1pN-]p6*օT[Wa)z-{H5qqMij}a2{$֒FXB˜ &?co6TU G^ % ݭfPa$ftrH@o{O_ 3gX2[GlxXgVo4<Z6ze1bI,"fLz$p^Ox8a*[y;3 yvG@zl$46; c/I>M/ƨ15QI|y}ן뺯׳ֳ}{}N.MBcK/x&zײ'\#s=\秱G?'=x'}Q[{ݿe[xe^]eC.h/'#|n`a~ü=78{u9}a7%]=nǷ,qf[8g;f?%rqγ_+{I:~#u'>z3=o_v~%>_ǽٛgu+x.Gc4ٖ_~2Gs䛞|~uȞ&^}cgmu];x|s~|?Qz_;ngޛ,Is?߿/ 8!-{5d?Lso7VW.{&9^/Ξy=^z%V~=l~?I^-yn{='/ɏy J;̼ۗ,/^f.;{%!ތzޗ=?eYAȟg\M|xx1w5{~=ٛsz+xE;y__}t/;>Ͼ<^Gx+>pz1m{Ic^9 ?˕^e8'DĹu]}y rJyW9Wy//IS5,{1rx*?>|2qdoӅ~ms=慉{]^mֿ>!7N1|Sחxc.GxI^c[3:߿/:oOxmGdw!^F Iع<ç^ٖyUiV,bxNHOMZmr+w>. 8+G%h‡c)Ώ;@> MB%a!÷=&٪ٖ~I^f90ѻ~')EG.1K|^~|^޶e^p9!WI9,q86%1Howrh/끉/ Yxۚ /Z,<2$1.ޘHS4<:ߤKlM}&7m:y Q>!;:q}1u`stgD?S<[=81H[ c$awmx1ע y|?;އ"=8qPDM> m$zJ)8b%{z&hR1vmDË9~]JrD¿t5;yِ2# OPvOܿy?-ҏ$CGCbo&fNroN|us*%/^E+m?Fw𸄷%:I="Nb nJܸ愇)D~~9%r9ч}F}Çs;^iGo`=<[Q`r^"q V4Q/w^K RC_e9'1umE\x;('tG+r^c#yߨSmM[Ǎrp1ѧ }c6jyM/mU]":i֤@i*vďr5O7#F}=Qbڑ%kRVsAr| g|e^Y86L eR}Ľi5wr^|c0˺qմcGnQ::nү_\2VҎu qn=r.1ӎ~%9i0[uF8/bv-9.yĊiDZ}ƸgbsAbI~}%1n+rgYDk~t5Q6C]CǐcV_]՜Luy9f]ڱM2"_ٍ%)msrwVΉ[rl{(1ie/NŊ2"9`Mr/̳rruN}0Uf??v~>]Q\L9Mgg3S눙bo:ɱ,Qq}}I ͸}o]K0QS }1/ϼq ,~ z?>rߺ.*}xߡ5 ߟA4Cx: e|v:h~:8+Kٻpx>s'wBNrcG~6[/xa?ȾC=r7_[|j\_{657F;s0}^;5PÏ7@hg?%;-܍ioV;6^ws΅~]$~skq{>; @~tϿ[]{F^FCשysץ~_UF>xE^f2ns{o?>5'y{΢ ˳H}_g*=$ξɽ︟x~Χs﹊<9g$? u'n_gt^/g4*{˸ُ޷/exﯜۃ7Ɯ>ḵ+<4'ڱߓ7{>{ۿ>vܗc3>:>o6{ߣRJ=g1fcK;pa.o*z~oz]c;9GV'/|{w{4ޟc|w8'K_ƾg_1}hїzy=vK~\ޅ0[{u}(yc^k(*x;r/U{_;ni~s~慞7Q=/9_z3z?xx;v_>>4c܆<1}'~{vُڃu|z}}f}A yHG,_zڈ}vT)>kpcu{ a\8z\Vۼ;4.3[o$Av׹o^:;xkyp ױd_;z|q[{{Y/Wގ=k 2/dc9+=?縏5 :|z{{wR%{}^ٿ׉kG~W;_x︌=_~cw뼎q|8}n4~}O=}k!>e>X稏כ5"z㏽}9Mmw.#ט!{;~4>_?eo_9ۙ2OxI!{nZ{>o},1^׼ ޏ$7~o{9\6gxMyL^ĵv#93xk3>kF?3i_X)ㇽMrue}c7^Mz}skOon}q&䱞Wxy_bk} oS.779vm~+by-B~oç_u!]s^}s/~$q0~FMړw/gv&^}&Og/s_Ǿmd/R{r\s=ktF.O>1s%^\߼"=q-iח{}ncoQzYWxOkoW|?=ӷzsNbѫ?9,{T6qg%ck4{bUڣǚ$\VkN<&G]NymJ\Krscu$%|>ϩXWut-<#qOړҎ*y;Cw\q^-k&}G^XozzF.ru{ycҾns&Gɉo&)AlM{5VfXbm^ϣ&qm#}6qo:.q[u8&84_H?h="q 1~^O쑸>N\Gm>Hz_w#֛i}xs}bGg9:qĚחŘN~!kמCPJ;w{D9m6]qCXcqTZyG=|X;(qMϡ~S8LrMr}upG'+-q>DWRߨOz@8;̏ueN&|[Xkj%q8Q~6|;PFXpčؖi8,q=69';Ey$OZXcMĉ='u?qmRqc+w~Ȋ5z{{S5cѯ{&O ? GW]='wI\'~}=6AsTY%8$tQu$Wr-qI7%>(#RKa}K\ 5qJs}5rmSK/j_iSޜ%tGk! DbH/ٖn#3~c#ю}߈1 O=<#I}ϣƽuS]{]}g<ַl|??Dv1"#rXAڳWFG8mHZo?bME+5!%-}ׅźGbz,ڈlsq[rt FuĵnB> |QYpDsycR?} F"?:.GumA>g_G?rbGx#WX/><XX>k*47%?~W ?v'| r(仨~u]~Xo>葓Px×~X6>=^2W>Ws~n/^QVx?v=m\M;o#'Wx=zG=E Sq,1o<}RpJꃟ5'ClO{իx=.'7Q^f4ץ%i沛^I量O飘7`Jw*;'}J}tJ~zEJ7=57'~j<+ҥoIȏJ颿H邫S:睍2F=)}N)N9t2IO<'z2}¹b2r,#tǣCYǡ]!1PB[\ [1_CZgo+~ ?z~:"W@oKdG>}MGG7\=#^6 }B*3 Pa;m:?Fu>TDL@½koEӡ¿AQ  ?[o@~p+|m)ן@h66~ ᘭ"O[m"~o::}q~;!a>}N}uw}_A?=z6(F콏*h{{s{=z0+!ٞhB7{b8>uwA/.p{G*9;{BhB?#׻? z,tv쎺z솾 cb0vCvøJ"a7r7oW]!ǻb6qpKvm\'!-- aLmA-[06< ?[P֖~nA67cox g!Pτ06ϛv[C̥]0v_vAvyzx .ar .\ڄل:mXuل yBg07^1^3&t) pf~Wn˜ڄy nD~7bmۈ~وyg.s#ڼ܈q߈8ǍO_QFFy؀,i9n@^6B;6 / &xPll؀m7,6!WkOBm}z'XYOПkk7Ю5p  XC?!k@kk`!c o t ^C# ~\9n=z̃둇B1c΅zG=cܮǘY7Kht }6-ϖО\跥[\'Ku.w sf ^BK`KKhq ~\]00%̫%%%o)}sڻ3l_w#׷Eq/0ƅŏB`"{c{."}{}E.@"" _]8_.3yrq- "r-bL,ϜYxX<ȵ 1F-nvmrk8<.  ,#3wZk0p~.܃.`- y^,`, w^1^ù|.m9]@.ppco\ƅ̫pdY@N0G0-    k `B.0000vq7 .0gcrqeryr6 qbC{Ὼ!C!b !o!~%_?`^ Ww 6cpf}7=]no]'/?jZD'` 9x 6p_9x  .jr{V nwan ` p=@߃]z6|<҅lp kNS]~~sƅ` }>8u }grl{`0{0&s]-"0_ N>x` 0^VoYa1y47rmw29Gg:XIރbnVܾSfט9ü?1s]]\ssC.ܧ387+2{/est~ce.]?t}E.Y\:.µ߇㫾/ߊ>bd s}]㳟rᾩo#S =?;2 ״y;Y~YY\>!%z譮}s{y \fu땮]C7ם;^s/!\?gbۦf>k'zO=Ud.p.}j\{|o.π.ҟDR{#彮L\z/O;]~W-S½̛?;Y`| ߬+zwDyߚ{\܉:?7ND/ۉp=uQwUWMSz݅sDv=˅-O)O{љ'nvݔ,,܋{L׉u=qJd-4-\sf'Rt.]*zѣkSO#]Eۉ.] lcC6e#:)5%\=|vw"\fN(:aJ>c]Lj:WUrJ ~oEG7B3pI:H ?YOikk_LsDpwf o~Uoy] SyלhV4rSC_DrNꗢ_[s%>zZ==xouD)w3 ~D'JbϚi}sJp}ݕv/BK9gEwO)'ߠt}|J!xDᾤߏ$CiP;џޝ=.JGQSz;;DowMV[\or% ׻^v'=W/ ]7U.d^.ם;^藸p3/?zyS]tVsvg'}RD薝鮧%)דE7'>YxҔn]?5'p5yo]g]9+ty>ZK&Ů?_=.Bs]٬ \DΝC\_1p&:U6,S6ZuB-C8ѱqu5gS*DzӎkT u2+;$D.n ښb홯wWe>.OXH?=B5SO'{N|'p5Ow<ƫ.q7]~7Mvœ9 8nwW_w[I~=& y]J^׭#;#;#;#;#;&qM5k$I\&qM-$n!q [HB-%n)qK[JR-%n%q+[IJVĭ$n%q+[KZĭ%n-qk[KZ6m$n#qHF6m%n+q[JVm%n'q;INv$n'qW#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W#Hx5^W&2 Lxe+^ʄW&2 Lxe+^ʄW&2 Lxe+^ʄW&2 Lxe+^ʄW&2 Lxe+^ʄW&2 Lxe+^ʄW&2 Lxe+^ʄW&2 Lxe+^ʄW&2 Lxe+^ʄW&2 Lxe+^ʄW&2 Lxe+^ʄW&2 Lxe+^ʄW&2 LxU U!*W^«BxU U!*W^«BxU U!*W^«BxU U!*W^«BxU U!*W^«BxU U!*W^«BxU U!*W^«BxU U!*W^«BxU U!*W^«BxU U!*W^«BxU U!*W^«BxU U!*W^«BxU U!*W^«RxU JU)*W^«RxU JU)*W^«RxU JU)*W^«RxU JU)*W^«RxU JU)*W^«RxU JU)*W^«RxU JU)*W^«RxU JU)*W^«RxU JU)*W^«RxU JU)*W^«RxU JU)*W^«RxU JU)*W^«RxU *U%W^U«JxU *U%W^U«JxU *U%W^U«JxU *U%W^U«JxU *U%W^U«JxU *U%W^U«JxU *U%W^U«JxU *U%W^U«JxU *U%W^U«JxU *U%W^U«JxU *U%W^U«JxU *U%W^U«JxU *U%W^«ZxU jU-W^«ZxU jU-W^«ZxU jU-W^«ZxU jU-W^«ZxU jU-W^«ZxU jU-W^«ZxU jU-W^«ZxU jU-W^«ZxU jU-W^«ZxU jU-W^«ZxU jU-W^«ZxU jU-W^«ZxU#jW^5«FxU#jW^5«FxU#jW^5«FxU#jW^5«FxU#jW^5«FxU#jW^5«FxU#jW^5«FxU#jW^5«FxU#jW^5«FxU#jW^5«FxU#jW^5«FxU#jW^5«FxU#jW^«Vx ZU+jW^«Vx ZU+jW^«Vx ZU+jW^«Vx ZU+jW^«Vx ZU+jW^«Vx ZU+jW^«Vx ZU+jW^«Vx ZU+jW^«Vx ZU+jW^«Vx ZU+jW^«Vx ZU+jW^«Vx ZU+jW^«Vx :U'W^u«Nx :U'W^u«Nx :U'W^u«Nx :U'W^u«Nx :U'W^u«Nx :U'W^u«Nx :U'W^u«Nx :U'W^u«Nx :U'W^u«Nx :U'W^u«Nx :U'W^u«Nx :U'W^u«Nx :U'no7M&vno7M&vno7M&vno7M&vno7M&v_KR-%n)qK[JJVĭ$n%q+[IJVĭ%n-qk[KZm$n#qHF6m$n#q[JVm%n+q[JNv$n'q;IN no7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7M&vno7ۭϦ4?xˎˮ}:ݐcu.sampling/data/rec99.rda0000644000176200001440000004717613762135132014442 0ustar liggesusersX6'NKm' m 4!Pw=NB݅:-PJKq+ݓIfp͠5Yc),c1j"Ru- f0݂z*sCOu> 0s B|yAE+h-&wlbw7(@tGwkLិqi! ocXѲ;?h@xV߱{? 3uEf9Xa9Zw^07#g ksx7Y㴼7šw3Rļkqn5D E4|!7oE;CK6ȺVNƩWtV`-;ɓ|𠰸-_lk:qT*"Fg 3h|vuU1GvRbE; [qh F'<$ˍ;+ϢMe>prhHf3"ibYqGpbr %Ϲ`50ȷʤ,G9C a ѓWɆ35 ;TD̢,%1(uj=uamh4X1y7/Y 5"iRE˃awzyjrr@#GvsѲ_d1AdC yD+%`Z |fI](T $[qFEΛbgq-bu pgUF}, [ S%@ŝvZXz g]MN V RSOPSNn>4 oyWnrlqx͊M^//xZ9:祱WTz{ތsuZ<ՐgG 2J"*9~ ņi| k%/Q-x * uh̰亗5b&KgQ9 ֶ+ԚXΔӽN5V{e! C7ڤ1? =VBě@ϴC$Cs0!a 6^ű TQ$Q ݑxZMJk㭑"-u乢p# TT.?0&NdL򸈭fTț״VruDZ[?77o^.V6:kПE?AN7r%R,9F'[4@V!=\8}`ML8Jhtaŕ9,An1x;9sd nvb= ysS"C|3jF' |EC*Xb֎9G~-UPs扝m\?q.Y,jd498* l F0׬V WE xs[op뭑:;g{g~Fr!Z,2ZD.A"/M]CkdqxSV e;#:8hQͽF.)QK3,!sB ~":?M.pΠi'k_UB1[˾^4*^z}.^Ww8+I0Pc//SFʱqT#!Euijr|*1Ehc'Qb ͕LA/׮3OWAH쭦\ m |@'y`ka)Ve ų[N>X'g5Ed >SCNk"{s QuEwc񽖅8l=\i<^:iw('vEDX)ު eˊ1bI80}*^;Ly*wQ)n^UP@lX_[xJy(U {_(ùުx녃Ȱro yQk= Ys C|+9z Ӂgv}G*~`!%^TݴS盛"ߤ;>u%o똟<1XS.!ưsnY#*~Ȟ67JIk5Q #-K뼗H`f3ddo}CӤu6KKc`֟/$YE$YD=]igqlcwzry䉐#].tmekY7~$?(lbH|]{.cr ?MvI*r\.ҺlYbmb,FHi!!dFB%Iv"m)וZ7Xb[N숴]d+D:ӥ}Źq$ *|hs&lnl]‚fC>ܮRl[s%"{1/*"$KzZ0 ,ٚ/Z9Ft"nDeuuCqg"5I9el^)eSe)EbĔ*|RKg5&I>$a7ֱFl7kLϕbՂIAګ./ߢ5&ݥqR~^)?)OԑgKQ|~O\EƙU${!f D3R ~kl+>M'rEc7 %_l 1[%-6W T4D{5[jtEͰf:kųTEHuQ!kأq,%g<)Dy>k]Ⱦum!n~"$?Kew2t5J=d&>P HGa|Gұ\ɵW؁<5l77'9 z ,囡K=~~' QCjևIꁂvc]OLg$"O8qf7G%s pqٮ6: xro@7*U=ܽx^Xe!" @^z8#.K?a/ {k_8+|G^X!%`.Tb~RA_f~hd߽ؿe؀T?M*&_9Gdk n!U))J3C`I^`=NLnnvc :pAK18ϱq&29]Q+rg]adhٖt  IZ ,'#G%A>rjY\|6+:!7 Gkl{7rjY6'\+!j;p"J@9TMC9T;4c,f f.\?#k-s8S݅ k2}K;rGU~}6!7ٜXZiboGXEAnQ!U=B>VSb{ OoxmYjW4::#b8ػ$;D~ؗ+*p=M` ]ͱMPw#8G׷|1]6([<3artԌU#M{;s(TĺK`jXjI`|w[_XBsfrb8AEV#R0X^RL͐l$SUsd_C,2b@v)/Y~`vf5Z,~sNoa7{ױ.*֓ 'ba~xְrS+o,&X.aU[9cy&:֜Śdb6`mI(qN1RLb|-Cޘu{LSXV8WX#0lG8V!2%߱\%e9Ja'zsXD,kK@/&x.U1é70r xiKV冘uC&'#ٖa;,w77f>e6E 6GH4akM13q%0 ||3lINK>xci$Ye.!wq)5I<[#acyvrR\ujq޶ayz1۲9id_8wbH6wcavΨ/᧔ٖ.pL9ay/ϒX8h*mlNJF B?+/ĚKr)&7)H6Aij(Y.C\֛e+-;,_훙[(*zs , C/%$J:?bkļdG~] a'_4b^"">4l6yL s;Xcr,5sO'⑻++bdos^μFIR[z{g3b^FܸޟᦸY6mkb[ H,w vg"a(e|gy4OZQZtX00Ir <Ñ&/*Ǩo!iϢ<_%i}Dq b{YK|'}5s!(#sp$K IW[itey'KIrgcY^a$'. = lnYIWGb6Ⱦv-_"\9} IcJ2֨"Kv>;I,f9KYڋ g'^WWZ+9'Ώͤ쿂:1N"cQaW c^ds&Hk;*ֲUk#O+35>A[yGk;>Jm[\㵿IiWbu?2@~=,IvJh\-T 5&uR]8:)BzF ]If{2lC"O:OԮ@8Cv ~B6{ #{W!o "5"_ok$h}0АHHa3=Uv Ʉq$c}gw6iCKP 70t|؃l,A">u"l!qj?ww2I k3X]nu9T"93BȌv6$h92E=|qbhtLVڮFz;KVt':#s Fs^rx{f:\dЧ\aXҸ_-V6y6WdV`$S7|YR#y_[;,s݌q- 5K|'?#p⿤r;{2*݆-ML&BNM#]&Ёݸr2IcI94q۟tMtx4;mO<" FvBTO=׭*RܳCeIs2\:"6`2dYsG!' hKWNtnaiCպMH$~mٍG? 'iu/s%lIDZoȮIHnIq>2e$Z3Y=ncNN5oa1B/V KUw6׹ _Ɋ3]i6 J2Ud|&da4 +:GBϋ IMH`B/fjHzS7ɁŔDHȮI}i\2ɦEUɸOHHI5H_tF9YGhdx2PUDWFUoE }Koz3.Dg2G-rc%5u1F}9.C.d{۩BR(i1L.2RNJ(a^iT?鞜E|vd{ Hò+ɩ~4+v&[W2xEC2wY[!,qvҦ.}(KVTy.ٸdINP ,CIg 6p՟]'GZ!V%S !#3HCelc}'Cۓ}S$$R×ޕ4)T2ˆOTNj$oCF&.M$σWjzuW&`bɤNoxL}?hʗ!]fp$Nw.Hk2u|0Ҳmn҉~$pRor;71t ٜ=F.@c|C\[+IM7Ȅ~2>u%9Tȓl>QXD޾+ﵞl^HLJj9)ӽ<9{5ٲSu5̶86;Q@*O #J!=6 ),S{֦>ܞO;pUo1KYZ\1?Xܵ1j~Bj~`{OOnQU.PS :䒚n'5/yY5?ռÃ|WRc#_槎PxKNe̲Oң Ϗh`2cT?_ͨ>'k5mewE=SƑqSrS{CwSc5w|Ճkߪ?n{{~9Ho~?vVgj~3vnToKig :p]UVʿ>05vmJUQ9ӭ߹YS{o/Zuo##zO CUJ3cVn7tVyeМ蚿{ C ŪM3 PG&`Oc]'w{{v?ηbxcr?twGU_p-d17=vS{f];l^_yy=W.}-ق&g_v-Z5qy͵Gwjb- Y 8}gy7pPۗj>uѱȺʻ=>ޤ@ط[1Sßv8Rh0Ǜ[ L]9BW>*eH>)o$˩!sl \wcO5?9v!tJkyzĺ{,|Ե WW"=0dO$z {uK.5MGF,I{V?,32ìsENkqӮ2Mtv\ \հ">oWn &?٤ˀq66FwbF[ ŎsaFV,<{{;meyPv'rԞ]r_/mJ6{Sw}8}s )y f=nCR쏚RǨkj=n[j~Ҽ[aȵuRF%raO "5o k8;^xQv_~^]^ֳ8=^iЕ[+ʍ洨 =^iu>OG_"7{쒚_ɮ!9<4q~]߳2߭;`[ {?=?z 䝩Y#~/^rq=<լ{7-5W s:T 9v?X4zkuy~K| ϋOڣB^R?k>Ӝ׸OD=9UQWvn:U>5~af&B 5K-|1>k7݀s'u>>ߵ,}LnԏpC:7u@ď{zنv{bqh?a?V8M*ԧMd%#oz`r}!;"7di>GŐ_hG#_.v,ptTg3Rsh_ʡUoo78\~e噼 ^k .|8ZU$36aõGVBԡû) {59ZRb5´oxjBE݋|]]Tp̻{Xkų,ykaN_a#B˼A~X>iG'Otl ~1GVj:>MoOǹm4t)M!-$~;p99v5>lr%@ǖJUy{kʮ6#fdX|bΈ-juZsv6jY0Ov̈MC^!i&=8 |ew/B%lxzsٌ*~ pٲ"op|eP+oD~jv<@_7]? }go>D>{޸u8E5b 34_S![&nEQˡs;+v?l9d£..)Xv&)╇sC_[ݾs A>ac-|QqJFxFK;JT˴] o}FN\L䃔M¯;T_vND#]Pڈ:7}ıgLB]q×ς_Wގ x߀a;cą yN<Ǡ?އwn:FPp}K`[62!OսP窞@:=@`UWs>^@7nvSB*9>z_ Z1u xYe#>a}r^g+<~ QON夣 u@qۥUpŻ@vnY`7YVRq Qρ¹ͦz˜{UڿE?xcpa'$m$C>y^?az:O"\Z~u͞'CwA826{"\ʳGvG?gN'KuP1ro,_%%||kV|u䍎c7}. z y5_7Vx aR/נ#?߾a|rTI_T` g%׶Lc}ԲN#KFWs,bbæ/FLY4~)}!&16rndz9ogL8gl-%:vO8|ܖ3읯X]D8zs4q cG_6}iUn}Z+&;:vѻ[wE'n7ʟ nR>h[ѷm㰽έhҟWO\ߝ/ %#/K;wL]nSl 7!]Ȯ0U; g@9hq 􋞺BQٓ eM.>|ԜV߱.hY8']^f |oP;:C*/NU?/-뇿lsQouڣޟ/$QSJt_rAME;Km/<|Jƽ꛻E j:}sJe,ٕcJ!5y,ŷp;N/vbU1U \GܹuC[7cEc¹?(c+>b}?p5xWյ{ʕZ9ͫZ~]#]2_f:D:Xޫ{^hV M&KHc"r" hL,Ew>4JpyE޳Ǘ_ wtLo=PꕆƩZ] 9fV{Nk[-a)4ov=+:F_&N~;K?} ikhfb}U}k4^ӬEV9%?D&?=FQtvj/'ܡn4HefԍQmT@\(fvHr~p?|o[Ҥ崃:i.dwm@ƕ)Ѝz\o4yv51=nM뤦5ukgdtIwػ.M66AGVv>]&_4rLz4%1~޽Vl uKa4yUԥq&}t>G6fe(^Mn|ShqgBmMNӏ~u_UF=*P~W៦{VnkGN{r%6=v ewnj&Ҥc4{HSgZsR%yw4!mh.?Y#hTENƱ.YT5 藃=vNu{8fP;Vg?mbxa:CsOO@f>XԱohϹn13]?UEV~;¼-i%Թ4{4= bs&Ѥa-5o2o oo^LSM1[GnC}Cٖ.Fw)мz;#Cs݉.CӸCk>O3޺&L[(}Ud#uX%4!7_ǕFvY6xθm4}Iҟ~)M:z)==OHX^O$UwϬfv=-i'^ӿ:)M]ǫOmPu M^uw4cՙ hzK~utS:ǿIu[uH2&|&gn p=4%]UhnGҟGN HSf։>H/e^GO{Mp~8Kd:K/3ݕRua^6GikCh2!Nӯ#/h JДa-xJ+4Ѷwiė&u|g^EcfϛWy̦KQUul+Qf.I\\|}9xGF75\ k*tGX#>J˺jvFSyiʅ&<sy Q\Š ]wDOk̻aԛ] s\MF;<;e/t9ܜ24{t.AǾjc"uq4oWG鏈Wr_#ksG|Oᾫ{԰ԍa44Į+sZDc~\ M߷S7z j]/3p|dZKcF(9|exh޺qi̎KƤI>fqA'4qЁ"П;]чfe-a.M}[Wi{f y2 b~A;#O?ǭ^e*-p iiǨ*iE J391sMK9H3 .v?MǧF/؟fx0eudd% Md|*OD{7mOW,4y|?<8WMpʔhGoֿGȜ5$mݝݷ{=ӣZ Ь B-ޣkH7Og|Nst֪kizU䤏c1;/FFJفƿޒ4~tF.>`O?}}_BIV 1~.3 4y`.I4Ԟq=נYڧtv`l4)'$_glO^Ѹ NSw?.M[e7yD㛽 {_I5 ?,I.L'?hم& N{SF ,h :ƌ&M"aN=!.7ŮL@Wm2E24}huvak\{ 4f|j{ݡ?`跛wi~shAC(Oc2|{{T`E1Q;fN &67LمyEi̯㍆ًLъMU7[}iJ-c]+nqi|~飫Є壅VҴ~~Q)Ge*д˷\?G{x#~taO蟟fIK7+O_T2&{yzkCߵ~k^[?x<юF?"y_RBi3ikRUtӭȾ4э=ozu:3UMҿ%ӬݫeyH~Չ~khᐁ׬jOc?ฃ~=skhҚu7S \LNcPg5Mh|k"t4foFBco_ΏzۤrY-Kv ;tW [C>9bOGPԟ_ߧ C԰)SF[r:4;j"kxN׾пJGc Sx;q~fʕ觳YneҘ%W9on3{.ru&ܿz}C{Cƪlzjx]C~~V]iJQAy/'Yc A]Ќӗ]ZBV=UԹ4{Nьm/eD\lʷF״}8:eqK`CQ7757KIdJSV 7ki_c܍Pkp?r;琾#|I9Cwj܃:X9 -ZH6Z7ANOFѯ?<53lSdֵj /r{pϑ,L>=GoY?laÅsampling/data/belgianmunicipalities.rda0000644000176200001440000007336310607636356020056 0ustar liggesusers xTU}NJ2@IH a S-B%I + 8""#**J;sm;ݭ6mӊoS{{{.ϳ8u^k}NUO9cYV|?۲Rf-, Z;́@GnYLc]S,w# d22\\9N۩dr0-m B ÑH#NxdBg^Я} >!A!ݑJ9)"36ی^UUN i`QHR1i;)ES"qM5v!y &m 1F \lD@E=֧_Nvr* iEه||'j2ghR~xB0AeF LD!!!D>F Ulcc½6!7#Q\(h-~^͢v#3do]>96H ¸~Lƾ7,DM 9QxH B{0E KΟVڿ yA(՟+-B6?6-loq.?q8 ^`S0vkl'6Q0 D f|5ZzDXr{lm3~ Y`s[0Ji뢰8_8,>?Q~SlSǯdѦ,$$lE#Ռ,F [;hÇw3K8~ .m!Ķ-x-j[j2W68"u9-oɸf-iش[0c10oglnKZ׳;m*J}>-xZu:G 6;] EQbkm89bVB,Z=R~V-8j6y8%}ἵc4Jp+IMbZ`:g,b!.mklق=2ya1ږ|WGQpE u1 Gg'[ʾM"d"_XA *gіp س 30$a طKi#"VX X[oBd cؗ\Mȷ죛M`8 F#[׽naK҂,r-YT)W#ІlE"|Gib62nQ7tI ӈKhSS\/@Xk6-,rn+94J V$#yĂ-rMޱ Ħf=5؂ifɸk ?XwrnQWhZ+-:JQQZ:!B˂f~GsX%jvvF"u:mYosvN-+@Bշ|.5ûmmmZ˺ZG:#:n[>\ر,;6CjE\w4fސmqmyPKkQ۝[_ }tcYXs[{ZBFՁezpgUA5|]c}OX/.msDk-&s'ȁ8c]ʎCmae]6PzXmx!p+Axc-A리P3ƩEZR_Dz(# E^c\j =PHHcjg{flkp C[nrkk3ql\N[K86Ht{` Xn?fl05ФbV #J{wpDghim?"زiQC-m8wvݔu_;n)'W82.vab"x Cb;v.%::ˑ03_0qs!SΥ 3 -- -8D8VN+q$bs(íkZI"ӐD(;@t+3.߲߹HhҹڹY:<^Csak Z¸`˿1H@-g8rklGq@9TrCHmCG "E)V;عq!Aa ZQSW/)c>qUĺPש߹{huhXp"%BH8Z"%K^m͹=lh_`ݡ.vۚab1tx(@;K}%K -HBC6h _ް8"6zm uB\CRu 8"oN#!tfDMG8Weki^pz֩x ȉvL F:WD `aD d<84jV؏8)I 1MY)6֎k!8k7alwvg:C~pY#MVFTA WԶ0t+@OW;7@2蔜CV 68 bS͈z(i<,mPq'=|N戙{<ۗ25 3!"67;;ڝ}!eiXL8tN:uO%\*:'E"rvNʮM5 5CD%N jf'{&'Y„P^#Ky du7{-xDߢp kq;1ǻΐs!4 ]qk0:aD#x 状6dHm .{-8p=3"i3چN w"9mWRR. Mov+Nu7gpO #>\&v|-p &BPX qhb;tDvwT˽ .Oua2YlM dnF">gǁ\l,D$..mq OE\G51QL `*H2/Ӑxu%Lz4ֹ&\L m؉1Ԝ"7F&zb8'I?sImR2ua}Dkg[(;)*&P&0Q,42U8`'[YE,_p#s` [&wErd@,kiġgu zSEwONq3m!j-N1EM"H,nJ- SZNڦΙ&NiVt ȣDzuJpy{ @B ZI/im#mpO $Gw"| [NY2 }OԚ:#|-]yIT]r 33oڤzCRq>aFq<iN9($,6c&oY~BmrP~gFוc='i/m@o "XŁpꥡp9o/e^:ָs2DLkcl:;!- 8EDbǥ4\-wL; 8`nً(Pču7`$v#89NmEyLmJImAs@jj5u4.opubէ8ƽ+ŧ.\t`uoa$n_*~J9S# x9_mTñ{_ML7u1'T3dMy/L;:B0VbXHgg5)Hɜ\SNq\dB&2-vv_[3Jpnl S qM .t]g|G=7k> V)b:Seú nv4;KrXH@ 9["?j`(`g##N@;ۛ5iA48{Usbo- 16V85[4 g)vIap̗gWD>5W+:#bk/iƲ@K4r 5#gsE%IdY=a6~Fp~*\"Y$NNg8Kۜ0O9+kNq5" MV--E6ڜyCQEO5YvL2)B(rje=|! 2AvbD$]R}fF/ +Ckj0 qgŔfIX mVgO1Xoq- fߙY5@_MOG9yM%l )fK) l5$ٕ$̖zѵH;{鳗Zeq1T;E5\,D$rS;/~hsf#b?;@>h;nvmCF쒭fTp ^skv"gw/vNssؔIs}G3ܵEL7\ye]b&x$u_ۆ+MΫ@JgN|BA3A{n@ zRq^_ -A"$.y't8B||A:C:ͰzG#9y0KeȫkțowG>C>G@BF"ߏXnJ@obMH`&lє"yH>mN~ AO?!y򟑿 {2=ϏA8|Oi{~w Ad(2 @F"kY DE~`rv\` c,N ]} Aׅf!:- {"g!^8i@#IyyyAߋѷ&Ezv^D_">E`mQ7 )Gl5\Fa5g vX~kY:^B:kc=؀6 |>߀&6Mixڄ6aMܻ _nÛEGǐ# ېۑ~r7rȲ\\lEB! ;,kj9zbI쏀w'c99 Ie6`=ux݃@CXnͽ|/6ۋy?Fc~x?`{x~}ݴy7q:A|q~i y¶!>2gX|>;aazC"apr@!!g $ƗK`%04ភhFd299ղ^!f^[{u׏Woo1ɷǷ౷[-}zy=ކko{=8|n_2/}y:ŒK0%ƗL$k|  ق/EpuFG#pl{|#\!#":#`?#b(y GQ(>:Q(~= ߣ~t&؎AQvQ82ƣ̅QQ:a1bv=M1r~1tqc-;k>r*Ҍ,CH ҆@" ȕuȍM7Gdd#KOQREF!_4NY%UՖ=F,GqD'ʲBo 1=]O zCsbꃖ=]&V#}aL 2'VnLAҐ )C72 fl׌횱]v5߅BD@G|eًcgKRlt#ݗnAhccȓϑWOX9e/Gsƻ,_Dv92ȿs'GS%IU;%I?!I%?Qr"(%+ߑRH@*@jRoHG2AF;2䟔OQe'eL'd?!3iwd? 2S7MYo [сGIZVћƿgY^W.Ǧwk,޲[H{-}{8ŴKS})\{>ϷLr\U^nY!\[?`x2W8M/81OOs)zڼ6-Bޖ5ϿQ3$^56ɨ? ]hiY"<ߠ/I؊!\Ew5[,>˧䝤q?cHcO+,c6_/Nl h/bp~chkE*xM8ꈂtv"F2;1+#8A?;eaiq: d`miv2o3vscHxƈŧ_XH<#Z8gl/N[&K[l?Fs)MaP>?ATuT/tͤ!βh;$|"z6ǥ2~eʥS~Cs,偡lB')n lr}{:N7z%۲N?J 66wȉy"^3؍ #n[`v,2dB 6Ⱦt\ d7SF'q9}>Ӫrw0/[aY8-5)2nto+N`1ǥʛlxlQN?Soyu qql> Ŏ-uu7ui?v=:6L8_}=߯c S,b≕yXA=5|Wo5[E.-vUl.`3>O/Ly~^BayC <'9<§YqC4x+$gye5D|vxI:xΔa>`/V?o!/-Ǿ^1ĨO2tYK 8Dɾ _#>{᳉LUSIJoQb:q`xgs؃Vy 5w 6Wy2Nb)I~ M){x ǹ›9 ?%a9v/ㅷ=≋ >x7x-e.U .x !GD8lCQ0t/~^X4}KY$~_r'#,dQG+ H$vQO6pps M$'%6y`2v1:asS;V;~x&[5b+LT^c8b4\^ 'ya,S֗sܟxj?Lt.=} O&^oaߞش>WN/9O.T:>2+kvh/4lZƘ#;pguL.2u2j1U #8睖p=^:>:|=4 ۾ClfSPZGӱC Mzo^Wui Qc%*]!u^s{!Ae/aZrSH1zmN5T`(^&X'N*i7qQwnB}NΧL-^–O> W5zgVJXNL\8ͱj\II2ua Ր pn]SP+Ab( gg|߫73je\)}.pg%, n$'пۥ}ٴ]uMl3'p~$աg \UD|d|eKN]3fPKf_y:y$Ujbni+gdrD"6&L^K≭LPQA~ݘߔRtc ;rwbBSsh&aLj: q$ FA+)f&8M-se&S`C˗M>-R$b0} /s!'MJ _EĭvK's}NeKL>n d>,/|޲QL$Ƈ%ٌa\3駔kwi jIpb~蚄}kɇU;e`ȁ'甃TtJ!$Πq-<E;\H yZ>EcX|n4rSG<5Xv p+ ]Ȝ* IG&r}UScxf"͇KpRjв۱]j:xlQн x2%{S87x U9\ Ls=*YqkgJRcC~?蘉y뙟 '2]ij' f qJB]\d?+ &g*qq Mp@>%J)H/ppl>75 b=i{w5W'WYv-~FFQdZ]OO%!Ue:fhA 8̞郍3y_Ƕ < +L15ۊ;z=SPj};^Sm[vGM[Wp)^]e3`uۇ69+6 >z!E!&*崅 (&$>M0Cϲ_3@8qL8|{଍e2_"y"&6V=%S1L߃yyvol>; kSIpue@ܕ|TKok+U͓ћkJ/e|'vSee؏د |V g}Q7̲{QP[Ŗc$vq| .Wjě'c:[y:@LO!Ns\}yɛ`casݥVypr1:*ơ0q]5K*K86.,?Z>1?{sYC\p) 8Nj$%,c^FKd94 }Z5\;j+:-GײCЉx zױ6G* U뵭i{fy䣔1 &<8{=:%S ^gi%q1\ 9]=ˬA2 8e(~+"f0 E)"沆uL8\!ˎ&-ByS4^T#',OIJyz\pKf)3M&98WJO^#N3O/`1]}E[ !@Km7,7p˸?Xn?ElLWrt7 W-/e ˱Q"MGmߤk`)X cO>L#̶f pgtΐL-Opy JzBmO%/ LSuu7G;OdA͐4G~9 {ɼdp|8X3sM2\?}JC7xYc>~T,: )j=RS"1?ovlD*ܕ"O4aG '׍d@R[G3w)D,͗4׹^*(Π̽"g`,>EG_'=>H$/E?njS$KooJ>򘪣:Uq~$^`4|u#f3X{P*Y7>,#/,Ma])X zS?ͪ<)Ly0E3ׄ^j +ܙG]@&Ⱥ-q@C%< uS~?t_83o\puXLwԲϢCcLb ߕ4pS:%sPu%#q~~Gmz:!TA<̼eѕ݇w 8/P~Nou:\H=0ܜ.79i}K 2?Ngv\!JJ2'Q7B?7y=qĨJ?KsE^E_KLp"]V""&^a5 y.(UI?[k{SaHkR>sFt& 9D:v"PBQ $_::'-YFbZW">\ C9W,05t^ǑgstuZ+[޷yFkQ$O{x,\~k>Vڌz+X)RsWD}ם֛ܲxuL3?pٚԪ G&cL:F\M8alnyN]\c9y7Ҫ׳dͰܖpTdi޳~ЍnYC[?tJ[>U<*r~L x)g7EDLt3lt sJ]_]C?rr-M\o1&{(q^7Y?&k0 ,zyodYYN%;V [rl<5$!2Jܙw\sg9*a0z"K]ku:g&SnO 6*!K9/1n}rpVHÜ8z|ړY{eP 2\<ƙzPıԞz1z}}!c7l_%>u5z-{NOex1G xQ??Α;k|_eXD0\[s22W~O;dqMKVn.Cп>Joվrjgy|)LE ;JO^Yc"f3K@ ȅQ_=o݉17t$k{ww߅zz ﺩ]Ԗq̅ذ:FfuyN%!yŐKitXmWi;~yn2O]c!n۞M<Qa2p[CQOX'.'fn\\(2e<3;8.|#YXl9Od\it[˸]H|+ɵ_w<]@<'ç8V~H%w] eS\'i{eݻt:GcKcUp_6Ed>"g l[a;ilS&xyt^v"|&s]: %nrR|~?&3~罊vvإẓ[2LqUIܥ)ZC_잟[nq,,A-pP˾kewN;䞫c|l殁g6yi;#6]2~]߃ԑ/%6oKUQS~t88Bܭj/ڲfwr_y`.w'߮)_ueyv԰6{[BO_ɡy:e@2G)s++ x+w^ ~ܟ&/uX%T]oo>9 e8N+[WȼLޯ٫[QZCn> OܬuRCoH"9blM~B>oؤHޭ$ "G/zѿI.}EcX5xJO #kg^x0SF,{ [}+Kg>ހiU 7;NaJ?~Bޙ\ڜ.hn1mǒV[cЮϋi ^^w278MO>m]y2^sem^ZKLNu~+l8W?/¾sljjtS/OwdJD [j~e˳9/vyKK/.j,Y2_wSکyjd]F9 ?V1gk˰4l%zܪ?Z"<8s.c3Я\٩?!e{NgLc'ρ*{gp2%,eW!vOxR,RG_W[v~/ i?\y< 2F^W=]t|}{A `dObž3L\ߟ%o+e9? |A~FKsI<,\/k)L^VL~' d39x)qUzJb>!.=݄;c`GóB72'.8M˖j`r@rP:U [?cFYW7OqO#I9?Hm]Ci'G!M"GW}{@}"ӹ,!&7tjeKeRO׆#kEgw;_ݠtɹ=dM“Z?ʜ>/k9EɵZb) ~<GD^If^;H}O%gSC/޸[,{}eįi$o{En| ,@\:́jw[!N ɰ. Lq@ `Y ;}5G 8PENǏ[@-QŜgU}V~we'c9"f&7ގ`m~r{B7 w39ԋE_y 4b,j{CuS&yX;Ì]ONkM':]*"N-l{yģ %!Wsq3M^njR- 8ϖǜmI-eQé9ݞ~\mlqۻb'8؝:C}^jg91 1Yf)vҌC|gIEd\#ܔalڴUe8Q|? %+M6@pMsoK5Ǥ}s~[ga$Ka2xvݍ]e\8RTeQKFcx=ec\O1zMӍX Cel#~XbYcS7Fܖ|c]_set4[: b͵.~4znsL?bK4yyy$3=S%&Gg7wXfPW|6ؤej]bIs1 sm?f! ^G1ƛv#;/?!_%qg*.- $|?=&w3 n?F65 .rM|dƚ I.t4(|Ujt"c2zTh(?nGj[DwcgئVbSeFh?Ҧ`y^sYOe^aKM!j>׌W|ErP'.Y/q(щž5[ ?,7; .7-=lF+|?Rgld+ymz ;:Qj#kl3~丞'Jl_mtaq~߲&qKu/oR'˺%~ex2`#hrK-]uwǝy|]9e_[^%ce$'*- Hl6 r#F8ЌE1iH)q`n|7C &~-Ẁ%k3R 5qFL3 'Hz$L0ƲjK_/,]o=6tJ{1eo/5yNrF'RYG'<*\[yWϭ{^YI<~dƑTzbͮߏne2L Hm!3+? 'HM`l`~$~s]kufsnb~=V$13K׎/  u|_r )ˮ7vs]uF=3_:s Vfc[Mfp;o?Yj'wdޯkp'ߍxo.{KG_!:}82[?Y d?^7r8{3 $ + {1I+^Y!R${oߨ>t&><`jN1CJ]w& JϢ Sڢb޵dJ">s7bY͉.Iwj<lZ%^Mj#VQU?}KQf}~)}wsoL󽣷*QyFx}ΎLkfÍ_]ؖ S_қR:{ǚU{3[2,~T+&UzlUֆFf5I+[_^⩝LNzr|e_u*۽Bwj^ʾVI٥$[6zK]Meʯ'O:Pq~Wvy篪qG;f;/Uqq_7+; [7(;쩨V1vRڣ/d~|RR?m].ۻfݥp>=?CW~Wz~R퇷O^/şS|ІTFkr g<ok6T(nHFmKHo[o}?^i뚕YqTCpի۵Nص 5=V7LuR`{o&M,NԸoPgϕ^]p~9*77v/ Qƽ社*^Q:қ_ߨ~.3] Pz|?v|ϩ*.o/?kI_ez-_d;r{4k7(ﳏS%}Ƶ}ę Wgny9kT溵Vt:3NgS嗋C)ڞ|3n/E\L?xqj<kvOs_in?u~g.X_KGϕ=>kO>Q[߽K㒗ޗdE5{ӻo=?_W]uʗ;rk߿*]L53Lj2ޗmr)=wNVmm>I]V,Q] 6kM7|6 _-Sqt~gESv}?n[͗]pnDeK?YTvz/U]ȥjWCFsNgScϧOQyH=Sj8ǵ\johKjSٳ+n3A"v G=UxILIPlvϕU/NPyL5FWv]W O? kNPow.P]ju\i5{ʮT2!^_PЕkF)/}Cޮg5_٬ juޞW<ʿ8xpgPP94F5ؙ;VUdgjsI(]{>(ZQzܹ.t~cO(/G}{0 ^sPߎ5߷so{~ Գ GEqt{|~VzԮ:}uխF?9׌noz/tŃ//_c5طfSζ둨sӨ=fLvFkQSȅ1c\ϛ<7n}| SEwЎN/1+hYo*>>svS@D#*(23gnM#M/$]޼  AUA (\E X7xcc?=e~3O>3,?`*lU|쑢K-1x2׿Iw#֡֎?wmɭڱ"y#+RX[/3)ݢ6k䁝j S>/(V>j^zuJ}s[Gf̲k?(եcG4=u'|}ٷNo%251̶O%ꆉm׺uoaQ3yչ״1h'\jߣ5h->=}mrNϞȦ'bU?}wt<\W۴ݓٙolV,#;=0dێ1i#+틼}/>Q5EmH?z}?çۮ:4b^U%e,blW${TK޵m/wb`|O=62/x-W,6@~AዶbhOv"MM_şJtZ9pLȶh~g5]=خi*>w8t5~ ? W0S[uno wW5 mW6EjQԯ7F.'sl%Vgc/솟:=qEMfW[6sk~T׶%9>:-ɾ9Ғ׳v&DLxk{Ӎ,%m6ƿ8'ښuٿ?b L-{7/mɋmobO{w{4>6c7[jU#>̾_yϽn{"[a[VnQ-o|1#ЖdUy5s6n,m?ͭl|'>!ܾI-]m히z^rs"/lmxqWDds]k^zQ=}_=a^[xmݲhnXi۳s"j_[O;,uO ^otOnQkڒmr#7O&ٷ|BvA/k͟cfLoslO{vC햮ӵӢX;yZ-_aSkӏ/ݎ]G;N_|[ىHG2vkw>9MsT;牎|܀Q9S+ߵ]U9βEکx5ޣ'"%v问vt;-wWFk ~|j֗OȷG%~dO<\; 2Ɲk-lSk37q o^62ں:x4|7kic{GWf;g[T PNɶ-nbW\_";2NV*3G;Km'Ol8? %h6kkwjm۾n?  ,g?]ǦvFQ]b'?OMb _<:gNf?; gObӧE]ߗc8k1sXتs~ wf^v sY5헵• 7js%zDԐ*[1۾x6?~؃|st-1D6^yᬶJEM;ɳ?Mv6hɈ{oů_eۻF{wm"Ɔs?lyk~[xz+~۟n| [l*,ap>}o?6cʋ^}Xɢ ^cIvZf+n̚6\Ц{<ޝ*0ߤE_}uk8f,IX<2V:XHG=ʱŭ8k?C֔a|EXOlkǸ|-Xqn'c%VuqbŘ_uU~J7`;0lC0xq3[0*tv(,K^&}72v̇yöolQqjw#se2v PW1d16^L[L1sꎟs/f&4a1;4 O*w36ulc -:@gZc q|R^3Jj*ƇT,ۛ}8w s̀b3-@,06[*,p7[j?)]_aaز~(A|bI?c¤ ƃcS:\" [Va Z{r0fH kfϘGR  "Jrq[1c%cًx¦Y>Ɲ. u E7Jc!ܛup}05Zrh8t14%1XɃ?-׈)/fr.B~#%#1lZ1~=EzlKaXycḠ ?@1d:sbc& >|,F~e6A'5Q2[?ȅtM.gN4Ҭ`W2_`GJ.Qb/GixTP7r&e9];MscϑC{z7~#aQE.5~ `~u!gIt8!SMa=BX7De}qc*@ }#kkXxQc/H7My6dC75*ۈm#LFzB#gL#&cOآ "|`zt140q'̜sOǵ7ۛ1Flpm&|711ȈUԅL>_>}` ֫)92tdԉ # Χ4Ecn(&3.$h^C^fgCP?2Xq]Z 1: I5̍zuaDw&da^0Z d 3q,.x$b7֟g/X# 8>xa;/_l!wY9xfr1#?=gn*ٰg;=8h|Mqt&+ yk"jkxpw./y󀿩nji*x2"|Lj4nܗ\9 ƥ` LAr1ЇX f~x Mp֍\"潈M]M`CӬ O:q{"&ӍjA"b>bi~'năycŋ9,6`l^܃q\2Gх:y/:|6]&lW7ߨIZ)&C?Nx/5:~pq`Ԇ3t(HA`ñM'Ri` dp! 1raL/9Uc x{ɢK7u!dą6{T\?C[#'uaI )mͺEnKA 5/|ĺ+xKB$ωĜCG0r`TRc}ܾ_謦暆SmF4556׌ׁoE O^cFBʿ_hKٿo^ O p7G`83kM᪊_ٮ&z,զ{f-cMeps & pik < 1-eps). The sample size must be small with respect to the population size; otherwise, the selection time can be very long. } \seealso{\code{\link{UPsampfordpi2}} } \references{ Sampford, M. (1967), On sampling without replacement with unequal probabilities of selection, \emph{Biometrika}, 54:499-513. } \examples{ #define the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) s=UPsampford(pik) #the sample is (1:length(pik))[s==1] } \keyword{survey} sampling/man/balancedstratification.Rd0000644000176200001440000000440313767151732017640 0ustar liggesusers\name{balancedstratification} \alias{balancedstratification} \title{Balanced stratification} \description{ Selects a stratified balanced sample (a vector of 0 and 1). Firstly, the flight phase is applied in each stratum. Secondly, the strata are aggregated and the flight phase is applied on the whole population. Finally, the landing phase is applied on the whole population. } \usage{balancedstratification(X,strata,pik,comment=TRUE,method=1)} \arguments{ \item{X}{matrix of auxiliary variables on which the sample must be balanced.} \item{strata}{vector of integers that specifies the stratification.} \item{pik}{vector of inclusion probabilities.} \item{comment}{a comment is written during the execution if \code{comment} is \code{TRUE}.} \item{method}{the used method in the function \code{samplecube}.} } \references{ Till, Y. (2006), \emph{Sampling Algorithms}, Springer.\cr Chauvet, G. and Till, Y. (2006). A fast algorithm of balanced sampling. \emph{Computational Statistics}, 21/1:53--62. \cr Chauvet, G. and Till, Y. (2005). New SAS macros for balanced sampling. In INSEE, editor, \emph{Journes de Mthodologie Statistique}, Paris.\cr Deville, J.-C. and Till, Y. (2004). Efficient balanced sampling: the cube method. \emph{Biometrika}, 91:893--912.\cr Deville, J.-C. and Till, Y. (2005). Variance approximation under balanced sampling. \emph{Journal of Statistical Planning and Inference}, 128/2:411--425. } \seealso{ \code{\link{samplecube}}, \code{\link{fastflightcube}}, \code{\link{landingcube}} } \examples{ ############ ## Example 1 ############ # variable of stratification (3 strata) strata=c(1,1,1,1,1,2,2,2,2,2,3,3,3,3,3) # matrix of balancing variables X=cbind(c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)) # Vector of inclusion probabilities. # the sample has its size equal to 9. pik=rep(3/5,times=15) # selection of a stratified sample s=balancedstratification(X,strata,pik,comment=TRUE) # the sample is (1:length(pik))[s==1] ############ ## Example 2 ############ data(MU284) X=cbind(MU284$P75,MU284$CS82,MU284$SS82,MU284$S82,MU284$ME84) strata=MU284$REG pik=inclusionprobabilities(MU284$P75,80) s=balancedstratification(X,strata,pik,TRUE) #the selected units are MU284$LABEL[s==1] } \keyword{survey} \encoding{latin1} sampling/man/UPmultinomial.Rd0000644000176200001440000000163513761417043015740 0ustar liggesusers\name{UPmultinomial} \alias{UPmultinomial} \title{Multinomial sampling} \description{ Uses the Hansen-Hurwitz method to select a sample of units (unequal probabilities, with replacement, fixed sample size). } \usage{ UPmultinomial(pik) } \arguments{ \item{pik}{vector of the the inclusion probabilities.} } \value{ Returns a vector of size N, the population size. Each element k of this vector indicates the number of replicates for unit k in the sample. } \references{ Hansen, M. and Hurwitz, W. (1943), On the theory of sampling from finite populations. \emph{Annals of Mathematical Statistics}, 14:333-362. } \examples{ #defines the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #selects a sample s=UPmultinomial(pik) #the selected units are (1:length(pik))[s!=0] #with the number of replicates s[s!=0] #or use rep((1:length(pik))[s!=0],s[s!=0]) } \keyword{survey} sampling/man/fastflightcube.Rd0000644000176200001440000000337511516307253016133 0ustar liggesusers\name{fastflightcube} \alias{fastflightcube} \title{Fast flight phase for the cube method} \description{Executes the fast flight phase of the cube method (algorithm of Chauvet and Till, 2005, 2006). The data are sorted following the argument \code{order}. Inclusion probabilities equal to 0 or 1 are tolerated. } \usage{fastflightcube(X,pik,order=1,comment=TRUE)} \arguments{ \item{X}{matrix of auxiliary variables on which the sample must be balanced.} \item{pik}{vector of inclusion probabilities.} \item{order}{ 1, the data are randomly arranged,\cr 2, no change in data order,\cr 3, the data are sorted in decreasing order. } \item{comment}{a comment is written during the execution if \code{comment} is \code{TRUE}.} } \references{ Till, Y. (2006), \emph{Sampling Algorithms}, Springer.\cr Chauvet, G. and Till, Y. (2006). A fast algorithm of balanced sampling. \emph{Computational Statistics}, 21/1:53--62. \cr Chauvet, G. and Till, Y. (2005). New SAS macros for balanced sampling. In INSEE, editor, \emph{Journes de Mthodologie Statistique}, Paris.\cr Deville, J.-C. and Till, Y. (2004). Efficient balanced sampling: the cube method. \emph{Biometrika}, 91:893--912.\cr Deville, J.-C. and Till, Y. (2005). Variance approximation under balanced sampling. \emph{Journal of Statistical Planning and Inference}, 128/2:411--425. } \seealso{ \code{\link{samplecube}} } \examples{ # Matrix of balancing variables X=cbind(c(1,1,1,1,1,1,1,1,1),c(1,2,3,4,5,6,7,8,9)) # Vector of inclusion probabilities. # The sample size is 3. pik=c(1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3) # pikstar is almost a balanced sample and is ready for the landing phase pikstar=fastflightcube(X,pik,order=1,comment=TRUE) pikstar } \keyword{survey} \encoding{latin1} sampling/man/samplecube.Rd0000644000176200001440000001064713767152020015261 0ustar liggesusers\name{samplecube} \alias{samplecube} \title{Sample cube method} \description{ Selects a balanced sample (a vector of 0 and 1) or an almost balanced sample. Firstly, the flight phase is applied. Next, if needed, the landing phase is applied on the result of the flight phase. } \usage{samplecube(X,pik,order=1,comment=TRUE,method=1)} \arguments{ \item{X}{matrix of auxiliary variables on which the sample must be balanced.} \item{pik}{vector of inclusion probabilities.} \item{order}{ 1, the data are randomly arranged,\cr 2, no change in data order,\cr 3, the data are sorted in decreasing order. } \item{comment}{a comment is written during the execution if \code{comment} is \code{TRUE}.} \item{method}{ 1, for a landing phase by linear programming,\cr 2, for a landing phase by suppression of variables.} } \seealso{ \code{\link{landingcube}}, \code{\link{fastflightcube}} } \references{ Till, Y. (2006), \emph{Sampling Algorithms}, Springer.\cr Chauvet, G. and Till, Y. (2006). A fast algorithm of balanced sampling. \emph{Computational Statistics}, 21/1:53--62. \cr Chauvet, G. and Till, Y. (2005). New SAS macros for balanced sampling. In INSEE, editor, \emph{Journes de Mthodologie Statistique}, Paris.\cr Deville, J.-C. and Till, Y. (2004). Efficient balanced sampling: the cube method. \emph{Biometrika}, 91:893--912.\cr Deville, J.-C. and Till, Y. (2005). Variance approximation under balanced sampling. \emph{Journal of Statistical Planning and Inference}, 128/2:411--425. } \examples{ ############ ## Example 1 ############ # matrix of balancing variables X=cbind(c(1,1,1,1,1,1,1,1,1),c(1.1,2.2,3.1,4.2,5.1,6.3,7.1,8.1,9.1)) # vector of inclusion probabilities # the sample size is 3. pik=c(1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3) # selection of the sample s=samplecube(X,pik,order=1,comment=TRUE) # The selected sample (1:length(pik))[s==1] ############ ## Example 2 ############ # 2 strata and 2 auxiliary variables # we verify the values of the inclusion probabilities by simulations X=rbind(c(1,0,1,2),c(1,0,2,5),c(1,0,3,7),c(1,0,4,9), c(1,0,5,1),c(1,0,6,5),c(1,0,7,7),c(1,0,8,6),c(1,0,9,9), c(1,0,10,3),c(0,1,11,3),c(0,1,12,2),c(0,1,13,3), c(0,1,14,6),c(0,1,15,8),c(0,1,16,9),c(0,1,17,1), c(0,1,18,2),c(0,1,19,3),c(0,1,20,4)) pik=rep(1/2,times=20) ppp=rep(0,times=20) sim=10 #for accurate results increase this value for(i in (1:sim)) ppp=ppp+samplecube(X,pik,1,FALSE) ppp=ppp/sim print(ppp) print(pik) ############ ## Example 3 ############ # unequal probability sampling by cube method # one auxiliary variable equal to the inclusion probability N=100 pik=runif(N) pikfin=samplecube(array(pik,c(N,1)),pik,1,TRUE) ############ ## Example 4 ############ # p auxiliary variables generated randomly N=100 p=7 x=rnorm(N*p,10,3) # random inclusion probabilities pik= runif(N) X=array(x,c(N,p)) X=cbind(cbind(X,rep(1,times=N)),pik) pikfin=samplecube(X,pik,1,TRUE) ############ ## Example 5 ############ # strata and an auxiliary variable N=100 a=rep(1,times=N) b=rep(0,times=N) V1=c(a,b,b) V2=c(b,a,b) V3=c(b,b,a) X=cbind(V1,V2,V3) pik=rep(2/10,times=3*N) pikfin=samplecube(X,pik,1,TRUE) ############ ## Example 6 ############ # Selection of a balanced sample using the MU284 population, # simulation and comparison of the variance with # unequal probability sampling of fixed sample size. ############ data(MU284) # Computation of the inclusion probabilities pik=inclusionprobabilities(MU284$P75,50) # Definition of the matrix of balancing variables X=cbind(MU284$P75,MU284$CS82,MU284$SS82,MU284$S82,MU284$ME84,MU284$REV84) # Computation of the Horvitz-Thompson estimator for a balanced sample s=samplecube(X,pik,1,FALSE) HTestimator(MU284$RMT85[s==1],pik[s==1]) # Computation of the Horvitz-Thompson estimator for an unequal probability sample s=samplecube(matrix(pik),pik,1,FALSE) HTestimator(MU284$RMT85[s==1],pik[s==1]) # simulations; for a better accuracy, increase the value of 'sim' sim=5 res1=rep(0,times=sim) res2=rep(0,times=sim) for(i in 1:sim) { cat("Simulation number ",i,"\n") s=samplecube(X,pik,1,FALSE) res1[i]=HTestimator(MU284$RMT85[s==1],pik[s==1]) s=samplecube(matrix(pik),pik,1,FALSE) res2[i]=HTestimator(MU284$RMT85[s==1],pik[s==1]) } # summary and boxplots summary(res1) summary(res2) ss=cbind(res1,res2) colnames(ss) = c("balanced sampling","uneq prob sampling") boxplot(data.frame(ss), las=1) } \keyword{survey} \encoding{latin1} sampling/man/UPbrewer.Rd0000644000176200001440000000167611516314722014675 0ustar liggesusers\name{UPbrewer} \alias{UPbrewer} \title{Brewer sampling} \description{ Uses the Brewer's method to select a sample of units (unequal probabilities, without replacement, fixed sample size). } \usage{ UPbrewer(pik,eps=1e-06) } \arguments{ \item{pik}{vector of the inclusion probabilities.} \item{eps}{the control value, by default equal to 1e-06; it is used to control pik (pik>eps & pik < 1-eps).} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). } \seealso{\code{\link{UPsystematic}} } \references{ Brewer, K. (1975), A simple procedure for $pi$pswor, \emph{Australian Journal of Statistics}, 17:166-172. } \examples{ #define the inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #select a sample s=UPbrewer(pik) #the sample is (1:length(pik))[s==1] } \keyword{survey} sampling/man/UPmidzuno.Rd0000644000176200001440000000227111516305250015060 0ustar liggesusers\name{UPmidzuno} \alias{UPmidzuno} \title{Midzuno sampling} \description{ Uses the Midzuno's method to select a sample of units (unequal probabilities, without replacement, fixed sample size). } \usage{ UPmidzuno(pik,eps=1e-6) } \arguments{ \item{pik}{vector of the inclusion probabilities.} \item{eps}{the control value, by default equal to 1e-6.} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). The value 'eps' is used to control pik (pik>eps & pik < 1-eps). } \seealso{\code{\link{UPtille}} } \references{ Midzuno, H. (1952), On the sampling system with probability proportional to sum of size. \emph{ Annals of the Institute of Statistical Mathematics}, 3:99-107.\cr Deville, J.-C. and Till, Y. (1998), Unequal probability sampling without replacement through a splitting method, \emph{Biometrika}, 85:89-101. } \examples{ #define the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #select a sample s=UPmidzuno(pik) #the sample is (1:length(pik))[s==1] } \keyword{survey} \encoding{latin1} sampling/man/cleanstrata.Rd0000644000176200001440000000113110723515654015433 0ustar liggesusers\name{cleanstrata} \alias{cleanstrata} \title{ Clean strata} \description{Renumbers a variable of stratification (categorical variable). The strata receive a number from 1 to the last stratum number. The empty strata are suppressed. This function is used in `balancedstratification'. } \usage{ cleanstrata(strata) } \arguments{ \item{strata}{vector of stratum numbers.} } \seealso{\code{\link{balancedstratification}}} \examples{ # definition of the stratification variable strata=c(-2,3,-2,3,4,4,4,-2,-2,3,4,0,0,0) # renumber the strata cleanstrata(strata) } \keyword{survey} sampling/man/UPpivotal.Rd0000644000176200001440000000233611516306165015061 0ustar liggesusers\name{UPpivotal} \alias{UPpivotal} \title{Pivotal sampling} \description{ Selects an unequal probability sample using the pivotal method (unequal probabilities, without replacement, fixed sample size). } \usage{ UPpivotal(pik,eps=1e-6) } \arguments{ \item{pik}{vector of the inclusion probabilities.} \item{eps}{the control value, by default equal to 1e-6.} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). The value eps is used to control pik (pik>eps & pik < 1-eps). } \seealso{\code{\link{UPrandompivotal}} } \references{ Deville, J.-C. and Till, Y. (1998), Unequal probability sampling without replacement through a splitting method, \emph{Biometrika}, 85:89-101.\cr Chauvet, G. and Till, Y. (2006). A fast algorithm of balanced sampling. \emph{to appear in Computational Statistics}.\cr Till, Y. (2006), \emph{Sampling Algorithms}, Springer. } \examples{ #define the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #select a sample s=UPpivotal(pik) #the sample is (1:length(pik))[s==1] } \keyword{survey} \encoding{latin1} sampling/man/srswr.Rd0000644000176200001440000000117113504341654014313 0ustar liggesusers\name{srswr} \alias{srswr} \title{Simple random sampling with replacement} \description{ Draws a simple random sampling with replacement of size n (equal probabilities, fixed sample size, with replacement). } \usage{ srswr(n,N) } \value{ Returns a vector of size N, the population size. Each element k of this vector indicates the number of replicates for unit k in the sample. } \arguments{ \item{n}{sample size.} \item{N}{population size.} } \seealso{\code{\link{UPmultinomial}} } \examples{ s=srswr(3,10) #the selected units are (1:10)[s!=0] #with the number of replicates s[s!=0] } \keyword{survey} sampling/man/inclusionprobabilities.Rd0000644000176200001440000000212311515601426017701 0ustar liggesusers\name{inclusionprobabilities} \alias{inclusionprobabilities} \title{Inclusion probabilities} \description{Computes the first-order inclusion probabilities from a vector of positive numbers (for a probability proportional-to-size sampling design). } \usage{inclusionprobabilities(a,n)} \arguments{ \item{a}{vector of positive numbers.} \item{n}{sample size.} } \seealso{ \code{\link{inclusionprobastrata}} } \examples{ ############ ## Example 1 ############ # a vector of positive numbers a=1:20 # computation of the inclusion probabilities for a sample size n=12 pik=inclusionprobabilities(a,12) pik ############ ## Example 2 ############ # Computation of the inclusion probabilities proportional to the number # of inhabitants in each municipality of the Belgian database. data(belgianmunicipalities) pik=inclusionprobabilities(belgianmunicipalities$Tot04,200) # the first-order inclusion probabilities for each municipality data.frame(pik=pik,name=belgianmunicipalities$Commune) # the inclusion probability sum is equal to the sample size sum(pik) } \keyword{survey} sampling/man/cluster.Rd0000644000176200001440000000511312223261737014614 0ustar liggesusers\name{cluster} \alias{cluster} \title{Cluster sampling} \description{Cluster sampling with equal/unequal probabilities.} \usage{cluster(data, clustername, size, method=c("srswor","srswr","poisson", "systematic"),pik,description=FALSE)} \arguments{ \item{data}{data frame or data matrix; its number of rows is N, the population size.} \item{clustername}{the name of the clustering variable.} \item{size}{sample size.} \item{method}{method to select clusters; the following methods are implemented: simple random sampling without replacement (srswor), simple random sampling with replacement (srswr), Poisson sampling (poisson), systematic sampling (systematic); if the method is not specified, by default the method is "srswor".} \item{pik}{vector of inclusion probabilities or auxiliary information used to compute them; this argument is only used for unequal probability sampling (Poisson, systematic). If an auxiliary information is provided, the function uses the \link{inclusionprobabilities} function for computing these probabilities.} \item{description}{a message is printed if its value is TRUE; the message gives the number of selected clusters, the number of units in the population and the number of selected units. By default, the value is FALSE.} } \value{ The function returns a data set with the following information: the selected clusters, the identifier of the units in the selected clusters, the final inclusion probabilities for these units (they are equal for the units included in the same cluster). If method is "srswr", the number of replicates is also given. } \seealso{ \code{\link{mstage}}, \code{\link{strata}}, \code{\link{getdata}}} \examples{ ############ ## Example 1 ############ # Uses the swissmunicipalities data to draw a sample of clusters data(swissmunicipalities) # the variable 'REG' has 7 categories in the population # it is used as clustering variable # the sample size is 3; the method is simple random sampling without replacement cl=cluster(swissmunicipalities,clustername=c("REG"),size=3,method="srswor") # extracts the observed data # the order of the columns is different from the order in the initial database getdata(swissmunicipalities, cl) ############ ## Example 2 ############ # the same data as in Example 1 # the sample size is 3; the method is systematic sampling # the pik vector is randomly generated using the U(0,1) distribution cl_sys=cluster(swissmunicipalities,clustername=c("REG"),size=3,method="systematic", pik=runif(7)) # extracts the observed data getdata(swissmunicipalities,cl_sys) } \keyword{survey} sampling/man/calib.Rd0000644000176200001440000001136313777315506014222 0ustar liggesusers\name{calib} \alias{calib} \title{g-weights of the calibration estimator} \description{Computes the g-weights of the calibration estimator. The g-weights should lie in the specified bounds for the truncated and logit methods. } \usage{calib(Xs,d,total,q=rep(1,length(d)),method=c("linear","raking","truncated", "logit"),bounds=c(low=0,upp=10),description=FALSE,max_iter=500)} \arguments{ \item{Xs}{matrix of calibration variables.} \item{d}{vector of initial weights.} \item{total}{vector of population totals.} \item{q}{vector of positive values accounting for heteroscedasticity; the variation of the g-weights is reduced for small values of q.} \item{method}{calibration method (linear, raking, logit, truncated).} \item{bounds}{vector of bounds for the g-weights used in the truncated and logit methods; 'low' is the smallest value and 'upp' is the largest value.} \item{description}{if description=TRUE, summary of initial and final weights are printed, and their boxplots and histograms are drawn; by default, its value is FALSE.} \item{max_iter}{maximum number of iterations in the Newton's method.} } \value{Returns the vector of g-weights.} \references{ Cassel, C.-M., Srndal, C.-E., and Wretman, J. (1976). Some results on generalized difference estimation and generalized regression estimation for finite population.\emph{Biometrika}, 63:615--620. \cr Deville, J.-C. and Srndal, C.-E. (1992). Calibration estimators in survey sampling. \emph{Journal of the American Statistical Association}, 87:376--382.\cr Deville, J.-C., Srndal, C.-E., and Sautory, O. (1993). Generalized raking procedure in survey sampling. \emph{Journal of the American Statistical Association}, 88:1013--1020.\cr } \details{The argument \emph{method} implements the methods given in the paper of Deville and Srndal(1992).} \seealso{ \code{\link{checkcalibration}}, \code{\link{calibev}}, \code{\link{gencalib}} } \examples{ ############ ## Example 1 ############ # matrix of sample calibration variables Xs=cbind( c(1,1,1,1,1,0,0,0,0,0), c(0,0,0,0,0,1,1,1,1,1), c(1,2,3,4,5,6,7,8,9,10) ) # inclusion probabilities piks=rep(0.2,times=10) # vector of population totals total=c(24,26,290) # the g-weights using the truncated method g=calib(Xs,d=1/piks,total,method="truncated",bounds=c(0.75,1.2)) # the calibration estimator of X is equal to 'total' vector tcal=t(g/piks)\%*\%Xs # the g-weights are between lower and upper bounds g ############ ## Example 2 ############ # Example of g-weights (linear, raking, truncated, logit), # with the data of Belgian municipalities as population. # Firstly, a sample is selected by means of Poisson sampling. # Secondly, the g-weights are calculated. data(belgianmunicipalities) attach(belgianmunicipalities) # matrix of calibration variables for the population X=cbind( Men03/mean(Men03), Women03/mean(Women03), Diffmen, Diffwom, TaxableIncome/mean(TaxableIncome), Totaltaxation/mean(Totaltaxation), averageincome/mean(averageincome), medianincome/mean(medianincome)) # selection of a sample with expectation size equal to 200 # by means of Poisson sampling # the inclusion probabilities are proportional to the average income pik=inclusionprobabilities(averageincome,200) N=length(pik) # population size s=UPpoisson(pik) # sample Xs=X[s==1,] # sample matrix of calibration variables piks=pik[s==1] # sample inclusion probabilities n=length(piks) # sample size # vector of population totals of the calibration variables total=c(t(rep(1,times=N))\%*\%X) # the population total total # computation of the g-weights # by means of different calibration methods. g1=calib(Xs,d=1/piks,total,method="linear") g2=calib(Xs,d=1/piks,total,method="raking") g3=calib(Xs,d=1/piks,total,method="truncated",bounds=c(0.5,1.5)) g4=calib(Xs,d=1/piks,total,method="logit",bounds=c(0.5,1.5)) # In some cases, the calibration does not exist # particularly when bounds are used. # if the calibration is possible, the calibration estimator of Xs is printed if(checkcalibration(Xs,d=1/piks,total,g1)$result) print(c((g1/piks) \%*\% Xs)) else print("error") if(!is.null(g2)) if(checkcalibration(Xs,d=1/piks,total,g2)$result) if(!is.null(g3)) if(checkcalibration(Xs,d=1/piks,total,g3)$result & all(g3<=1.5) & all(g3>=0.5)) print(c((g3/piks) \%*\% Xs)) else print("error") if(!is.null(g4)) if(checkcalibration(Xs,d=1/piks,total,g4)$result & all(g4<=1.5) & all(g4>=0.5)) print(c((g4/piks) \%*\% Xs)) else print("error") ############ ## Example 3 ############ # Example of calibration and adjustment for nonresponse in the 'calibration' vignette # vignette("calibration", package="sampling") } \keyword{survey} \encoding{latin1} sampling/man/UPmidzunopi2.Rd0000644000176200001440000000173611516305271015503 0ustar liggesusers\name{UPmidzunopi2} \alias{UPmidzunopi2} \title{Joint inclusion probabilities for Midzuno sampling} \description{ Computes the joint (second-order) inclusion probabilities for Midzuno sampling. } \usage{ UPmidzunopi2(pik) } \arguments{ \item{pik}{vector of the first-order inclusion probabilities.} } \value{ Returns a NxN matrix of the following form: the main diagonal contains the first-order inclusion probabilities for each unit k in the population; elements (k,l) are the joint inclusion probabilities of units k and l, with k not equal to l. N is the population size. } \seealso{\code{\link{UPmidzuno}} } \references{ Midzuno, H. (1952), On the sampling system with probability proportional to sum of size. \emph{ Annals of the Institute of Statistical Mathematics}, 3:99-107. } \examples{ #define the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #matrix of the joint inclusion probabilities UPmidzunopi2(pik) } \keyword{survey} sampling/man/regest.Rd0000644000176200001440000000471213761417226014434 0ustar liggesusers\name{regest} \alias{regest} \title{The regression estimator} \description{Computes the regression estimator of the population total, using the design-based approach. The underling regression model is a model without intercept.} \usage{regest(formula,Tx,weights,pikl,n,sigma=rep(1,length(weights)))} \arguments{ \item{formula}{the regression model formula (y~x).} \item{Tx}{population total of x, the auxiliary variable.} \item{weights}{vector of the weights; its length is equal to n, the sample size.} \item{pikl}{the matrix of joint inclusion probabilities for the sample.} \item{n}{the sample size.} \item{sigma}{vector of positive values accounting for heteroscedasticity.} } \value{The function returns a list containing the following components: \item{regest}{the value of the regression estimator.} \item{coefficients}{a vector of beta coefficients.} \item{std_error}{the standard error of coefficients.} \item{t_value}{the t-values associated to the coefficients.} \item{p_value}{the p-values associated to the coefficients.} \item{cov_mat}{the covariance matrix of the coefficients.} \item{weights}{the specified weights.} \item{y}{the response variable.} \item{x}{the model matrix.} } \seealso{ \code{\link{ratioest}},\code{\link{regest_strata}} } \examples{ # uses the MU284 population to draw a systematic sample data(MU284) # there are 3 outliers which are deleted from the population MU281=MU284[MU284$RMT85<=3000,] attach(MU281) # computes the inclusion probabilities using the variable P85; sample size 40 pik=inclusionprobabilities(P85,40) # the joint inclusion probabilities for systematic sampling pikl=UPsystematicpi2(pik) # draws a systematic sample of size 40 s=UPsystematic(pik) # defines the variable of interest y=RMT85[s==1] # defines the auxiliary information x1=CS82[s==1] x2=SS82[s==1] # the joint inclusion probabilities for s pikls=pikl[s==1,s==1] # the first-order inclusion probabilities for s piks=pik[s==1] # computes the regression estimator with the model y~x1+x2-1 r=regest(formula=y~x1+x2-1,Tx=c(sum(CS82),sum(SS82)),weights=1/piks,pikl=pikls,n=40) # the regression estimator is r$regest # the beta coefficients are r$coefficients # regression estimator is the same as the calibration estimator Xs=cbind(x1,x2) total=c(sum(CS82),sum(SS82)) g1=calib(Xs,d=1/piks,total,method="linear") checkcalibration(Xs,d=1/piks,total,g1) calibev(y,Xs,total,pikls,d=1/piks,g1,with=TRUE,EPS=1e-6) } \keyword{survey} sampling/man/UPmaxentropy.Rd0000644000176200001440000000741113777315660015623 0ustar liggesusers\name{UPmaxentropy} \alias{UPmaxentropy} \alias{UPmaxentropypi2} \alias{UPMEqfromw} \alias{UPMEpikfromq} \alias{UPMEpiktildefrompik} \alias{UPMEsfromq} \alias{UPMEpik2frompikw} \title{Maximum entropy sampling with fixed sample size and unequal probabilities} \description{ Maximum entropy sampling with fixed sample size and unequal probabilities (or Conditional Poisson sampling) is implemented by means of a sequential method. } \usage{ UPmaxentropy(pik) UPmaxentropypi2(pik) UPMEqfromw(w,n) UPMEpikfromq(q) UPMEpiktildefrompik(pik,eps=1e-6) UPMEsfromq(q) UPMEpik2frompikw(pik,w) } \arguments{ \item{n}{sample size.} \item{pik}{vector of prescribed inclusion probabilities.} \item{eps}{tolerance in the Newton's method; by default is 1E-6.} \item{q}{matrix of the conditional selection probabilities for the sequential algorithm.} \item{w}{parameter vector of the maximum entropy design.} } \details{ The maximum entropy sampling maximizes the entropy criterion: \deqn{I(p) = - \sum_s p(s)\log[p(s)]}{% I(p) = -\sum_s p(s)log[p(s)].} The main procedure is \code{UPmaxentropy} which selects a sample (a vector of 0 and 1) from a given vector of inclusion probabilities. The procedure \code{UPmaxentropypi2} returns the matrix of joint inclusion probabilities from the first-order inclusion probability vector. The other procedures are intermediate steps. They can be useful to run simulations as shown in the examples below. The procedure \code{UPMEpiktildefrompik} computes the vector of the inclusion probabilities (denoted \code{pikt}) of a Poisson sampling from the vector of the inclusion probabilities of the maximum entropy sampling. The maximum entropy sampling is the conditional design given the fixed sample size. The vector \code{w} can be easily obtained by \code{w=pikt/(1-pikt)}. Once \code{piktilde} and \code{w} are deduced from \code{pik}, a matrix of selection probabilities \code{q} can be derived from the sample size \code{n} and the vector \code{w} via \code{UPMEqfromw}. Next, a sample can be selected from \code{q} using \code{UPMEsfromq}. In order to generate several samples, it is more efficient to compute the matrix \code{q} (which needs some calculation), and then to use the procedure \code{UPMEsfromq}. The vector of the inclusion probabilities can be recomputed from \code{q} using \code{UPMEpikfromq}, which also checks the numerical precision of the algorithm. The procedure \code{UPMEpik2frompikw} computes the matrix of the joint inclusion probabilities from \code{q} and \code{w}. } \references{ Chen, S.X., Liu, J.S. (1997). Statistical applications of the Poisson-binomial and conditional Bernoulli distributions, \emph{Statistica Sinica}, 7, 875-892;\cr Deville, J.-C. (2000). \emph{Note sur l'algorithme de Chen, Dempster et Liu.} Technical report, CREST-ENSAI, Rennes.\cr Matei, A., Till, Y. (2005) Evaluation of variance approximations and estimators in maximum entropy sampling with unequal probability and fixed sample size, \emph{Journal of Official Statistics}, Vol. 21, No. 4, p. 543-570.\cr Till, Y. (2006), \emph{Sampling Algorithms}, Springer. } \examples{ ############ ## Example 1 ############ # Simple example - sample selection pik=c(0.07,0.17,0.41,0.61,0.83,0.91) # First method UPmaxentropy(pik) # Second method by using the intermediate procedures n=sum(pik) pikt=UPMEpiktildefrompik(pik) w=pikt/(1-pikt) q=UPMEqfromw(w,n) UPMEsfromq(q) # The matrix of inclusion probabilities # First method: direct computation from pik UPmaxentropypi2(pik) # Second method: computation from pik and w UPMEpik2frompikw(pik,w) ############ ## Example 2 ############ # other examples in the 'UPexamples' vignette # vignette("UPexamples", package="sampling") } \keyword{survey} \encoding{latin1} sampling/man/belgianmunicipalities.Rd0000644000176200001440000000323713762116772017510 0ustar liggesusers\name{belgianmunicipalities} \alias{belgianmunicipalities} \docType{data} \title{ The Belgian municipalities population} \description{This data provides information about the Belgian population of July 1, 2004 compared to that of July 1, 2003, and some financial information about the municipality incomes at the end of 2001. } \usage{data(belgianmunicipalities)} \format{ A data frame with 589 observations on the following 17 variables: \describe{ \item{Commune}{municipality name.} \item{INS}{`Institut National de statistique' code.} \item{Province}{province number.} \item{Arrondiss}{administrative division number.} \item{Men04}{number of men on July 1, 2004.} \item{Women04}{number of women on July 1, 2004.} \item{Tot04}{total population on July 1, 2004.} \item{Men03}{number of men on July 1, 2003.} \item{Women03}{number of women on July 1, 2003.} \item{Tot03}{total population on July 1, 2003.} \item{Diffmen}{number of men on July 1, 2004 minus the number of men on July 1, 2003.} \item{Diffwom}{number of women on July 1, 2004 minus the number of women on July 1, 2003.} \item{DiffTOT}{difference between the total population on July 1, 2004 and on July 1, 2003.} \item{TaxableIncome}{total taxable income in euros in 2001.} \item{Totaltaxation}{total taxation in euros in 2001.} \item{averageincome}{average of the income-tax return in euros in 2001.} \item{medianincome}{median of the income-tax return in euros in 2001.} } } \source{http://https://statbel.fgov.be/fr} \examples{ data(belgianmunicipalities) hist(belgianmunicipalities$medianincome) } \keyword{datasets} sampling/man/srswor.Rd0000644000176200001440000000163612235730571014500 0ustar liggesusers\name{srswor} \alias{srswor} \title{Simple random sampling without replacement} \description{ Draws a simple random sampling without replacement of size n (equal probabilities, fixed sample size, without replacement). } \usage{ srswor(n,N) } \arguments{ \item{n}{sample size.} \item{N}{population size.} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). } \seealso{\code{\link{srswr}}} \examples{ ############ ## Example 1 ############ #select a sample s=srswor(3,10) #the sample is (1:10)[s==1] ############ ## Example 2 ############ data(belgianmunicipalities) Tot=belgianmunicipalities$Tot04 name=belgianmunicipalities$Commune n=200 #select a sample s=srswor(n,length(Tot)) #the sample is as.vector(name[s==1]) } \keyword{survey} sampling/man/swissmunicipalities.Rd0000644000176200001440000000300110723532234017231 0ustar liggesusers\name{swissmunicipalities} \alias{swissmunicipalities} \docType{data} \title{The Swiss municipalities population} \description{This population provides information about the Swiss municipalities in 2003. } \usage{data(swissmunicipalities)} \format{ A data frame with 2896 observations on the following 22 variables: \describe{ \item{CT}{Swiss canton.} \item{REG}{Swiss region.} \item{COM}{municipality number.} \item{Nom}{municipality name.} \item{HApoly}{municipality area.} \item{Surfacesbois}{wood area.} \item{Surfacescult}{area under cultivation.} \item{Alp}{mountain pasture area.} \item{Airbat}{area with buildings.} \item{Airind}{industrial area.} \item{P00BMTOT}{number of men.} \item{P00BWTOT}{number of women.} \item{Pop020}{number of men and women aged between 0 and 19.} \item{Pop2040}{number of men and women aged between 20 and 39.} \item{Pop4065}{number of men and women aged between 40 and 64.} \item{Pop65P}{number of men and women aged between 65 and over.} \item{H00PTOT}{number of households.} \item{H00P01}{number of households with 1 person.} \item{H00P02}{number of households with 2 persons.} \item{H00P03}{number of households with 3 persons.} \item{H00P04}{number of households with 4 persons.} \item{POPTOT}{total population.} } } \source{Swiss Federal Statistical Office. } \examples{ data(swissmunicipalities) hist(swissmunicipalities$POPTOT) } \keyword{datasets} sampling/man/varest.Rd0000644000176200001440000000344713777316067014463 0ustar liggesusers\name{varest} \alias{varest} \title{Variance estimation using the Deville's method} \description{Computes the variance estimation of an estimator of the population total using the Deville's method.} \usage{varest(Ys,Xs=NULL,pik,w=NULL)} \arguments{ \item{Ys}{vector of the variable of interest; its length is equal to n, the sample size.} \item{Xs}{matrix of the auxiliary variables; for the calibration estimator, this is the matrix of the sample calibration variables.} \item{pik}{vector of the first-order inclusion probabilities; its length is equal to n, the sample size.} \item{w}{vector of the calibrated weights (for the calibration estimator); its length is equal to n, the sample size.} } \details{ The function implements the following estimator: \deqn{\widehat{Var}(\widehat{Ys})=\frac{1}{1-\sum_{k\in s} a_k^2}\sum_{k\in s}(1-\pi_k)\left(\frac{y_k}{\pi_k}-\frac{\sum_{l\in s} (1-\pi_{l})y_l/\pi_l}{\sum_{l\in s} (1-\pi_l)}\right)} where \eqn{a_k=(1-\pi_k)/\sum_{l\in s} (1-\pi_l)}. } \references{ Deville, J.-C. (1993). \emph{Estimation de la variance pour les enqutes en deux phases}. Manuscript, INSEE, Paris. } \seealso{ \code{\link{calibev}} } \examples{ # Belgian municipalities data base data(belgianmunicipalities) attach(belgianmunicipalities) # Computes the inclusion probabilities pik=inclusionprobabilities(Tot04,200) N=length(pik) n=sum(pik) # Defines the variable of interest y=TaxableIncome # Draws a Tille sample of size 200 s=UPtille(pik) # Computes the Horvitz-Thompson estimator HTestimator(y[s==1],pik[s==1]) # Computes the variance estimation of the Horvitz-Thompson estimator varest(Ys=y[s==1],pik=pik[s==1]) # for an example using calibration estimator see the 'calibration' vignette # vignette("calibration", package="sampling") } \keyword{survey} sampling/man/Hajekstrata.Rd0000644000176200001440000000371612511713122015371 0ustar liggesusers\name{Hajekstrata} \alias{Hajekstrata} \title{The Hajek estimator for a stratified design} \description{Computes the Hjek estimator of the population total or population mean for a stratified design.} \usage{Hajekstrata(y,pik,strata,N=NULL,type=c("total","mean"),description=FALSE)} \arguments{ \item{y}{vector of the variable of interest; its length is equal to n, the sample size.} \item{pik}{vector of the first-order inclusion probabilities for the sampled units; its length is equal to n, the sample size.} \item{strata}{vector of size n, with elements indicating the unit stratum.} \item{N}{vector of population sizes of strata; N is only used for the total estimator; for the mean estimator its value is NULL.} \item{type}{the estimator type: total or mean.} \item{description}{if TRUE, the estimator is printed for each stratum; by default, FALSE.} } \seealso{ \code{\link{HTstrata}} } \examples{ # Swiss municipalities data base data(swissmunicipalities) # the variable 'REG' has 7 categories in the population # it is used as stratification variable # computes the population stratum sizes table(swissmunicipalities$REG) # do not run # 1 2 3 4 5 6 7 # 589 913 321 171 471 186 245 # the sample stratum sizes are given by size=c(30,20,45,15,20,11,44) # the method is simple random sampling without replacement # (equal probability, without replacement) st=strata(swissmunicipalities,stratanames=c("REG"),size=c(30,20,45,15,20,11,44), method="srswor") # extracts the observed data # the order of the columns is different from the order in the swsissmunicipalities database x=getdata(swissmunicipalities, st) # computes the population sizes of strata N=table(swissmunicipalities$REG) N=N[unique(x$REG)] #the strata 1 2 3 4 5 6 7 #corresponds to REG 4 1 3 2 5 6 7 # computes the Hajek estimator of the variable Pop020 Hajekstrata(x$Pop020,x$Prob,x$Stratum,N,type="total",description=TRUE)} \keyword{survey} sampling/man/landingcube.Rd0000644000176200001440000000323410723516336015411 0ustar liggesusers\name{landingcube} \alias{landingcube} \title{Landing phase for the cube method} \description{ Landing phase of the cube method using linear programming. } \usage{landingcube(X,pikstar,pik,comment=TRUE)} \arguments{ \item{X}{matrix of auxiliary variables on which the sample must be balanced.} \item{pikstar}{vector obtained at the end of the flight phase.} \item{pik}{vector of inclusion probabilities.} \item{comment}{a comment is written during the execution if \code{comment} is \code{TRUE}.} } \references{ Till, Y. (2006), \emph{Sampling Algorithms}, Springer.\cr Chauvet, G. and Till, Y. (2006). A fast algorithm of balanced sampling. \emph{Computational Statistics}, 21/1:53--62. \cr Chauvet, G. and Till, Y. (2005). New SAS macros for balanced sampling. In INSEE, editor, \emph{Journes de Mthodologie Statistique}, Paris.\cr Deville, J.-C. and Till, Y. (2004). Efficient balanced sampling: the cube method. \emph{Biometrika}, 91:893--912.\cr Deville, J.-C. and Till, Y. (2005). Variance approximation under balanced sampling. \emph{Journal of Statistical Planning and Inference}, 128/2:411--425. } \seealso{ \code{\link{samplecube}}, \code{\link{fastflightcube}} } \examples{ # matrix of balancing variables X=cbind(c(1,1,1,1,1,1,1,1,1),c(1.1,2.2,3.1,4.2,5.1,6.3,7.1,8.1,9.1)) # Vector of inclusion probabilities # The sample has the size equal to 3. pik=c(1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3) # pikstar is almost a balanced sample and is ready for the landing phase pikstar=fastflightcube(X,pik,order=1,comment=TRUE) # selection of the sample s s=landingcube(X,pikstar,pik,comment=TRUE) round(s) } \keyword{survey} \encoding{latin1} sampling/man/UPtille.Rd0000644000176200001440000000246513777316002014521 0ustar liggesusers\name{UPtille} \alias{UPtille} \title{Tille sampling} \description{ Uses the Till's method to select a sample of units (unequal probabilities, without replacement, fixed sample size). } \usage{ UPtille(pik,eps=1e-6) } \arguments{ \item{pik}{vector of the inclusion probabilities.} \item{eps}{the control value, by default equal to 1e-6.} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). The value eps is used to control pik (pik>eps & pik < 1-eps). } \seealso{\code{\link{UPsystematic}} } \references{ Till, Y. (1996), An elimination procedure of unequal probability sampling without replacement, \emph{Biometrika}, 83:238-241.\cr Deville, J.-C. and Till, Y. (1998), Unequal probability sampling without replacement through a splitting method, \emph{Biometrika}, 85:89-101. } \examples{ ############ ## Example 1 ############ #defines the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #selects a sample s=UPtille(pik) #the sample is (1:length(pik))[s==1] ############ ## Example 2 ############ # see in the 'UPexamples' vignette # vignette("UPexamples", package="sampling") } \keyword{survey} \encoding{latin1} sampling/man/ratioest.Rd0000644000176200001440000000211111024463372014755 0ustar liggesusers\name{ratioest} \alias{ratioest} \title{The ratio estimator} \description{Computes the ratio estimator of the population total.} \usage{ratioest(y,x,Tx,pik)} \arguments{ \item{y}{vector of the variable of interest; its length is equal to n, the sample size.} \item{x}{vector of auxiliary information; its length is equal to n, the sample size.} \item{Tx}{population total of x.} \item{pik}{vector of the first-order inclusion probabilities; its length is equal to n, the sample size.} } \value{The function returns the value of the ratio estimator.} \seealso{ \code{\link{regest}} } \examples{ data(MU284) # there are 3 outliers which are deleted from the population MU281=MU284[MU284$RMT85<=3000,] attach(MU281) # computes the inclusion probabilities using the variable P85; sample size 120 pik=inclusionprobabilities(P85,120) # defines the variable of interest y=RMT85 # defines the auxiliary information x=CS82 # draws a systematic sample of size 120 s=UPsystematic(pik) # computes the ratio estimator ratioest(y[s==1],x[s==1],sum(x),pik[s==1]) } \keyword{survey}sampling/man/UPsystematicpi2.Rd0000644000176200001440000000171211516306305016174 0ustar liggesusers\name{UPsystematicpi2} \alias{UPsystematicpi2} \title{Joint inclusion probabilities for systematic sampling} \description{ Computes the joint (second-order) inclusion probabilities for systematic sampling. } \usage{ UPsystematicpi2(pik) } \arguments{ \item{pik}{vector of the first-order inclusion probabilities.} } \value{ Returns a NxN matrix of the following form: the main diagonal contains the first-order inclusion probabilities for each unit k in the population; elements (k,l) are the joint inclusion probabilities of units k and l, with k not equal to l. N is the population size. } \seealso{\code{\link{UPsystematic}} } \references{ Madow, W.G. (1949), On the theory of systematic sampling, II, \emph{Annals of Mathematical Statistics}, 20, 333-354. } \examples{ #define the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #matrix of the joint inclusion probabilities UPsystematicpi2(pik) } \keyword{survey} sampling/man/ratioest_strata.Rd0000644000176200001440000000656411415615566016363 0ustar liggesusers\name{ratioest_strata} \alias{ratioest_strata} \title{The ratio estimator for a stratified design} \description{Computes the ratio estimator of the population total for a stratified design. The ratio estimator of a total is the sum of ratio estimator in each stratum.} \usage{ratioest_strata(y,x,TX_strata,pik,strata,description=FALSE)} \arguments{ \item{y}{vector of the variable of interest; its length is equal to n, the sample size.} \item{x}{vector of auxiliary information; its length is equal to n, the sample size.} \item{TX_strata}{vector of population x-total in each stratum; its length is equal to the number of strata.} \item{pik}{vector of the first-order inclusion probabilities; its length is equal to n, the sample size.} \item{strata}{vector of size n, with elements indicating the unit stratum.} \item{description}{if TRUE, the ratio estimator in each stratum is printed; by default, it is FALSE.} } \value{The function returns the value of the ratio estimator.} \seealso{ \code{\link{ratioest}} } \examples{ ########### # Example 1 ########### # this example uses MU284 data with the 'REG' variable for stratification data(MU284) attach(MU284) # there are 3 outliers which are deleted from the population MU281=MU284[RMT85<=3000,] detach(MU284) attach(MU281) # computes the inclusion probabilities using the variable P85 pik=inclusionprobabilities(P85,120) # defines the variable of interest y=RMT85 # defines the auxiliary information x=CS82 # computes the population stratum sizes table(MU281$REG) # not run # 1 2 3 4 5 6 7 8 # 24 48 32 37 55 41 15 29 # a sample is drawn in each region # the sample stratum sizes are given by size=c(4,10,8,4,6,4,6,7) s=strata(MU281,c("REG"),size=c(4,10,8,4,6,4,6,7), method="systematic",pik=P85) # extracts the observed data MU281sample=getdata(MU281,s) # computes the population x-totals in each stratum TX_strata=as.vector(tapply(CS82,list(REG),FUN=sum)) # computes the ratio estimator ratioest_strata(MU281sample$RMT85,MU281sample$CS82,TX_strata, MU281sample$Prob,MU281sample$Stratum) ########### # Example 2 ########### # this is an artificial example (see Example 1 in the 'strata' function) # there are 4 columns: state, region, income and aux # 'income' is the variable of interest, and 'aux' is the auxiliary information # which is correlated to the income data=rbind(matrix(rep("nc",165),165,1,byrow=TRUE),matrix(rep("sc",70),70,1,byrow=TRUE)) data=cbind.data.frame(data,c(rep(1,100), rep(2,50), rep(3,15), rep(1,30),rep(2,40)), 1000*runif(235)) names(data)=c("state","region","income") attach(data) aux=income+rnorm(length(income),0,1) data=cbind.data.frame(data,aux) # computes the population stratum sizes table(data$region,data$state) # not run # nc sc # 1 100 30 # 2 50 40 # 3 15 0 # there are 5 cells with non-zero values; one draws 5 samples (1 sample in each stratum) # the sample stratum sizes are 10,5,10,4,6, respectively # the method is 'srswor' (equal probability, without replacement) s=strata(data,c("region","state"),size=c(10,5,10,4,6), method="srswor") # extracts the observed data xx=getdata(data,s) # computes the population x-total for each stratum TX_strata=na.omit(as.vector(tapply(aux,list(region,state),FUN=sum))) # computes the ratio estimator ratioest_strata(xx$income,xx$aux,TX_strata,xx$Prob,xx$Stratum,description=TRUE) } \keyword{survey} sampling/man/poststrata.Rd0000644000176200001440000000264611415615450015344 0ustar liggesusers\name{poststrata} \alias{poststrata} \title{Postratification} \description{Poststratification using several criteria.} \usage{poststrata(data, postnames = NULL)} \arguments{ \item{data}{data frame or data matrix; its number of rows is n, the sample size.} \item{postnames}{vector of poststratification variables.} } \value{ \item{The function}{produces an object, which contains the following information:} \item{data}{the final data frame with a new column ('poststratum') containg the unit poststratum.} \item{npost}{the number of poststrata.} } \seealso{ \code{\link{postest}}} \examples{ # Example from An and Watts (New SAS procedures for Analysis of Sample Survey Data) # generates artificial data (a 235X3 matrix with 3 columns: state, region, income). # the variable "state" has 2 categories ('nc' and 'sc'). # the variable "region" has 3 categories (1, 2 and 3). # the income variable is randomly generated data=rbind(matrix(rep("nc",165),165,1,byrow=TRUE),matrix(rep("sc",70),70,1,byrow=TRUE)) data=cbind.data.frame(data,c(rep(1,100), rep(2,50), rep(3,15), rep(1,30),rep(2,40)), 1000*runif(235)) names(data)=c("state","region","income") # computes the population stratum sizes table(data$region,data$state) # not run # nc sc # 1 100 30 # 2 50 40 # 3 15 0 # postratification using two criteria: state and region poststrata(data,postnames=c("state","region")) } \keyword{survey} sampling/man/balancedtwostage.Rd0000644000176200001440000000364611516306536016454 0ustar liggesusers\name{balancedtwostage} \alias{balancedtwostage} \title{Balanced two-stage sampling} \description{ Selects a balanced two-stage sample.} \usage{balancedtwostage(X,selection,m,n,PU,comment=TRUE,method=1)} \arguments{ \item{X}{matrix of auxiliary variables on which the sample must be balanced.} \item{selection}{1, for simple random sampling without replacement at each stage,\cr 2, for self-weighting two-stage selection.} \item{m}{number of primary sampling units to be selected.} \item{n}{number of second-stage sampling units to be selected.} \item{PU}{vector of integers that defines the primary sampling units.} \item{comment}{a comment is written during the execution if \code{comment} is \code{TRUE}.} \item{method}{the used method in the function \code{samplecube}.} } \value{The function returns a matrix whose columns are the following five vectors: the selected second-stage sampling units (0 - unselected, 1 - selected), the final inclusion probabilities, the selected primary sampling units, the inclusion probabilities of the first stage, the inclusion probabilities of the second stage.} \seealso{ \code{\link{samplecube}}, \code{\link{fastflightcube}}, \code{\link{landingcube}}, \code{\link{balancedstratification}}, \code{\link{balancedcluster}} } \examples{ ############ ## Example 1 ############ # definition of the primary units (3 primary units) PU=c(1,1,1,1,1,2,2,2,2,2,3,3,3,3,3) # matrix of balancing variables X=cbind(c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)) # selection of 2 primary sampling units and 4 second-stage sampling units s=balancedtwostage(X,1,2,4,PU,comment=TRUE) # the sample and the inclusion probabilities s ############ ## Example 2 ############ data(MU284) X=cbind(MU284$P75,MU284$CS82,MU284$SS82,MU284$ME84) N=dim(X)[1] PU=MU284$CL m=20 n=60 res=balancedtwostage(X,1,m,n,PU,TRUE) # the sample and the inclusion probabilities res } \keyword{survey} sampling/man/UPrandomsystematic.Rd0000644000176200001440000000210311516306230016752 0ustar liggesusers\name{UPrandomsystematic} \alias{UPrandomsystematic} \title{Random systematic sampling} \description{ Selects a sample using the systematic method, when the order of the population units is random (unequal probabilities, without replacement, fixed sample size). } \usage{ UPrandomsystematic(pik,eps=1e-6) } \arguments{ \item{pik}{vector of the inclusion probabilities.} \item{eps}{the control value, by default equal to 1e-6.} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). The value 'eps' is used to control pik (pik>eps and pik<1-eps). } \seealso{\code{\link{UPsystematic}} } \references{ Madow, W.G. (1949), On the theory of systematic sampling, II, \emph{Annals of Mathematical Statistics}, 20, 333-354. } \examples{ #define the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #select a sample s=UPrandomsystematic(pik) #the sample is (1:length(pik))[s==1] } \keyword{survey} sampling/man/UPminimalsupport.Rd0000644000176200001440000000235611516305310016457 0ustar liggesusers\name{UPminimalsupport} \alias{UPminimalsupport} \title{Minimal support sampling} \description{ Uses the minimal support method to select a sample of units (unequal probabilities, without replacement, fixed sample size). } \usage{ UPminimalsupport(pik) } \arguments{ \item{pik}{vector of the inclusion probabilities.} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). } \references{ Deville, J.-C., Till, Y. (1998), Unequal probability sampling without replacement through a splitting method, \emph{Biometrika }, 85, 89-101.\cr Till, Y. (2006), \emph{Sampling Algorithms}, Springer. } \examples{ ############ ## Example 1 ############ #defines the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #selects a sample s=UPminimalsupport(pik) #the sample is (1:length(pik))[s==1] ############ ## Example 2 ############ data(belgianmunicipalities) Tot=belgianmunicipalities$Tot04 name=belgianmunicipalities$Commune pik=inclusionprobabilities(Tot,200) #selects a sample s=UPminimalsupport(pik) #the sample is as.vector(name[s==1]) } \keyword{survey} sampling/man/checkcalibration.Rd0000644000176200001440000000270513214440620016413 0ustar liggesusers\name{checkcalibration} \alias{checkcalibration} \title{Check calibration} \description{Checks the validity of the calibration. In some cases, the calibration estimators do not exist, and the g-weights do not allow calibration.} \value{ The function returns the following three objects: \item{message}{a message concerning the calibration,} \item{result}{TRUE if the calibration is possible and FALSE, otherwise.} \item{value}{value of max(abs(tr-total)/total, which is used as criterium to validate the calibration, where tr=crossprod(Xs, g*d). If the vector total contains zeros, the value is max(abs(tr-total)).} } \usage{checkcalibration(Xs, d, total, g, EPS=1e-6)} \arguments{ \item{Xs}{matrix of calibration variables.} \item{d}{vector of initial weights.} \item{total}{vector of population totals.} \item{g}{vector of g-weights.} \item{EPS}{the control value used to verify the calibration, by default equal to 1e-6.} } \details{In the case where calibration is not possible, the 'value' indicates the difference in obtaining the calibration.} \seealso{ \code{\link{calib}} } \examples{ # matrix of auxiliary variables Xs=cbind(c(1,1,1,1,1,0,0,0,0,0),c(0,0,0,0,0,1,1,1,1,1),c(1,2,3,4,5,6,7,8,9,10)) # inclusion probabilities pik=rep(0.2,times=10) # vector of totals total=c(24,26,280) # the g-weights g=calib(Xs,d=1/pik,total,method="raking") # the calibration is possible checkcalibration(Xs,d=1/pik,total,g) } \keyword{survey} sampling/man/UPrandompivotal.Rd0000644000176200001440000000223411516306216016254 0ustar liggesusers\name{UPrandompivotal} \alias{UPrandompivotal} \title{Random pivotal sampling} \description{ Selects a sample using the pivotal method, when the order of the population units is random (unequal probabilities, without replacement, fixed sample size). } \usage{ UPrandompivotal(pik,eps=1e-6) } \arguments{ \item{pik}{vector of the inclusion probabilities.} \item{eps}{the control value, by default equal to 1e-6.} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). The value 'eps' is used to control pik (pik>eps and pik<1-eps). } \seealso{\code{\link{UPpivotal}} } \references{ Deville, J.-C. and Till, Y. (1998), Unequal probability sampling without replacement through a splitting method, \emph{Biometrika}, 85:89--101.\cr Till, Y. (2006), \emph{Sampling Algorithms}, Springer. } \examples{ #define the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #select a sample s=UPrandompivotal(pik) #the sample is (1:length(pik))[s==1] } \keyword{survey} \encoding{latin1} sampling/man/varHT.Rd0000644000176200001440000000356612542732503014167 0ustar liggesusers\name{varHT} \alias{varHT} \title{Variance estimators of the Horvitz-Thompson estimator} \description{Computes variance estimators of the Horvitz-Thompson estimator of the population total.} \usage{varHT(y,pikl,method)} \arguments{ \item{y}{vector of the variable of interest; its length is equal to n, the sample size.} \item{pikl}{matrix of second-order inclusion probabilities; its dimension is nxn.} \item{method}{if 1, an unbiased variance estimator is computed; if 2, the Sen-Yates-Grundy variance estimator for fixed sample size is computed; be default, the method is 1.} } \details{ If method is 1, the following estimator is implemented \deqn{\widehat{Var}(\widehat{Y}_{HT})_1=\sum_{k\in s}\sum_{\ell\in s} \frac{y_k y_\ell}{\pi_{k\ell} \pi_k \pi_\ell}(\pi_{k\ell} - \pi_k \pi_\ell)} If method is 2, the following estimator is implemented \deqn{\widehat{Var}(\widehat{Y}_{HT})_2=\frac{1}{2}\sum_{k\in s}\sum_{\ell\in s} \left(\frac{y_k}{\pi_k} - \frac{y_\ell}{\pi_\ell}\right)^2 \frac{\pi_k \pi_\ell-\pi_{k\ell}}{\pi_{k\ell}}}} \seealso{ \code{\link{HTestimator}} } \examples{ pik=c(0.2,0.7,0.8,0.5,0.4,0.4) N=length(pik) n=sum(pik) # Defines the variable of interest y=rnorm(N,10,2) # Draws a Poisson sample of expected size n s=UPpoisson(pik) # Computes the Horvitz-Thompson estimator HTestimator(y[s==1],pik[s==1]) # Computes the second-order inclusion prob. for Poisson sampling pikl=outer(pik,pik,"*") diag(pikl)=pik # Computes the variance estimator (method=1, the sample size is not fixed) varHT(y[s==1],pikl[s==1,s==1],1) # Draws a Tille sample of size n s=UPtille(pik) # Computes the Horvitz-Thompson estimator HTestimator(y[s==1],pik[s==1]) # Computes the second-order inclusion prob. for Tille sampling pikl=UPtillepi2(pik) # Computes the variance estimator (method=2, the sample size is fixed) varHT(y[s==1],pikl[s==1,s==1],2) } \keyword{survey}sampling/man/MU284.Rd0000644000176200001440000000237210562037436013717 0ustar liggesusers\name{MU284} \alias{MU284} \docType{data} \title{ The MU284 population } \description{ This data is from Srndal et al (1992), see Appendix B, p. 652. } \usage{data(MU284)} \format{ A data frame with 284 observations on the following 11 variables. \describe{ \item{LABEL}{identifier number from 1 to 284.} \item{P85}{1985 population (in thousands).} \item{P75}{1975 population (in thousands).} \item{RMT85}{revenues from 1985 municipal taxation (in millions of kronor).} \item{CS82}{number of Conservative seats in municipal council.} \item{SS82}{number of Social-Democratic seats in municipal council.} \item{S82}{total number of seats in municipal council.} \item{ME84}{number of municipal employees in 1984.} \item{REV84}{real estate values according to 1984 assessment (in millions of kronor).} \item{REG}{geographic region indicator.} \item{CL}{cluster indicator (a cluster consists of a set of neighboring).} } } \references{ Srndal, C.-E., Swensson, B., and Wretman, J. (1992), \emph{Model Assisted Survey Sampling}, Springer Verlag, New York. } \source{ http://lib.stat.cmu.edu/datasets/mu284 } \examples{ data(MU284) hist(MU284$RMT85) } \keyword{datasets} \encoding{latin1} sampling/man/postest.Rd0000644000176200001440000001101011515601510014613 0ustar liggesusers\name{postest} \alias{postest} \title{The poststratified estimator} \description{Computes the poststratified estimator of the population total.} \usage{postest(data, y, pik, NG, description=FALSE)} \arguments{ \item{data}{data frame or data matrix; its number of rows is n, the sample size.} \item{y}{vector of the variable of interest; its length is equal to n, the sample size.} \item{pik}{vector of the first-order inclusion probabilities for the sampled units; its length is equal to n, the sample size.} \item{NG}{vector of population frequency in each group G; for stratified sampling with poststratification, NG is a matrix of population frequency in each cell GH.} \item{description}{if TRUE, the estimator is printed for each poststratum; by default, FALSE.} } \seealso{ \code{\link{poststrata}}} \examples{ ############ ## Example 1 ############ #stratified sampling and poststratification # Swiss municipalities data base data(swissmunicipalities) attach(swissmunicipalities) # the variable 'REG' has 7 categories in the population # it is used as stratification variable # Computes the population stratum sizes table(swissmunicipalities$REG) # do not run # 1 2 3 4 5 6 7 # 589 913 321 171 471 186 245 # the sample stratum sizes are given by size=c(30,20,45,15,20,11,44) # the method is simple random sampling without replacement st=strata(swissmunicipalities,stratanames=c("REG"), size=c(30,20,45,15,20,11,44), method="srswor") # extracts the observed data # the order of the columns is different from the order in the initial database x=getdata(swissmunicipalities, st) px=poststrata(x,"REG") ct=unique(px$data$REG) yy=numeric(length(ct)) for(i in 1:length(ct)) {xx=swissmunicipalities[REG==ct[i],] yy[i]=nrow(xx) } yy postest(px$data,y=px$data$Pop020,pik=px$data$Prob,NG=diag(yy),description=TRUE) HTstrata(x$Pop020,x$Prob,x$Stratum) #the two estimators are equal ############ ## Example 2 ############ # systematic sampling and poststratification # Belgian municipalities data base data(belgianmunicipalities) Tot=belgianmunicipalities$Tot04 name=belgianmunicipalities$Commune pik=inclusionprobabilities(Tot,200) #selects a sample s=UPsystematic(pik) #the sample is as.vector(name[s==1]) # extracts the observed data b=getdata(belgianmunicipalities,s) attach(belgianmunicipalities) pb=poststrata(b,"Province") #computes the population frequency in each group ct=unique(pb$data$Province) yy=numeric(length(ct)) for(i in 1:length(ct)) {xx=belgianmunicipalities[Province==ct[i],] yy[i]=nrow(xx) } postest(pb$data,y=pb$data$TaxableIncome,pik=pik[s==1],NG=yy,description=TRUE) HTestimator(pb$data$TaxableIncome,pik=pik[s==1]) ############ ## Example 3 ############ #cluster sampling and postratification # Swiss municipalities data base data(swissmunicipalities) # the variable 'REG' has 7 categories in the population # it is used as clustering variable # the sample size is 3; the method is simple random sampling without replacement cl=cluster(swissmunicipalities,clustername=c("REG"),size=3,method="srswor") # extracts the observed data # the order of the columns is different from the order in the initial database c=getdata(swissmunicipalities, cl) pc=poststrata(c,"CT") #computes the population frequency in each group ct=unique(pc$data$CT) yy=numeric(length(ct)) for(i in 1:length(ct)) {xx=swissmunicipalities[CT==ct[i],] yy[i]=nrow(xx) } postest(pc$data,y=pc$data$Pop020,pik=pc$data$Prob,NG=yy,description=TRUE) ############ ## Example 4 ############ #postratification with two criteria #artificial data frame data=rbind(matrix(rep("nc",165),165,1,byrow=TRUE),matrix(rep("sc",70),70,1,byrow=TRUE)) data=cbind.data.frame(data,c(rep(1,100), rep(2,50), rep(3,15), rep(1,30),rep(2,40)), 1000*runif(235)) names(data)=c("state","region","income") # computes the population stratum sizes table(data$region,data$state) # not run # nc sc # 1 100 30 # 2 50 40 # 3 15 0 #selects a sample of size 10 s=srswor(10,nrow(data)) # postratification using region and state ps=poststrata(data[s==1,],c("region","state")) #computes the population frequency in each group ct=unique(ps$data$poststratum) yy=numeric(length(ct)) for(i in 1:length(ct)) { xy=ps$data[ps$data$poststratum==ct[i],] xstate=unique(xy$state) ystate=unique(xy$region) xx=data[data$state==xstate & data$region==ystate,] yy[i]=nrow(xx) } postest(ps$data,y=ps$data$income,pik=rep(10/nrow(data),10),NG=yy,description=TRUE) } \keyword{survey} sampling/man/calibev.Rd0000644000176200001440000000733312542734625014553 0ustar liggesusers\name{calibev} \alias{calibev} \title{Calibration estimator and its variance estimation} \description{Computes the calibration estimator of the population total and its variance estimation using the residuals' method. } \usage{calibev(Ys,Xs,total,pikl,d,g,q=rep(1,length(d)),with=FALSE,EPS=1e-6)} \arguments{ \item{Ys}{vector of interest variable; its size is n, the sample size.} \item{Xs}{matrix of sample calibration variables.} \item{total}{vector of population totals for calibration.} \item{pikl}{matrix of joint inclusion probabilities of the sample units.} \item{d}{vector of initial weights of the sample units.} \item{g}{vector of g-weights; its size is n, the sample size.} \item{q}{vector of positive values accounting for heteroscedasticity; its size is n, the sample size.} \item{with}{if TRUE, the variance estimation takes into account the initial weights d; otherwise, the final weights w=g*d are taken into account; by default, its value is FALSE.} \item{EPS}{the tolerance in checking the calibration; by default, its value is 1e-6.} } \value{ The function returns two values: \item{cest}{the calibration estimator,} \item{evar}{its estimated variance.} } \details{ If with is TRUE, the following formula is used \deqn{\widehat{Var}(\widehat{Ys})=\sum_{k\in s}\sum_{\ell\in s}((\pi_{k\ell}-\pi_k\pi_{\ell})/\pi_{k\ell})(d_ke_k)(d_\ell e_\ell)}{\hat{Var}(\hat{Ys})=\sum_{k\in s}\sum_{\ell\in s}((\pi_{k\ell}-\pi_k\pi_{\ell})/\pi_{k\ell})(d_ke_k)(d_\ell e_\ell)} else \deqn{\widehat{Var}(\widehat{Ys})=\sum_{k\in s}\sum_{\ell\in s}((\pi_{k\ell}-\pi_k\pi_{\ell})/\pi_{k\ell})(w_ke_k)(w_\ell e_\ell)}{\hat{Var}(\hat{Ys})=\sum_{k\in s}\sum_{\ell\in s}((\pi_{k\ell}-\pi_k\pi_{\ell})/\pi_{k\ell})(w_ke_k)(w_\ell e_\ell)} where \eqn{e_k} denotes the residual of unit k. } \references{ Deville, J.-C. and Srndal, C.-E. (1992). Calibration estimators in survey sampling. \emph{Journal of the American Statistical Association}, 87:376--382.\cr Deville, J.-C., Srndal, C.-E., and Sautory, O. (1993). Generalized raking procedure in survey sampling. \emph{Journal of the American Statistical Association}, 88:1013--1020.\cr } \seealso{ \code{\link{calib}} } \examples{ ############ ## Example ############ # Example of g-weights (linear, raking, truncated, logit), # with the data of Belgian municipalities as population. # Firstly, a sample is selected by means of systematic sampling. # Secondly, the g-weights are calculated. data(belgianmunicipalities) attach(belgianmunicipalities) # matrix of calibration variables for the population X=cbind( Men03/mean(Men03), Women03/mean(Women03), Diffmen, Diffwom, TaxableIncome/mean(TaxableIncome), Totaltaxation/mean(Totaltaxation), averageincome/mean(averageincome), medianincome/mean(medianincome)) # selection of a sample of size 200 # using systematic sampling # the inclusion probabilities are proportional to the average income pik=inclusionprobabilities(averageincome,200) N=length(pik) # population size s=UPsystematic(pik) # draws a sample s using systematic sampling Xs=X[s==1,] # matrix of sample calibration variables piks=pik[s==1] # sample inclusion probabilities n=length(piks) # sample size # vector of population totals of the calibration variables total=c(t(rep(1,times=N))\%*\%X) g1=calib(Xs,d=1/piks,total,method="linear") # computes the g-weights pikl=UPsystematicpi2(pik) # computes the matrix of the joint inclusion probabilities pikls=pikl[s==1,s==1] # the same matrix for the units in s Ys=Tot04[s==1] # the variable of interest is Tot04 (for the units in s) calibev(Ys,Xs,total,pikls,d=1/piks,g1,with=FALSE,EPS=1e-6) } \keyword{survey} \encoding{latin1} sampling/man/disjunctive.Rd0000644000176200001440000000105210562047204015453 0ustar liggesusers\name{disjunctive} \alias{disjunctive} \title{Disjunctive combination} \description{ Transforms a categorical variable into a matrix of indicators. The values of the categorical variable are integer numbers (positive or negative). } \usage{disjunctive(strata)} \arguments{ \item{strata}{vector of integer numbers.} } \seealso{\code{ \link{balancedstratification}} } \examples{ # definition of the variable of stratification strata=c(-2,3,-2,3,4,4,4,-2,-2,3,4,0,0,0) # computation of the matrix disjunctive(strata) } \keyword{survey} sampling/man/HTstrata.Rd0000644000176200001440000000304011415614334014657 0ustar liggesusers\name{HTstrata} \alias{HTstrata} \title{The Horvitz-Thompson estimator for a stratified design} \description{Computes the Horvitz-Thompson estimator of the population total for a stratified design.} \usage{HTstrata(y,pik,strata,description=FALSE)} \arguments{ \item{y}{vector of the variable of interest; its length is equal to n, the sample size.} \item{pik}{vector of the first-order inclusion probabilities for the sampled units; its length is equal to n, the sample size.} \item{strata}{vector of size n, with elements indicating the unit stratum.} \item{description}{if TRUE, the estimator is printed for each stratum; by default, FALSE.} } \seealso{ \code{\link{HTestimator}} } \examples{ # Swiss municipalities data base data(swissmunicipalities) # the variable 'REG' has 7 categories in the population # it is used as stratification variable # computes the population stratum sizes table(swissmunicipalities$REG) # do not run # 1 2 3 4 5 6 7 # 589 913 321 171 471 186 245 # the sample stratum sizes are given by size=c(30,20,45,15,20,11,44) # the method is simple random sampling without replacement # (equal probability, without replacement) st=strata(swissmunicipalities,stratanames=c("REG"),size=c(30,20,45,15,20,11,44), method="srswor") # extracts the observed data # the order of the columns is different from the order in the initial database x=getdata(swissmunicipalities, st) # computes the HT estimator of the variable Pop020 HTstrata(x$Pop020,x$Prob,x$Stratum,description=TRUE) } \keyword{survey} sampling/man/srswor1.Rd0000644000176200001440000000150511516305113014543 0ustar liggesusers\name{srswor1} \alias{srswor1} \title{Selection-rejection method} \description{ Draws a simple random sampling without replacement of size n using the selection-rejection method. } \usage{ srswor1(n,N) } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). } \arguments{ \item{n}{sample size.} \item{N}{population size.} } \references{Fan, C.T., Muller, M.E., Rezucha, I. (1962), Development of sampling plans by using sequential (item by item) selection techniques and digital computer, \emph{Journal of the American Statistical Association}, 57, 387-402. } \seealso{\code{\link{srswor}}} \examples{ s=srswor1(3,10) #the sample is (1:10)[s==1] } \keyword{survey} sampling/man/rhg.Rd0000644000176200001440000000323211502676400013707 0ustar liggesusers\name{rhg} \alias{rhg} \title{Response homogeneity groups} \description{Computes the response homogeneity groups and the response probability for each unit in these groups. } \usage{rhg(X,selection)} \arguments{ \item{X}{sample data frame; it should contain the columns 'ID_unit' and 'status'; 'ID_unit' denotes the unit identifier (a number); 'status' is a 1/0 variable denoting the response/non-response of a unit.} \item{selection}{vector of variable names in X used to construct the groups.} } \details{ Into a response homogeneity group, the reponse probability is the same for all units. Data are missing at random within groups, conditionally on the selected sample. } \value{ The initial sample data frame and also the following components: \item{rhgroup}{the response homogeneity group for each unit.} \item{prob_response}{the response probability for each unit; for the units with status=0, this probability is 0.} } \references{ Srndal, C.-E., Swensson, B. and Wretman, J. (1992). Model Assisted Survey Sampling. \emph{Springer} } \seealso{ \code{\link{rhg_strata}}, \code{\link{calib}} } \examples{ # defines the inclusion probabilities for the population pik=c(0.2,0.7,0.8,0.5,0.4,0.4) # X is the population data frame X=cbind.data.frame(pik,c("A","B","A","A","C","B")) names(X)=c("Prob","town") # selects a sample using systematic sampling s=UPsystematic(pik) # Xs is the sample data frame Xs=getdata(X,s) # adds the status column to Xs (1 - sample respondent, 0 otherwise) Xs=cbind.data.frame(Xs,status=c(1,0,1)) # creates the response homogeneity groups using the 'town' variable rhg(Xs,selection="town") } \keyword{survey} sampling/man/strata.Rd0000644000176200001440000001055212223261003014416 0ustar liggesusers\name{strata} \alias{strata} \title{Stratified sampling} \description{Stratified sampling with equal/unequal probabilities.} \usage{strata(data, stratanames=NULL, size, method=c("srswor","srswr","poisson", "systematic"), pik,description=FALSE)} \arguments{ \item{data}{data frame or data matrix; its number of rows is N, the population size.} \item{stratanames}{vector of stratification variables.} \item{size}{vector of stratum sample sizes (in the order in which the strata are given in the input data set).} \item{method}{method to select units; the following methods are implemented: simple random sampling without replacement (srswor), simple random sampling with replacement (srswr), Poisson sampling (poisson), systematic sampling (systematic); if "method" is missing, the default method is "srswor".} \item{pik}{vector of inclusion probabilities or auxiliary information used to compute them; this argument is only used for unequal probability sampling (Poisson and systematic). If an auxiliary information is provided, the function uses the \link{inclusionprobabilities} function for computing these probabilities. } \item{description}{a message is printed if its value is TRUE; the message gives the number of selected units and the number of the units in the population. By default, the value is FALSE.} } \value{ The function produces an object, which contains the following information: \item{ID_unit}{the identifier of the selected units.} \item{Stratum}{the unit stratum.} \item{Prob}{the unit inclusion probability.} } \details{The data should be sorted in ascending order by the columns given in the stratanames argument before applying the function. Use, for example, data[order(data$state,data$region),]. } \seealso{ \code{\link{getdata}}, \code{\link{mstage}}} \examples{ ############ ## Example 1 ############ # Example from An and Watts (New SAS procedures for Analysis of Sample Survey Data) # generates artificial data (a 235X3 matrix with 3 columns: state, region, income). # the variable "state" has 2 categories ('nc' and 'sc'). # the variable "region" has 3 categories (1, 2 and 3). # the sampling frame is stratified by region within state. # the income variable is randomly generated data=rbind(matrix(rep("nc",165),165,1,byrow=TRUE),matrix(rep("sc",70),70,1,byrow=TRUE)) data=cbind.data.frame(data,c(rep(1,100), rep(2,50), rep(3,15), rep(1,30),rep(2,40)), 1000*runif(235)) names(data)=c("state","region","income") # computes the population stratum sizes table(data$region,data$state) # not run # nc sc # 1 100 30 # 2 50 40 # 3 15 0 # there are 5 cells with non-zero values # one draws 5 samples (1 sample in each stratum) # the sample stratum sizes are 10,5,10,4,6, respectively # the method is 'srswor' (equal probability, without replacement) s=strata(data,c("region","state"),size=c(10,5,10,4,6), method="srswor") # extracts the observed data getdata(data,s) # see the result using a contigency table table(s$region,s$state) ############ ## Example 2 ############ # The same data as in Example 1 # the method is 'systematic' (unequal probability, without replacement) # the selection probabilities are computed using the variable 'income' s=strata(data,c("region","state"),size=c(10,5,10,4,6), method="systematic",pik=data$income) # extracts the observed data getdata(data,s) # see the result using a contigency table table(s$region,s$state) ############ ## Example 3 ############ # Uses the 'swissmunicipalities' data as population for drawing a sample of units data(swissmunicipalities) # the variable 'REG' has 7 categories in the population # it is used as stratification variable # Computes the population stratum sizes table(swissmunicipalities$REG) # do not run # 1 2 3 4 5 6 7 # 589 913 321 171 471 186 245 # sort the data to obtain the same order of the regions in the sample data=swissmunicipalities data=data[order(data$REG),] # the sample stratum sizes are given by size=c(30,20,45,15,20,11,44) # 30 units are drawn in the first stratum, 20 in the second one, etc. # the method is simple random sampling without replacement # (equal probability, without replacement) st=strata(data,stratanames=c("REG"),size=c(30,20,45,15,20,11,44), method="srswor") # extracts the observed data getdata(data, st) # see the result using a contingency table table(st$REG) } \keyword{survey} sampling/man/Hajekestimator.Rd0000644000176200001440000000227711515601346016112 0ustar liggesusers\name{Hajekestimator} \alias{Hajekestimator} \title{The Hajek estimator} \description{Computes the Hjek estimator of the population total or population mean.} \usage{Hajekestimator(y,pik,N=NULL,type=c("total","mean"))} \arguments{ \item{y}{vector of the variable of interest; its length is equal to n, the sample size.} \item{pik}{vector of the first-order inclusion probabilities; its length is equal to n, the sample size.} \item{N}{population size; N is only used for the total estimator; for the mean estimator its value is NULL.} \item{type}{the estimator type: total or mean.} } \seealso{ \code{\link{HTestimator}} } \examples{ # Belgian municipalities data base data(belgianmunicipalities) # Computes the inclusion probabilities pik=inclusionprobabilities(belgianmunicipalities$Tot04,200) N=length(pik) n=sum(pik) # Defines the variable of interest y=belgianmunicipalities$TaxableIncome # Draws a Poisson sample of expected size 200 s=UPpoisson(pik) # Computes the Hajek estimator of the population mean Hajekestimator(y[s==1],pik[s==1],type="mean") # Computes the Hajek estimator of the population total Hajekestimator(y[s==1],pik[s==1],N=N,type="total") } \keyword{survey} sampling/man/UPtillepi2.Rd0000644000176200001440000000213711516306331015121 0ustar liggesusers\name{UPtillepi2} \alias{UPtillepi2} \title{Joint inclusion probabilties for Tille sampling} \description{ Computes the joint (second-order) inclusion probabilities for Till sampling. } \usage{ UPtillepi2(pik,eps=1e-6) } \arguments{ \item{pik}{vector of the first-order inclusion probabilities.} \item{eps}{the control value, by default equal to 1e-6.} } \value{ Returns a NxN matrix of the following form: the main diagonal contains the first-order inclusion probabilities for each unit k in the population; elements (k,l) are the joint inclusion probabilities of units k and l, with k not equal to l. N is the population size. The value \code{eps} is used to control \code{pik} (pik>eps & pik < 1-eps). } \seealso{\code{\link{UPtille}} } \references{ Till, Y. (1996), An elimination procedure of unequal probability sampling without replacement, \emph{Biometrika}, 83:238-241. } \examples{ #defines the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) pik_joint=UPtillepi2(pik) #the joint inclusion probabilities pik_joint } \keyword{survey} \encoding{latin1} sampling/man/regest_strata.Rd0000644000176200001440000000326413761417331016010 0ustar liggesusers\name{regest_strata} \alias{regest_strata} \title{The regression estimator for a stratified design} \description{Computes the regression estimator of the population total, using the design-based approach, for a stratified sampling. The same regression model is used for all strata. The underling regression model is a model without intercept.} \usage{regest_strata(formula,weights,Tx_strata,strata,pikl, sigma=rep(1,length(weights)),description=FALSE)} \arguments{ \item{formula}{the regression model formula (y~x).} \item{weights}{vector of the weights; its length is equal to n, the sample size.} \item{Tx_strata}{population total of x, the auxiliary variable.} \item{strata}{vector of stratum identificator.} \item{pikl}{the joint inclusion probabilities for the sample.} \item{sigma}{vector of positive values accounting for heteroscedasticity.} \item{description}{if TRUE, the following components are printed for each stratum: the Horvitz-Thompson estimator, the beta coefficients, their standard error, t_values, p_values, and the covariance matrix. By default, FALSE.} } \value{ The function returns the value of the regression estimator computed as the sum of the stratum estimators. } \seealso{ \code{\link{regest}} } \examples{ # generates artificial data y=rgamma(10,3) x=y+rnorm(10) Stratum=c(1,1,2,2,2,3,3,3,3,3) # population size N=200 # sample size n=10 # assume proportional allocation, nh/Nh=n/N pikl=matrix(0,n,n) for(i in 1:n) {for(j in 1:n) if(i!=j) pikl[i,j]=pikl[j,i]=n*(n-1)/(N*(N-1)) pikl[i,i]=n/N } regest_strata(formula=y~x-1,weights=rep(N/n,n),Tx_strata=c(50,30,40), strata=Stratum,pikl,description=TRUE) } \keyword{survey} sampling/man/balancedcluster.Rd0000644000176200001440000000337611516306470016275 0ustar liggesusers\name{balancedcluster} \alias{balancedcluster} \title{Balanced cluster} \description{ Selects a balanced cluster sample. } \usage{balancedcluster(X,m,cluster,selection=1,comment=TRUE,method=1)} \arguments{ \item{X}{matrix of auxiliary variables on which the sample must be balanced.} \item{m}{number of clusters to be selected.} \item{cluster}{vector of integers that defines the clusters.} \item{selection}{1, selection of the clusters with probabilities proportional to size,\cr 2, selection of the clusters with equal probabilities.} \item{comment}{a comment is written during the execution if \code{comment} is \code{TRUE}.} \item{method}{the used method in the function \code{samplecube}.} } \value{Returns a matrix containing the vector of inclusion probabilities and the selected sample.} \seealso{ \code{\link{samplecube}}, \code{\link{fastflightcube}}, \code{\link{landingcube}} } \examples{ ############ ## Example 1 ############ # definition of the clusters; there are 15 units in 3 clusters cluster=c(1,1,1,1,1,2,2,2,2,2,3,3,3,3,3) # matrix of balancing variables X=cbind(c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)) # selection of 2 clusters s=balancedcluster(X,2,cluster,2,TRUE) # the sample of clusters with the inclusion probabilities of the clusters s # the selected clusters unique(cluster[s[,1]==1]) # the selected units (1:length(cluster))[s[,1]==1] # with the probabilities s[s[,1]==1,2] ############ ## Example 2 ############ data(MU284) X=cbind(MU284$P75,MU284$CS82,MU284$SS82,MU284$S82,MU284$ME84) s=balancedcluster(X,10,MU284$CL,1,TRUE) cluster=MU284$CL # the selected clusters unique(cluster[s[,1]==1]) # the selected units (1:length(cluster))[s[,1]==1] # with the probabilities s[s[,1]==1,2] } \keyword{survey} sampling/man/rmodel.Rd0000644000176200001440000000405711415616266014426 0ustar liggesusers\name{rmodel} \alias{rmodel} \title{Response probability using logistic regression} \description{Computes the response probabilities using logistic regression for non-response adjustment. For stratified sampling, the same logistic model is used for all strata.} \usage{rmodel(formula,weights,X)} \arguments{ \item{formula}{the regression model formula (y~x).} \item{weights}{vector of the weights; its length is equal to n, the sample size.} \item{X}{the sample data frame.} } \value{The function returns the sample data frame with a new column 'prob_resp', which contains the response probabilities.} \seealso{ \code{\link{rhg}} } \examples{ # Example from An and Watts (New SAS procedures for Analysis of Sample Survey Data) # generates artificial data (a 235X3 matrix with 3 columns: state, region, income). # the variable "state" has 2 categories ('nc' and 'sc'). # the variable "region" has 3 categories (1, 2 and 3). # the sampling frame is stratified by region within state. # the income variable is randomly generated data=rbind(matrix(rep("nc",165),165,1,byrow=TRUE),matrix(rep("sc",70),70,1,byrow=TRUE)) data=cbind.data.frame(data,c(rep(1,100), rep(2,50), rep(3,15), rep(1,30),rep(2,40)), 1000*runif(235)) names(data)=c("state","region","income") # computes the population stratum sizes table(data$region,data$state) # not run # nc sc # 1 100 30 # 2 50 40 # 3 15 0 # there are 5 cells with non-zero values; one draws 5 samples (1 sample in each stratum) # the sample stratum sizes are 10,5,10,4,6, respectively # the method is 'srswor' (equal probability, without replacement) s=strata(data,c("region","state"),size=c(10,5,10,4,6), method="srswor") # extracts the observed data x=getdata(data,s) # generates randomly the 'status' column (1 - respondent, 0 - nonrespondent) status=round(runif(nrow(x))) x=cbind(x,status) # computes the response probabilities rmodel(x$status~x$income+x$Stratum,weights=1/x$Prob,x) # the same example without stratification rmodel(x$status~x$income,weights=1/x$Prob,x) } \keyword{survey} sampling/man/UPopips.Rd0000644000176200001440000000177511516306153014540 0ustar liggesusers\name{UPopips} \alias{UPopips} \title{Order pips sampling} \description{ Implements order \eqn{\pi ps} sampling (unequal probabilities, without replacement, fixed sample size). } \usage{ UPopips(lambda,type=c("pareto","uniform","exponential")) } \arguments{ \item{lambda}{vector of working inclusion probabilities or target ones.} \item{type}{the type of order sampling (pareto, uniform, exponential).} } \value{ Returns a vector of selected units of size n, the sample size. } \seealso{\code{\link{inclusionprobabilities}} } \references{ Rosn, B. (1997), Asymptotic theory for order sampling, \emph{Journal of Statistical Planning and Inference}, 62:135-158.\cr Rosn, B. (1997), On sampling with probability proportional to size, \emph{Journal of Statistical Planning and Inference}, 62:159-191.\cr } \examples{ #define the working inclusion probabilities lambda=c(0.2,0.7,0.8,0.5,0.4,0.4) #draw a Pareto sample s=UPopips(lambda, type="pareto") #the sample is s } \keyword{survey} sampling/man/HTestimator.Rd0000644000176200001440000000147512235721745015410 0ustar liggesusers\name{HTestimator} \alias{HTestimator} \title{The Horvitz-Thompson estimator} \description{Computes the Horvitz-Thompson estimator of the population total.} \usage{HTestimator(y,pik)} \arguments{ \item{y}{vector of the variable of interest; its length is equal to n, the sample size.} \item{pik}{vector of the first-order inclusion probabilities; its length is equal to n, the sample size.} } \seealso{ \code{\link{UPtille}} } \examples{ data(belgianmunicipalities) attach(belgianmunicipalities) # Computes the inclusion probabilities pik=inclusionprobabilities(Tot04,200) N=length(pik) n=sum(pik) # Defines the variable of interest y=TaxableIncome # Draws a Poisson sample of expected size 200 s=UPpoisson(pik) # Computes the Horvitz-Thompson estimator HTestimator(y[s==1],pik[s==1]) } \keyword{survey}sampling/man/inclusionprobastrata.Rd0000644000176200001440000000121611515601462017375 0ustar liggesusers\name{inclusionprobastrata} \alias{inclusionprobastrata} \title{Inclusion probabilities for a stratified design} \description{Computes the inclusion probabilities for a stratified design. The inclusion probabilities are equal in each stratum.} \usage{inclusionprobastrata(strata,nh)} \arguments{ \item{strata}{vector that defines the strata.} \item{nh}{vector with the number of units to be selected in each stratum.} } \seealso{ \code{\link{balancedstratification}} } \examples{ # the strata strata=c(1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3) # sample size in each stratum nh=c(2,3,3) inclusionprobastrata(strata,nh) } \keyword{survey} sampling/man/UPpoisson.Rd0000644000176200001440000000213111516306203015057 0ustar liggesusers\name{UPpoisson} \alias{UPpoisson} \title{Poisson sampling} \description{ Draws a Poisson sample using a prescribed vector of first-order inclusion probabilities (unequal probabilities, without replacement, random sample size). } \usage{UPpoisson(pik)} \arguments{ \item{pik}{vector of the first-order inclusion probabilities.} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). The value 'eps' is used to control pik (pik>eps & pik < 1-eps). } \seealso{ \code{\link{inclusionprobabilities}} } \examples{ ############ ## Example 1 ############ # definition of pik pik=c(1/3,1/3,1/3) # selects a sample s=UPpoisson(pik) #the sample is (1:length(pik))[s==1] ############ ## Example 2 ############ data(belgianmunicipalities) Tot=belgianmunicipalities$Tot04 name=belgianmunicipalities$Commune n=200 pik=inclusionprobabilities(Tot,n) # select a sample s=UPpoisson(pik) #the sample is getdata(name,s) } \keyword{survey} sampling/DESCRIPTION0000644000176200001440000000115613777557156013624 0ustar liggesusersPackage: sampling Version: 2.9 Date: 2021-01-12 Title: Survey Sampling Author: Yves Till , Alina Matei Maintainer: Alina Matei Description: Functions to draw random samples using different sampling schemes are available. Functions are also provided to obtain (generalized) calibration weights, different estimators, as well some variance estimators. Imports: MASS, lpSolve License: GPL (>= 2) Encoding: latin1 RoxygenNote: 7.1.1 NeedsCompilation: yes Packaged: 2021-01-12 13:01:24 UTC; mateia Repository: CRAN Date/Publication: 2021-01-13 11:50:05 UTC sampling/build/0000755000176200001440000000000013777316644013205 5ustar liggesuserssampling/build/vignette.rds0000644000176200001440000000050713777316644015546 0ustar liggesusersQO0 C"jB}Մ} BH|!o`lO~qla3$koc1Vg z`A׆}-{ '!yڈT:|+_LGIcY\@, TUf8UI&lbAs] b*9qj"J. .D6 K;$)ԩ$Y:G>sʼ>yN7BPّznCOԮtbc b/L'?pךw)w[l^Rra!˲ߎ1hȋ Kem ` // for NULL #include /* FIXME: Check these declarations against the C/Fortran source code. */ /* .C calls */ extern void str(void *, void *, void *, void *); static const R_CMethodDef CEntries[] = { {"str", (DL_FUNC) &str, 4}, {NULL, NULL, 0} }; void R_init_sampling(DllInfo *dll) { R_registerRoutines(dll, CEntries, NULL, NULL, NULL); R_useDynamicSymbols(dll, FALSE); } sampling/src/str.c0000644000176200001440000000021010712632106013616 0ustar liggesusersvoid str(double *st, int *h, int *n, double *s) { int i; for(i = 0; i < *n; i++) {s[i]=0; if(st[i]==*h) s[i] = 1; } } sampling/vignettes/0000755000176200001440000000000013777316644014116 5ustar liggesuserssampling/vignettes/calibration.Snw0000644000176200001440000003676713762142022017076 0ustar liggesusers\documentclass[a4paper]{article} \usepackage{pdfpages} %\VignetteIndexEntry{calibration and adjustment for nonresponse} %\VignettePackage{sampling} \newcommand{\sampling}{{\tt sampling}} \newcommand{\R}{{\tt R}} \setlength{\parindent}{0in} \setlength{\parskip}{.1in} \setlength{\textwidth}{140mm} \setlength{\oddsidemargin}{10mm} \title{Calibration and generalized calibration} \author{} \usepackage{Sweave} \usepackage[latin1]{inputenc} \usepackage{amsmath} \begin{document} \maketitle <>= library(sampling) ps.options(pointsize=12) options(width=60) @ \section{Example 1} This is an example of using the \verb@calib@ function for calibration and nonresponse adjustment (with response homogeneity groups). @ \noindent We create the following population data frame (the population size is $N=250$): \begin{itemize} \item there are four variables: \verb@state@, \verb@region@, \verb@income@ and \verb@sex@; \item the \verb@state@ variable has 2 categories: 'A' and 'B'; the \verb@region@ variable has 3 categories: 1, 2, 3 (regions within states); \item the \verb@income@ and \verb@sex@ variables are randomly generated using the uniform distribution. \end{itemize} <>= data = rbind(matrix(rep("A", 150), 150, 1, byrow = TRUE), matrix(rep("B", 100), 100, 1, byrow = TRUE)) data = cbind.data.frame(data, c(rep(1, 60), rep(2,50), rep(3, 60), rep(1, 40), rep(2, 40)), 1000 * runif(250)) sex = runif(nrow(data)) for (i in 1:length(sex)) if (sex[i] < 0.3) sex[i] = 1 else sex[i] = 2 data = cbind.data.frame(data, sex) names(data) = c("state", "region", "income", "sex") summary(data) @ \noindent We compute the population stratum sizes: <>= table(data$state) @ We select a stratified sample. The \verb@state@ variable is used as a stratification variable. The sample stratum sizes are 25 and 20, respectively. The method is 'srswor' (equal probability, without replacement). <>= s=strata(data,c("state"),size=c(25,20), method="srswor") @ We obtain the observed data: <>= s=getdata(data,s) @ The \verb@status@ variable is used in the \verb@rhg_strata@ function. The \verb@status@ column is added to $s$ (1 - sample respondent, 0 otherwise); it is randomly generated using the uniform distribution U(0,1). The response probability for all units is 0.3. <>= status=runif(nrow(s)) for(i in 1:length(status)) if(status[i]<0.3) status[i]=0 else status[i]=1 s=cbind.data.frame(s,status) @ We compute the response homeogeneity groups using the \verb@region@ variable: <>= s=rhg_strata(s,selection="region") @ We select only the sample respondents: <>= sr=s[s$status==1,] @ We create the population data frame of sex and region indicators: <>= X=cbind(disjunctive(data$sex),disjunctive(data$region)) @ We compute the population totals for each sex and region: <>= total=c(t(rep(1,nrow(data)))%*%X) @ The first method consists in calibrating with all strata. The respondent data frame of \verb@sex@ and \verb@region@ indicators is created. The initial weights using the inclusion prob. and the response probabilities are computed. <>= Xs = X[sr$ID_unit,] d = 1/(sr$Prob * sr$prob_resp) summary(d) @ We compute the g-weights using the linear method: <>= g = calib(Xs, d, total, method = "linear") summary(g) @ The final weights are: <>= w=d*g summary(w) @ We check the calibration: <>= checkcalibration(Xs, d, total, g) @ The second method consists in calibrating in each stratum. The respondent data frame of \verb@sex@ and \verb@region@ indicators is created in each stratum. The initial weights using the inclusion prob. and response probabilities are computed in each stratum. <>= cat("stratum 1\n") data1=data[data$state=='A',] X1=X[data$state=='A',] total1=c(t(rep(1, nrow(data1))) %*% X1) sr1=sr[sr$Stratum==1,] Xs1=X[sr1$ID_unit,] d1 = 1/(sr1$Prob * sr1$prob_resp) g1=calib(Xs1, d1, total1, method = "linear") checkcalibration(Xs1, d1, total1, g1) cat("stratum 2\n") data2=data[data$state=='B',] X2=X[data$state=='B',] total2=c(t(rep(1, nrow(data2))) %*% X2) sr2=sr[sr$Stratum==2,] Xs2=X[sr2$ID_unit,] d2 = 1/(sr2$Prob * sr2$prob_resp) g2=calib(Xs2, d2, total2, method = "linear") checkcalibration(Xs2, d2, total2, g2) @ <>= <> <> <> <> <> <> <> <> <> <> <> <> <> <> sampling.newpage() @ \section{Example 2} This is an example of: \begin{itemize} \item variance estimation of the calibration estimator (using the \verb@calibev@ and \verb@varest@ functions), \item variance estimator of the Horvitz-Thompson estimator (using the \verb@varest@ and \verb@varHT@ functions). \end{itemize} We generate an artificial population and use Till\'e sampling. The population size is 100, and the sample size is 20. There are three auxiliary variables (two categorical and one continuous; the matrix $X$). The vector $Z=(150, 151, \dots, 249)'$ is used to compute the first-order inclusion probabilities. The variable of interest $Y$ is computed using the model $Y_j=5*Z_j*(\varepsilon_j+\sum_{i=1}^{100} X_{ij}), \varepsilon_j\sim N(0,1/3), iid, j=1,\dots, 100.$ The calibration estimator uses the linear method. Simulations are conducted to estimate the MSE of the two variance estimators of the calibration estimator. Since the linear method is used in calibration, the calibration estimator corresponds to the generalized regression estimator. For the latter an approximate variance can be computed on the population level and used in the bias estimation of the variance estimators. For the Horvitz-Thompson estimator, the variance can be computed on the population level and compared with the simulations' result. Use 10000 simulation runs to obtain accurate results (for time consuming reason, in the following program, the number of runs is only 10). <>= X=cbind(c(rep(1,50),rep(0,50)),c(rep(0,50),rep(1,50)),1:100) # vector of population totals total=apply(X,2,"sum") Z=150:249 # the variable of interest Y=5*Z*(rnorm(100,0,sqrt(1/3))+apply(X,1,"sum")) # inclusion probabilities pik=inclusionprobabilities(Z,20) # joint inclusion probabilities pikl=UPtillepi2(pik) # number of runs; let nsim=10000 for an accurate result nsim=10 c1=c2=c3=c4=c5=c6=numeric(nsim) for(i in 1:nsim) { # draws a sample s=UPtille(pik) # computes the inclusion prob. for the sample piks=pik[s==1] # the sample matrix of auxiliary information Xs=X[s==1,] # computes the g-weights g=calib(Xs,d=1/piks,total,method="linear") # computes the variable of interest in the sample Ys=Y[s==1] # computes the joint inclusion prob. for the sample pikls=pikl[s==1,s==1] # computes the calibration estimator and its variance estimation cc=calibev(Ys,Xs,total,pikls,d=1/piks,g,with=FALSE,EPS=1e-6) c1[i]=cc$calest c2[i]=cc$evar # computes the variance estimator of the calibration estimator (second method) c3[i]=varest(Ys,Xs,pik=piks,w=g/piks) # computes the variance estimator of the HT estimator using varest() c4[i]=varest(Ys,pik=piks) # computes the variance estimator of the HT estimator using varHT() c5[i]=varHT(Ys,pikls,2) # computes the Horvitz-Thompson estimator c6[i]=HTestimator(Ys,piks) } cat("the population total:",sum(Y),"\n") cat("the calibration estimator under simulations:", mean(c1),"\n") N=length(Y) delta=matrix(0,N,N) for(k in 1:(N-1)) for(l in (k+1):N) delta[k,l]=delta[l,k]=pikl[k,l]-pik[k]*pik[l] diag(delta)=pik*(1-pik) var_HT=0 var_asym=0 e=lm(Y~X)$resid for(k in 1:N) for(l in 1:N) {var_HT=var_HT+Y[k]*Y[l]*delta[k,l]/(pik[k]*pik[l]) var_asym=var_asym+e[k]*e[l]*delta[k,l]/(pik[k]*pik[l])} cat("the approximate variance of the calibration estimator:",var_asym,"\n") cat("first variance estimator of the calibration est. using calibev function:\n") cat("MSE of the first variance estimator:", var(c2)+(mean(c2)-var_asym)^2,"\n") cat("second variance estimator of the calibration est. using varest function:\n") cat("MSE of the second variance estimator:", var(c3)+(mean(c3)-var_asym)^2,"\n") cat("the Horvitz-Thompson estimator under simulations:", mean(c6),"\n") cat("the variance of the HT estimator:", var_HT, "\n") cat("the variance estimator of the HT estimator under simulations:", mean(c4),"\n") cat("MSE of the variance estimator 1 of HT estimator:", var(c4)+(mean(c4)-var_HT)^2,"\n") cat("MSE of the variance estimator 2 of HT estimator:", var(c5)+(mean(c5)-var_HT)^2,"\n") @ <>= <> sampling.newpage() @ \section{Example 3} This is an example of generalized calibration used to handle unit nonresponse with different forms of response probabilities. Consider the population $U$, the sample $s$ and the set of respondents $r$ with $r\subseteq s \subseteq U.$ The response mechanism is given by the distribution $q(r|s)$ such that for every fixed $s$ we have $$q(r|s)\geq 0, \mbox{ for all } r\in \mathcal{R}_s \mbox{ and } \sum_{s\in {\mathcal R}_s} q(r|s)=1,$$ where ${\mathcal R}_s=\{r | r \subseteq s\}.$ The variable of interest $y_k$ is known only for $k\in r.$ Under unit nonresponse we define the response indicator $R_k=1$ if unit $k\in r$ and 0 otherwise and the response probabilities $p_k=Pr(R_k=1| k\in s).$ It is assumed that $R_k$ are independent Bernoulli variables with expected value equal to $p_k.$ We assume that the units respond independently of each other and of $s$ and so $$q(r|s)=\prod_{k\in r} p_k \prod_{k \in \bar{r}} (1-p_k).$$ The nonresponse model can be rewritten as $$q(r|s, \boldsymbol{\gamma})=\prod_{k\in r} F_k^{-1}(\boldsymbol{\gamma}) \prod_{k \in \bar{r}} (1-F^{-1}_k(\boldsymbol{\gamma})).$$ In calibration method it is assumed that $$\sum_{k\in r} \mathbf{x}_kd_kF_k(\boldsymbol{\gamma})=\sum_{k\in r} \mathbf{x}_kd_kF(\boldsymbol{\gamma}^T\mathbf{x}_k)=\sum_{k\in U} \mathbf{x}_k,$$ where $F_k(\boldsymbol{\gamma})=F(\boldsymbol{\gamma}^T\mathbf{x}_k), p_k=F_k(\boldsymbol{\gamma})^{-1},$ and $d_k$ are the initial weigths. In generalized calibration a different equation is used $$\sum_{k\in r} \mathbf{x}_kd_kF(\boldsymbol{\gamma}^T\mathbf{z}_k)=\sum_{k\in U} \mathbf{x}_k,$$ where $\mathbf{z}_k$ is not necessary equal to $\mathbf{x}_k,$ but $\mathbf{z}_k$ and $\mathbf{x}_k$ have to be highly correlated. $\mathbf{z}_k$ should be known only for $k\in r.$ The components of $\mathbf{z}_k$ that are not also components of $\mathbf{x}_k$ are often known as \emph{instrumental variables}. Let $w_k$ be the final weights (obtained after applying generalized calibration). It is possible to assume different forms of response probabilities: \begin{itemize} \item Linear weight adjustment (it can be implemented by using the argument \texttt{method="linear"} in gencalib() function or \texttt{method="truncated"} if bounds are allowed): $p_k=1/(1+ {\boldsymbol\gamma}^T\mathbf{z}_k)$ and $w_k=d_k(1+\mathbf{h}^T\mathbf{z}_k),$ where $\mathbf{h}$ is a consistent estimate of ${\boldsymbol\gamma}.$ \item Raking weight adjustment (it can be implemented by using the argument \texttt{method="raking"} in gencalib()): $p_k=1/\exp(\boldsymbol{\gamma}^T\mathbf{z}_k)$ and $w_k=d_k \exp(\mathbf{h}^T\mathbf{z}_k).$ \item Logistic weight adjustment (it can be implemented by using the argument \texttt{method="raking"} in gencalib()): $p_k=1/(1+\exp(\boldsymbol{\gamma}^T\mathbf{z}_k)), w_k=d_k (1+\exp(\mathbf{h}^T\mathbf{z}_k)),$ but we calibrate on $\sum_{k\in U} \mathbf{x}_k-\sum_{k\in r} \mathbf{x}_k d_k$ instead of $\sum_{k\in U} \mathbf{x}_k.$\item Generalized exponential weight adjustment (Folsom and Singh, 2000; it can be implemented by using the argument \texttt{method="logit"} in gencalib()): $$p_k=1/F(\boldsymbol{\gamma}^T\mathbf{z}_k), w_k=d_kF(\mathbf{h}^T\mathbf{z}_k),$$ $$F(\mathbf{h}^T\mathbf{z}_k)=\frac{L(U-C)+U(C-L)\exp(A\mathbf{h}^T\mathbf{z}_k)}{(U-C)+(C-L)\exp(A\mathbf{h}^T\mathbf{z}_k)}\in (L, U),$$ where $A=(U-L)/((C-L)(U-C))$ and $L\geq 0,1C>L,$ ($C=1$ in the paper of Deville and Sarndal, 1992). The g-weights are centered around of $C.$ For $L=1, C=2$ and $U=\infty, F(\mathbf{h}^T\mathbf{z}_k)$ approaches $1+\exp(\mathbf{h}^T\mathbf{z}_k)$ and for $C=1, L=0, U=\infty,$ $\exp(\mathbf{h}^T\mathbf{z}_k).$ \end{itemize} We exemplify the last form of response probabilities (generalized exponential weight adjustment) using artificial data. We generate a population of size $N=400$ and consider the auxiliary information $X$ following a Gamma distribution with parameters 3 and 4. The instrumental variable $Z$ is generated using the model $Z=2X+\varepsilon,$ where $\varepsilon\sim U(0,1).$ The variable of interest is $Y$ generated using the model $Y=3X+\varepsilon_1,$ where $\varepsilon_1\sim N(0,1).$ We consider here that the nonresponse is not missing at random and the response probabilities $p$ depend on the variable of interest $y$ which may be missing. We draw a simple random sampling without replecement of size $n=100$ and generate the set of respondents $r$ using Poisson sampling with the probabilties $p.$ The bounds are fixed to 1 and 5, and the constant $C=1.5.$ Three estimators are computed: \begin{itemize} \item the generalized calibration estimator using $Z$ as instrumental variable, \item the generalized calibration estimator using $Y$ as instrumental variable, \item the generalized calibration estimator using $X$ as instrumental variable, which is the same with the calibration estimator, but the g-weights are centered around $C$. \end{itemize} The convergence of the method is not guaranteed due to the bounds. Thus $g1, g2, g3$ can be null. If it the case, repeat the code (considering another $s$ and $r$). <>= N=400 n=100 X=rgamma(N,3,4) total=sum(X) Z=2*X+runif(N) Y=3*X+rnorm(N) print(cor(X,Y)) print(cor(X,Z)) L=1 U=5 C=1.5 A=(U-L)/((C-L)*(U-C)) p=((U-C)+(C-L)*exp(A*Y*0.3))/(L*(U-C)+U*(C-L)*exp(A*Y*0.3)) summary(p) bounds=c(L,U) s=srswor(n,N) r=numeric(n) for(j in 1:n) if(runif(1)>= <> sampling.newpage() @ \end{document} sampling/vignettes/UPexamples.Snw0000644000176200001440000001055313767204550016665 0ustar liggesusers\documentclass[a4paper]{article} %\VignetteIndexEntry{UP - unequal probability sampling designs} %\VignettePackage{sampling} \newcommand{\sampling}{{\tt sampling}} \newcommand{\R}{{\tt R}} \setlength{\parindent}{0in} \setlength{\parskip}{.1in} \setlength{\textwidth}{140mm} \setlength{\oddsidemargin}{10mm} \title{Unequal probability sampling designs} \author{} \usepackage{Sweave} \usepackage[latin1]{inputenc} \usepackage{amsmath} \begin{document} \maketitle <>= library(sampling) ps.options(pointsize=12) options(width=60) @ 1) Some examples of using maximum entropy sampling design and related functions: a) First example @ Sample of Belgian municipalities, sample size 50 <>= data(belgianmunicipalities) attach(belgianmunicipalities) n=50 @ Inclusion probabilties proportional to the 'averageincome' variable <>= pik=inclusionprobabilities(averageincome,n) @ Draw a sample <>= s=UPmaxentropy(pik) @ The sample is <>= as.character(Commune[s==1]) @ Joint inclusion probabilities <>= pi2=UPmaxentropypi2(pik) @ Check the result <>= rowSums(pi2)/pik/n detach(belgianmunicipalities) @ b) Second example @ Selection of samples from Belgian municipalities data set, sample size 50. Once matrix q is computed, a sample is quickly selected. Simulations can be run to compare the results. <>= data(belgianmunicipalities) attach(belgianmunicipalities) pik=inclusionprobabilities(averageincome,50) pik=pik[pik!=1] n=sum(pik) pikt=UPMEpiktildefrompik(pik) w=pikt/(1-pikt) q=UPMEqfromw(w,n) @ Draw a sample using the q matrix <>= UPMEsfromq(q) @ Simulations to check the sample selection; the difference between pik and the computed inclusion prob. tt is almost 0. <>= sim=10000 N=length(pik) tt=rep(0,N) for(i in 1:sim) tt = tt+UPMEsfromq(q) tt=tt/sim max(abs(tt-pik)) detach(belgianmunicipalities) @ 2) This is an example of unequal probability (UP) sampling functions: selection of samples using the Belgian municipalities data set, with equal or unequal probabilities, and study of the Horvitz-Thompson estimator accuracy using boxplots. The following sampling schemes are used: Poisson, random systematic, random pivotal, Till\'e, Midzuno, systematic, pivotal, and simple random sampling without replacement. Monte Carlo simulations are used to study the accuracy of the Horvitz-Thompson estimator of a population total. The aim of this example is to demonstrate the effect of the auxiliary information incorporation in the sampling design. We use: \begin{itemize} \item some $\pi$ ps sampling designs with Horvitz-Thompson estimation, using in the sampling design the information on size measures of population units; \item simple random sampling without replacement with Horvitz-Thompson estimation, where no auxiliary information is used. \end{itemize} <>= b=data(belgianmunicipalities) pik=inclusionprobabilities(belgianmunicipalities$Tot04,200) N=length(pik) n=sum(pik) @ Number of simulations (for an accurate result, increase this value to 10000): <>= sim=10 ss=array(0,c(sim,8)) @ Defines the variable of interest: <>= y=belgianmunicipalities$TaxableIncome @ Simulation and computation of the Horvitz-Thompson estimator: <>= ht=numeric(8) for(i in 1:sim) { cat("Step ",i,"\n") s=UPpoisson(pik) ht[1]=HTestimator(y[s==1],pik[s==1]) s=UPrandomsystematic(pik) ht[2]=HTestimator(y[s==1],pik[s==1]) s=UPrandompivotal(pik) ht[3]=HTestimator(y[s==1],pik[s==1]) s=UPtille(pik) ht[4]=HTestimator(y[s==1],pik[s==1]) s=UPmidzuno(pik) ht[5]=HTestimator(y[s==1],pik[s==1]) s=UPsystematic(pik) ht[6]=HTestimator(y[s==1],pik[s==1]) s=UPpivotal(pik) ht[7]=HTestimator(y[s==1],pik[s==1]) s=srswor(n,N) ht[8]=HTestimator(y[s==1],rep(n/N,n)) ss[i,]=ht } @ Boxplots of the estimators: <>= colnames(ss) <- c("poisson","rsyst","rpivotal","tille","midzuno","syst","pivotal","srswor") boxplot(data.frame(ss), las=3) <>= <> <> <> <> <> sampling.newpage() @ \end{document} sampling/vignettes/HT_Hajek_estimators.Snw0000644000176200001440000001167313214675503020472 0ustar liggesusers\documentclass[a4paper]{article} %\VignetteIndexEntry{Horvitz-Thompson estimator and Hajek estimator} %\VignettePackage{sampling} \newcommand{\sampling}{{\tt sampling}} \newcommand{\R}{{\tt R}} \setlength{\parindent}{0in} \setlength{\parskip}{.1in} \setlength{\textwidth}{140mm} \setlength{\oddsidemargin}{10mm} \title{Comparing the Horvitz-Thompson estimator and Hajek estimator} \author{} \usepackage{Sweave} \usepackage[latin1]{inputenc} \usepackage{amsmath} \begin{document} \maketitle <>= library(sampling) ps.options(pointsize=12) options(width=60) @ Consider a finite population with labels $U=\{1, 2, \dots, N\}.$ Suppose $y_k, k\in U$ are values of the variable of interest in the population. We wish to estimate the total $\sum_{k=1}^N y_k$ based on a sample $s$ taken from the population $U.$ Assume that the sample is taken according to a sampling scheme having inclusion probabilities $\pi_k= Pr(k\in s).$ When the $\pi_k$ is proportional to a positive quantity $x_k$ available over $U,$ and $s$ has a predetermined sample size $n,$ then $$\pi_k=\frac{nx_k}{\sum_{i=1}^N x_i},$$ and the sampling scheme is said to be probability proportional to size ($\pi ps$). Under this scheme, the H\'ajek estimator of the population total is defined by $$\hat{y}_{Hajek}=N\frac{\sum_{k\in s} y_k/\pi_k}{\sum_{k\in s} 1/\pi_k}.$$ S$\ddot{a}$rndal, Swenson, and Wretman (1992, p. 182) give several cases for regarding the H\'ajek as `usually the better estimator' comparing to the Horvitz-Thompson estimator $$\hat{y}_{HT}=\sum_{k\in s} y_k/\pi_k:$$ \begin{itemize} \item[a)] the $y_k-\bar{y}_U$ tend to be small, \item[b)] sample size is not fixed, \item[c)] $\pi_k$ are weakly or negatively correlated with the $y_k$. \end{itemize} Monte Carlo simulation is used here to compare the accuracy of both estimators for a sample size (or expected value of the sample size) equal to 20. Four cases are considered: \begin{itemize} \item[Case 1.] $y_k$ is constant for $k=1, \dots, N$; this case corresponds to the case a) above; \item[Case 2.] Poisson sampling is used to draw a sample $s$; this case corresponds to the case b) above; \item[Case 3.] $y_k$ are generated using the following model: $x_k=k, \pi_k=nx_k/\sum_{i=1}^N x_i, y_k=1/\pi_k;$ this case corresponds to the case c) above; \item[Case 4.] $y_k$ are generated using the following model: $x_k=k, y_k=5(x_k+\epsilon_k),\epsilon_k\sim N(0, 1/3);$ in this case the Horvitz-Thompson estimator should perform better than the H\'ajek estimator. \end{itemize} Till\'e sampling is used in Cases 1, 3 and 4. Poisson sampling is used in Case 2. The \verb@belgianmunicipalities@ dataset is used in Cases 1 and 2 with $x_k=Tot04_k.$ In Case 2, the variable of interest is TaxableIncome. The mean square error (MSE) is computed using simulations for each case and estimator. The H\'ajek estimator should perform better than the Horvitz-Thompson estimator in Cases 1, 2 and 3. <>= data(belgianmunicipalities) attach(belgianmunicipalities) # sample size n=20 pik=inclusionprobabilities(Tot04,n) N=length(pik) @ Number of runs (for an accurate result, increase this value to 10000): <>= sim=10 ss=ss1=array(0,c(sim,4)) @ Defines the variables of interest: <>= cat("Case 1\n") y1=rep(3,N) cat("Case 2\n") y2=TaxableIncome cat("Case 3\n") x=1:N pik3=inclusionprobabilities(x,n) y3=1/pik3 cat("Case 4\n") epsilon=rnorm(N,0,sqrt(1/3)) pik4=pik3 y4=5*(x+epsilon) @ Simulation and computation of the Horvitz-Thompson estimator and H\'ajek estimator: <>= ht=numeric(4) hajek=numeric(4) for(i in 1:sim) { cat("Simulation ",i,"\n") cat("Case 1\n") s=UPtille(pik) ht[1]=HTestimator(y1[s==1],pik[s==1]) hajek[1]=Hajekestimator(y1[s==1],pik[s==1],N,type="total") cat("Case 2\n") s1=UPpoisson(pik) ht[2]=HTestimator(y2[s1==1],pik[s1==1]) hajek[2]=Hajekestimator(y2[s1==1],pik[s1==1],N,type="total") cat("Case 3\n") ht[3]=HTestimator(y3[s==1],pik3[s==1]) hajek[3]=Hajekestimator(y3[s==1],pik3[s==1],N,type="total") cat("Case 4\n") ht[4]=HTestimator(y4[s==1],pik4[s==1]) hajek[4]=Hajekestimator(y4[s==1],pik4[s==1],N,type="total") ss[i,]=ht ss1[i,]=hajek } @ Estimation of the MSE and the ratio $\frac{MSE_{HT}}{MSE_{Hajek}}:$ <>= #true values tv=c(sum(y1),sum(y2),sum(y3),sum(y4)) for(i in 1:4) { cat("Case ",i,"\n") cat("The mean of the Horvitz-Thompson estimators:",mean(ss[,i])," and the true value:",tv[i],"\n") MSE1=var(ss[,i])+(mean(ss[,i])-tv[i])^2 cat("MSE Horvitz-Thompson estimator:",MSE1,"\n") cat("The mean of the Hajek estimators:",mean(ss1[,i])," and the true value:",tv[i],"\n") MSE2=var(ss1[,i])+(mean(ss1[,i])-tv[i])^2 cat("MSE Hajek estimator:",MSE2,"\n") cat("Ratio of the two MSE:", MSE1/MSE2,"\n") } <>= <> <> <> <> <> sampling.newpage() @ \end{document} sampling/R/0000755000176200001440000000000013767174335012305 5ustar liggesuserssampling/R/UPrandompivotal.R0000644000176200001440000000031513214454617015542 0ustar liggesusers"UPrandompivotal" <- function(pik,eps=1e-6) { if(any(is.na(pik))) stop("there are missing values in the pik vector") N=length(pik) v=sample.int(N,N) s=numeric(N) s[v]=UPpivotal(pik[v],eps) s } sampling/R/regest_strata.r0000644000176200001440000000241211022253752015315 0ustar liggesusersregest_strata<-function(formula,weights,Tx_strata,strata,pikl,sigma=rep(1,length(weights)),description=FALSE) { cl <- match.call() mf <- match.call(expand.dots = FALSE) m <- match(c("formula", "weights"), names(mf), 0) mf <- mf[c(1, m)] mf$drop.unused.levels <- TRUE mf[[1]] <- as.name("model.frame") mf <- eval(mf, parent.frame()) mt <- attr(mf, "terms") y <- model.response(mf, "numeric") w <- as.vector(model.weights(mf)) x <- model.matrix(mt, mf, contrasts) str <- function(st, h, n) .C("str", as.double(st), as.integer(h), as.integer(n), s = double(n), PACKAGE = "sampling")$s sample.size = length(y) h = unique(strata) s1 = 0 for (i in 1:length(h)) { s=str(strata, h[i], sample.size) ys=y[s==1] xs=x[s==1,] r=regest(ys~xs-1,Tx=Tx_strata[h[i]],weights=weights[s==1],pikl=pikl[s==1,s==1],n=length(s[s==1]),sigma[s==1]) est=r$regest s1 = s1 + est if(description) {cat("Stratum ",h[i],", the regression estimator is:",est,"\n") cat("Number of units:",sum(s),"\n") cat("Beta coefficient(s):", r$coefficients,"\n") cat("Std. error:", r$std_error,"\n") cat("t-value:", r$t_value, "\n") cat("p_value:",r$p_value,"\n") cat("cov_matrix:\n") print(r$cov_matrix) } } if(description) cat("The regression estimator is:\n") s1 } sampling/R/UPsampford.R0000644000176200001440000000117012056075702014473 0ustar liggesusersUPsampford<-function(pik,eps=1e-6,max_iter=500) { if(any(is.na(pik))) stop("there are missing values in the pik vector") n=sum(pik) n=.as_int(n) list= pik>eps & pik < 1-eps pikb=pik[list] n=sum(pikb) N=length(pikb) s=pik if(N<1) stop("the pik vector has all elements outside of the range [eps,1-eps]") else { sb=rep(2,N) y=pikb/(1-pikb)/sum(pikb/(1-pikb)) step=0 while(sum(sb<=1)!=N & step<=max_iter) { sb=as.vector(rmultinom(1,1,pikb/sum(pikb))+rmultinom(1,.as_int(n-1),y)) step=step+1 } if(sum(sb<=1)==N) s[list]=sb else stop("Too many iterations. The algorithm was stopped.") } s } sampling/R/vartaylor_ratio.r0000644000176200001440000000154511312713776015706 0ustar liggesusersvartaylor_ratio=function(Ys,Xs,pikls) { if (any(is.na(pikls))) stop("there are missing values in pikls") if(nrow(pikls)!=ncol(pikls)) stop("pikls is not a square matrix") if (any(is.na(Ys))) stop("there are missing values in y") if (any(is.na(Xs))) stop("there are missing values in x") if (length(Ys) != nrow(pikls) | length(Xs) != nrow(pikls) | length(Xs) != length(Ys)) stop("y, x and pikls have different sizes") pik=diag(pikls) n=length(pik) xhat=sum(Xs/pik) yhat=sum(Ys/pik) r=yhat/xhat z=(Ys-r*Xs)/xhat delta=matrix(0,nrow=nrow(pikls),ncol=ncol(pikls)) for(i in 1:(n-1)) {for(j in (i+1):n) delta[i,j]=delta[j,i]=(1-pik[i]*pik[j]/pikls[i,j])*z[i]*z[j]/(pik[i]*pik[j]) delta[i,i]=(1-pik[i])*z[i]^2/pik[i]^2} delta[n,n]=(1-pik[n])*z[n]^2/pik[n]^2 list(ratio=r, estvar=sum(delta)) } sampling/R/fastflightcube.R0000644000176200001440000000601013407116505015401 0ustar liggesusers"fastflightcube" <- function(X,pik,order=1,comment=TRUE) { EPS = 1e-11 "algofastflightcube" <- function(X,pik) { "jump" <- function(X,pik){ N = length(pik) p = round(length(X)/length(pik)) X<-array(X,c(N,p)) X1=cbind(X,rep(0,times=N)) kern<-svd(X1)$u[,p+1] listek=abs(kern)>EPS buff1<-(1-pik[listek])/kern[listek] buff2<- -pik[listek]/kern[listek] la1<-min( c(buff1[(buff1>0)] , buff2[(buff2>0)]) ) pik1<- pik+la1*kern buff1<- -(1-pik[listek])/kern[listek] buff2<- pik[listek]/kern[listek] la2<-min(c(buff1[(buff1>0)] , buff2[(buff2>0)])) pik2<- pik-la2*kern q<-la2/(la1+la2) if (runif(1)(1-EPS) | psikEPS & pik<(1-EPS))])==(p+1)) psik <- jump(B,psik) pik[ind]=psik pik } "reduc" <- function(X) { EPS=1e-11 N=dim(X)[1] Re=svd(X) array(Re$u[,(Re$d>EPS)] , c(N,sum(as.integer(Re$d>EPS)))) } N = length(pik); p = round(length(X)/length(pik)) X<-array(X,c(N,p)) if (order==1) o<-sample.int(N,N) else { if(order==2) o<-seq(1,N,1) else o<-order(pik,decreasing=TRUE) } liste<-o[(pik[o]>EPS & pik[o]<(1-EPS))] if(comment==TRUE){ cat("\nBEGINNING OF THE FLIGHT PHASE\n") cat("The matrix of balanced variable has",p," variables and ",N," units\n") cat("The size of the inclusion probability vector is ",length(pik),"\n") cat("The sum of the inclusion probability vector is ",sum(pik),"\n") cat("The inclusion probability vector has ",length(liste)," non-integer elements\n") } pikbon<-pik[liste]; Nbon=length(pikbon); Xbon<-array(X[liste,] ,c(Nbon,p)) pikstar<-pik flag=0 if(Nbon>p){if(comment==TRUE) cat("Step 1 ") pikstarbon<-algofastflightcube(Xbon,pikbon) pikstar[liste]=pikstarbon flag=1 } liste<-o[(pikstar[o]>EPS & pikstar[o]<(1-EPS))] pikbon<-pikstar[liste] Nbon=length(pikbon) Xbon<-array(X[liste,] ,c(Nbon,p)) pbon=dim(Xbon)[2] if(Nbon>0){ Xbon=reduc(Xbon) pbon=dim(Xbon)[2] } k=2 while(Nbon>pbon & Nbon>0){ if(comment==TRUE) cat("Step ",k,", ") k=k+1 pikstarbon<-algofastflightcube(Xbon/pik[liste]*pikbon,pikbon) pikstar[liste]=pikstarbon liste<-o[(pikstar[o]>EPS & pikstar[o]<(1-EPS))] pikbon<-pikstar[liste] Nbon=length(pikbon) Xbon<-array(X[liste,] ,c(Nbon,p)) if(Nbon>0) { Xbon=reduc(Xbon) pbon=dim(Xbon)[2] } flag=1 } if(comment==TRUE) if(flag==0) cat("NO FLIGHT PHASE") if(comment==TRUE) cat("\n") pikstar } sampling/R/UPminimalsupport.R0000644000176200001440000000114213214454557015750 0ustar liggesusers"UPminimalsupport" <- function(pik) { if(any(is.na(pik))) stop("there are missing values in the pik vector") basicsplit<-function(pik) { N=length(pik) n=sum(pik) A=(1:N)[pik==0] B=(1:N)[pik==1] C=setdiff(setdiff(1:N,A),B) D=C[sample.int(length(C), round(n-length(B)))] s1v=rep(0,times=N) s1v[c(B,D)]=1 alpha=min(1-max(pik[setdiff(C,D)]),min(pik[D])) pikb= (pik-alpha*s1v)/(1-alpha) if(runif(1,0,1) 0 & pik < 1] N = length(pik1) Vk = cumsum(pik1) Vk1=Vk%%1 if(Vk1[N]!=0) Vk1[N]=0 r = c(sort(Vk1), 1) cent = (r[1:N] + r[2:(N + 1)])/2 p = r[2:(N + 1)] - r[1:N] A = matrix(c(0, Vk), nrow = N + 1, ncol = N) - t(matrix(cent,nrow = N, ncol = N + 1)) A = A%%1 M = matrix(as.integer(A[1:N, ] > A[2:(N + 1), ]), N, N) pi21 = M %*% diag(p) %*% t(M) pi2 = pik %*% t(pik) pi2[pik > 0 & pik < 1, pik > 0 & pik < 1] = pi21 pi2 } sampling/R/landingcube.R0000644000176200001440000000354612235722341014674 0ustar liggesusers"landingcube" <- function(X,pikstar,pik,comment=TRUE) # landing phase of the cube method ###################################################### { # extraction of the non-integer values for the landing phase EPS=1e-11 p=dim(X)[2] N=dim(X)[1] liste=(pikstar>EPS & pikstar<(1-EPS)) pikland=pikstar[liste] Nland=length(pikland) Xland=array(X[liste,] ,c(Nland,p)) nland=sum(pikland) FLAGI=(abs(nland-round(nland))EPS,]/pik[pik>EPS] cost=rep(0,times=lll) for(i in 1:lll) cost[i]=t(Asmp[,i]) %*% ginv(t(A) %*% A) %*% Asmp[,i] # linear programming V = t(cbind(SSS,rep(1,times=lll))) b=c(pikland,1) constdir=rep("==",times=(Nland+1)) x=lp("min",cost,V,constdir,b)$solution # choice of the sample u=runif(1,0,1) i=0 ccc=0 while(ccc= C || bounds[1] > bounds[2]) stop("The conditions low bounds[2])) { g[g < bounds[1]] = bounds[1] g[g > bounds[2]] = bounds[2] list = (1:length(g))[g > bounds[1] & g < bounds[2]] if (length(list) != 0) { g1 = g[list] t2 = total - c(t(g[-list] * d[-list]) %*% Xs[-list, ]) Xs1 = Xs[list, ] Zs1 = Zs[list, ] d1 = d[list] q1 = q[list] list1 = list } } t1 = c(t(d1) %*% Xs1) lambda1 = ginv(t(Xs1 * d1 * q1) %*% Zs1, tol = EPS) %*% (t2 - t1) if (length(list1) > 1) g1 = 1 + q1 * c(Zs1 %*% lambda1) else if (length(list1) == 1) { g1 = 1 + q1 * c(as.vector(Zs1) %*% as.vector(lambda1)) } g[list1] = g1 tr = crossprod(Xs, g * d) expression = max(abs(tr - total)/total) if(any(total==0)) expression = max(abs(tr - total)) if (expression < EPS1 & all(g >= bounds[1] & g <= bounds[2])) break } if (l == max_iter) { cat("No convergence in", max_iter, "iterations with the given bounds. \n") cat("The bounds for the g-weights are:", min(g), " and ", max(g), "\n") g=NULL } } else if (method == "raking") { lambda = as.matrix(rep(0, ncol(Xs))) w1 = as.vector(d * exp(Zs %*% lambda * q)) T = t(Xs) for (l in 1:max_iter) { phi = t(Xs) %*% w1 - total T1 = t(Xs * w1) phiprim = T1 %*% Zs lambda = lambda - ginv(phiprim, tol = EPS) %*% phi w1 = as.vector(d * exp(Zs %*% lambda * q)) if (any(is.na(w1)) | any(is.infinite(w1)) | any(is.nan(w1))) { warning("No convergence") g = NULL der = g l = max_iter break } tr = crossprod(Xs, w1) expression = max(abs(tr - total)/total) if(any(total==0)) expression = max(abs(tr - total)) if (expression < EPS1) break } if (l == max_iter) { warning("No convergence") g = NULL der = g } else {g = w1/d; der=g} } else if (method == "logit") if (missing(bounds)) stop("Specify the bounds") else { if (bounds[2] <= C || bounds[1] >= C || bounds[1] > bounds[2]) stop("The conditions low EPS1 | any(g < bounds[1]) | any(g > bounds[2])) { lambda1 = rep(0, ncol(Xs)) list = 1:length(g) t2 = total Xs1 = Xs d1 = d Zs1 = Zs g1 = g q1 = q list1 = 1:length(g) for (l in 1:max_iter) { if (any(g < bounds[1]) | any(g > bounds[2])) { g[g < bounds[1]] = bounds[1] g[g > bounds[2]] = bounds[2] list = (1:length(g))[g > bounds[1] & g < bounds[2]] if (length(list) != 0) { g1 = g[list] t2 = total - c(t(g[-list] * d[-list]) %*% Xs[-list, ]) Xs1 = Xs[list, ] Zs1 = Zs[list, ] d1 = d[list] q1 = q[list] list1 = list } else break } if (is.vector(Xs1)) { warning("no convergence") g1 = g = NULL break } t1 = c(t(d1) %*% Xs1) phi = t(Xs1) %*% as.vector(d1 * g1) T = t(Xs1 * as.vector(d1 * g1)) phiprime = T %*% Zs1 lambda1 = lambda1 - ginv(phiprime, tol = EPS) %*% (as.vector(phi) - t2) u = exp(A * (Zs1 %*% lambda1 * q1)) F = g1 = (bounds[1] * (bounds[2] - C) + bounds[2] * (C - bounds[1]) * u)/(bounds[2] - C + (C - bounds[1]) * u) if (any(is.na(g1))) { warning("no convergence") g1 = g = NULL break } g[list1] = g1 der = g-1 tr = crossprod(Xs, g * d) expression = max(abs(tr - total)/total) if(any(total==0)) expression = max(abs(tr - total)) if (expression < EPS1 & all(g >= bounds[1] & g <= bounds[2])) break } if (l == max_iter) { cat("no convergence in", max_iter, "iterations with the given bounds. \n") cat("the bounds for the g-weights are:", min(g), " and ", max(g), "\n") cat(" and the g-weights are given by g\n") g = NULL der = g } } } if (description && !is.null(g)) { par(mfrow = c(3, 2), pty = "s") hist(g) boxplot(g, main = "Boxplot of g") hist(d) boxplot(d, main = "Boxplot of d") hist(g * d) boxplot(g * d, main = "Boxplot of w=g*d") if (method %in% c("truncated", "raking", "logit")) cat("number of iterations ", l, "\n") cat("summary - initial weigths d\n") print(summary(d)) cat("summary - final weigths w=g*d\n") print(summary(as.vector(g * d))) } g } sampling/R/srswor.R0000644000176200001440000000011313214454245013746 0ustar liggesusers"srswor" <- function(n,N) {s<-rep(0,times=N);s[sample.int(N,n)]<-1;s} sampling/R/srswor1.R0000644000176200001440000000016610417201372014030 0ustar liggesusers"srswor1" <- function(n,N) {j=0 s=numeric(N) for(k in 1:N) if(runif(1)<(n-j)/(N-k+1)) {j=j+1;s[k]=1;} s } sampling/R/cluster.r0000644000176200001440000001365113026705753014147 0ustar liggesuserscluster<-function (data, clustername, size, method = c("srswor", "srswr", "poisson", "systematic"), pik, description = FALSE) { if (size == 0) stop("the size is zero") if (missing(method)) { warning("the method is not specified; by default, the method is srswor") method = "srswor" } if (!(method %in% c("srswor", "srswr", "poisson", "systematic"))) stop("the name of the method is wrong") if (method %in% c("poisson", "systematic") & missing(pik)) stop("the vector of probabilities is missing") if (method %in% c("poisson", "systematic") & !missing(pik)) if(!is.vector(pik)) pik=as.vector(pik) data = data.frame(data) index = 1:nrow(data) if (missing(clustername)) { if (method == "srswor") result = data.frame(index[srswor(size, nrow(data)) == 1], rep(size/nrow(data), size)) if (method == "srswr") { s = srswr(size, nrow(data)) st = s[s != 0] l = length(st) result = data.frame(index[s != 0]) result = cbind.data.frame(result, st, prob = rep(1-(1-1/nrow(data))^size,l)) colnames(result) = c("ID_unit", "Replicates", "Prob") } if (method == "poisson") { pikk = inclusionprobabilities(pik, size) s = (UPpoisson(pikk) == 1) if (length(s) > 0) result = data.frame(index[s], pikk[s]) if (description) cat("\nNumber of units in the population and number of selected units:", nrow(data), length(s), "\n") } if (method == "systematic") { pikk = inclusionprobabilities(pik, size) s = (UPsystematic(pikk) == 1) result = data.frame(index[s], pikk[s]) } if (method != "srswr") colnames(result) = c("ID_unit", "Prob") if (description) cat("\nNumber of units in the population and number of selected units:", nrow(data), sum(size), "\n") } else { data = data.frame(data) m = match(clustername, colnames(data)) if (length(m) > 1) stop("there are too many specified variables as clusters") if (is.na(m)) stop("the cluster name is wrong") x1 = factor(data[, m]) result = NULL if (nlevels(x1) == 0) stop("the cluster variable has 0 categories") else { nr_cluster = nlevels(x1) if (method == "srswor") { s = as.data.frame(levels(x1)[srswor(size, nr_cluster) == 1]) names(s) = c("cluster") r = cbind.data.frame(index, data[, m]) names(r) = c("index", "cluster") r = merge(r, s, by.x = "cluster", by.y = "cluster", sort = TRUE) result = cbind.data.frame(r, rep(size/nr_cluster, nrow(r))) } if (method == "srswr") { s = srswr(size, nr_cluster) st = cbind.data.frame(levels(x1)[s != 0], s[s != 0]) names(st) = c("cluster", "repl") r = cbind.data.frame(index, data[, m]) names(r) = c("index", "cluster") r = merge(r, st, by.x = "cluster", by.y = "cluster") result = cbind.data.frame(r, rep(1-(1-1/nr_cluster)^size, nrow(r))) } if (method == "systematic") { pikk = inclusionprobabilities(pik, size) s = (UPsystematic(pikk) == 1) st = cbind.data.frame(levels(x1)[s], pikk[s]) names(st) = c("cluster", "prob") r = cbind.data.frame(index, data[, m]) names(r) = c("index", "cluster") result = merge(r, st, by.x = "cluster", by.y = "cluster") } if (method == "poisson") { pikk = inclusionprobabilities(pik, size) s = (UPpoisson(pikk) == 1) if (any(s)) { st = cbind.data.frame(levels(x1)[s], pikk[s]) names(st) = c("cluster", "prob") r = cbind.data.frame(index, data[, m]) names(r) = c("index", "cluster") result = merge(r, st, by.x = "cluster", by.y = "cluster") if (description) { cat("Number of selected clusters:", sum(s), "\n") cat("\nNumber of units in the population and number of selected units:", nrow(data), nrow(result), "\n") } } else { if (description) { cat("Number of selected clusters: 0\n") cat("Population total and number of selected units:", nrow(data), 0, "\n") } result = NULL } } if (method == "srswr") { colnames(result) = c(clustername, "ID_unit", "Replicates", "Prob") if (description) { cat("Number of selected clusters:", length(s[s != 0]), "\n") cat("Number of units in the population and number of selected units:", nrow(data), nrow(result), "\n") } } else if (!is.null(result)) colnames(result) = c(clustername, "ID_unit", "Prob") if (description & !(method %in% c("poisson", "srswr"))) { cat("Number of selected clusters:", size, "\n") cat("Number of units in the population and number of selected units:", nrow(data), nrow(result), "\n") } } } result } sampling/R/ratioest.r0000644000176200001440000000064710753033764014321 0ustar liggesusersratioest<-function(y,x,Tx,pik) {if (any(is.na(pik))) stop("there are missing values in pik") if (any(is.na(y))) stop("there are missing values in y") if (any(is.na(x))) stop("there are missing values in x") if (length(y) != length(pik) | length(x)!=length(pik) | length(x)!=length(y)) stop("y, x and pik have different lengths") sum(y/pik)*Tx/sum(x/pik) } sampling/R/srswr.R0000644000176200001440000000011010331363200013547 0ustar liggesusers"srswr" <- function(n,N) as.vector(rmultinom(1,n,rep(n/N,times=N))) sampling/R/balancedtwostage.R0000644000176200001440000000157410645360636015737 0ustar liggesusers"balancedtwostage" <- function(X,selection,m,n,PU,comment=TRUE,method=1) { N=dim(X)[1] p=dim(X)[2] str=cleanstrata(PU) M=max(PU) res1=balancedcluster(X,m,PU,method,comment) if(selection==2) { pik2=rep(n/N*M/m,times=N); if(n/N*M/m>1) stop("at the second stage, inclusion probabilities larger than 1"); } if(selection==1) { pik2=inclusionprobastrata(str,rep(n/m ,times=max(str))); if(max(pik2)>1) stop("at the second stage, inclusion probabilities larger than 1"); } liste=(res1[,1]==1) sf=rep(0,times=N) sf[liste]=balancedstratification(array(X[liste,]/res1[,2][liste],c(sum(as.integer(liste)),p)),cleanstrata(str[liste]),pik2[liste],comment,method) x=cbind(sf,res1[,2]*pik2,res1[,1],res1[,2],pik2) colnames(x)=c("second_stage","final_pik", "primary","pik_first_stage", "pik_second_stage") x } sampling/R/Hajekestimator.r0000644000176200001440000000107611371024052015421 0ustar liggesusersHajekestimator<-function(y,pik,N=NULL,type=c("total","mean")) { if(any(is.na(pik))) stop("there are missing values in pik") if(any(is.na(y))) stop("there are missing values in y") if(length(y)!=length(pik)) stop("y and pik have different sizes") if(missing(type) | is.null(N)) { if(missing(type)) warning("the type estimator is missing") warning("by default the mean estimator is computed") est<-crossprod(y,1/pik)/sum(1/pik)} else if(type=="total") est<-N*crossprod(y,1/pik)/sum(1/pik) est } sampling/R/cleanstrata.R0000644000176200001440000000020710416445612014713 0ustar liggesusers"cleanstrata" <- function(strata) { a=sort(unique(strata)) b=1:length(a) names(b)=a as.vector(b[as.character(strata)]) } sampling/R/UPmidzunopi2.R0000644000176200001440000000017210417201070014745 0ustar liggesusers"UPmidzunopi2" <- function(pik) { N=length(pik) UN=rep(1,times=N) b=1-pik%*%t(UN) 1-b-t(b)+UPtillepi2(1-pik) } sampling/R/UPmultinomial.R0000644000176200001440000000024110723534474015215 0ustar liggesusers"UPmultinomial" <- function(pik) {if(any(is.na(pik))) stop("there are missing values in the pik vector") as.vector(rmultinom(1,sum(pik),pik/sum(pik))) } sampling/R/disjunctive.R0000644000176200001440000000023510416445752014747 0ustar liggesusers"disjunctive" <- function(strata) {ss=cleanstrata(strata) m=matrix(0,length(strata),length(unique(strata))) for(i in 1:length(ss)) m[i,ss[i]]=1 m } sampling/R/UPpoisson.R0000644000176200001440000000022011714740723014347 0ustar liggesusers"UPpoisson" <- function(pik) {if(any(is.na(pik))) stop("there are missing values in the pik vector") as.numeric(runif(length(pik))=eps & a<= 1-eps & b>=eps & b<= 1-eps) if(a+b>1) { if(u<(1-b)/(2-a-b)) {b<-a+b-1;a<-1} else {a<-a+b-1;b<-1} } else{ if(u< b/(a+b)) {b<- a+b;a<-0} else {a<- a+b;b<-0} } if( (a 1-eps)& (k<=N)) {s[i]=a;a=pik[k];i=k;k=k+1;} if( (b 1-eps)& (k<=N) ) {s[j]=b;b=pik[k];j=k;k=k+1;} } u<-runif(1) if(a>=eps & a<= 1-eps & b>=eps & b<= 1-eps) if(a+b>1) { if(u<(1-b)/(2-a-b)) {b<-a+b-1;a<-1} else {a<-a+b-1;b<-1} } else{ if(u< b/(a+b)) {b<-a+b;a<-0} else {a<- a+b;b<-0} } s[i]=a; s[j]=b; s } sampling/R/writesample.R0000644000176200001440000000066410645363350014757 0ustar liggesusers"writesample" <- function(n,N) { if(n==N) samples=rep(1,times=N) else{ x=numeric(N) row=1 for(i in (n+1):N) row=row*i k=1 for(i in 1:(N-n)) k=k*i row=row/k samples=matrix(0,row,N) k=1 sol=0 x[1]=-1 while(k<=N && k>0) { while(x[k]<1) { x[k]=x[k]+1 s=0 for(i in 1:N) s=s+x[i] if(s==n) { sol=sol+1 samples[sol,]=x } else if(keps) { w=(pikt)/(1-pikt) q=UPMEqfromw(w,n) pikt1=pikt+pik-UPMEpikfromq(q) arr=sum(abs(pikt-pikt1)) pikt=pikt1 } pikt } sampling/R/rhg_strata.r0000644000176200001440000000141210721310560014577 0ustar liggesusersrhg_strata<-function(X,selection) { if(is.matrix(X)) X=as.data.frame(X) m=match(selection,names(X),nomatch=0) if(sum(m)==0) stop("the 'selection' should be the name of one the X columns") if(!("Stratum" %in% names(X))) stop("the column 'Stratum' is missing") result=NULL u=unique(X$Stratum) for(i in 1:length(u)) {si=X[X$Stratum==u[i],] x=cbind.data.frame(si$ID_unit,si$status,si[,m]) names(x)=c("ID_unit","status",names(X)[m]) result=rbind.data.frame(result,rhg(x,selection)) } res = NULL mm = match(names(X), names(result), nomatch = 0) index = (1:ncol(X))[mm == 0] if (length(index) > 0) { res = cbind.data.frame(X[X$ID_unit==result$ID_unit, index], result) names(res)[1:length(index)] = names(X)[index] } res } sampling/R/UPsampfordpi2.r0000644000176200001440000000151612234667674015167 0ustar liggesusersUPsampfordpi2<-function(pik) { n=sum(pik) n=.as_int(n) if(n<2) stop("the sample size<2") N=length(pik) p=pik/n pikl=matrix(0,N,N) Lm=rep(0, n) lambda=p/(1-n*p) Lm[1]=1 if(n>=2) for (i in 2:n) { for (r in 1:(i-1)) Lm[i]=Lm[i]+((-1)^(r-1))*sum(lambda^r)*Lm[i-r] Lm[i]=Lm[i]/(i - 1) } if(any(Lm<0)) stop("it is not possible to compute pik2 for this example") t1=(n + 1) - (1:n) Kn=1/sum(t1*Lm/n^t1) Lm2=rep(0, n - 1) t2=(1:(n - 1)) t3=n - t2 for (i in 2:N) { for (j in 1:(i - 1)) { Lm2[1]=1 Lm2[2]=Lm[2] - (lambda[i] + lambda[j]) if(n>3) for (m in 3:(n - 1)) { Lm2[m]=Lm[m] - (lambda[i] + lambda[j]) * Lm2[m -1] - lambda[i] * lambda[j] * Lm2[m - 2] } pikl[i, j]=Kn * lambda[i] * lambda[j] * sum((t2+1-n*(p[i] + p[j]))*Lm2[t3]/n^(t2 - 1)) pikl[j, i]=pikl[i, j] } pikl[i, i]=pik[i] } pikl[1, 1]=pik[1] pikl } sampling/R/poststrata.r0000644000176200001440000000160111022255024014643 0ustar liggesuserspoststrata<-function(data, postnames = NULL) { if (missing(data) | missing(postnames)) stop("incomplete input") data = data.frame(data) if(is.null(colnames(data))) stop("the column names in data are missing") index = 1:nrow(data) m = match(postnames, colnames(data)) if (any(is.na(m))) stop("the names of the poststrata are wrong") data2 = cbind.data.frame(data[, m]) x1 = data.frame(unique(data[, m])) colnames(x1) = postnames nr_post=0 post=numeric(nrow(data)) nh=numeric(nrow(x1)) for(i in 1:nrow(x1)) { expr=rep(FALSE, nrow(data2)) for(j in 1:nrow(data2)) expr[j]=all(data2[j, ]==x1[i, ]) y=index[expr] if(is.matrix(y)) nh[i]=nrow(y) else nh[i]=length(y) post[expr]=i } result=cbind.data.frame(data,post) names(result)=c(names(data),"poststratum") list(data=result, npost=nrow(x1)) } sampling/R/UPbrewer.R0000644000176200001440000000113611714741701014147 0ustar liggesusers"UPbrewer" <- function(pik, eps = 1e-06) { if(any(is.na(pik))) stop("there are missing values in the pik vector") n=sum(pik) n=.as_int(n) list = pik > eps & pik < 1 - eps pikb = pik[list] N = length(pikb) s=pik if(N<1) stop("the pik vector has all elements outside of the range [eps,1-eps]") else { sb=rep(0,N) n=sum(pikb) for (i in 1:n) { a = sum(pikb*sb) p = (1-sb)*pikb*((n-a)-pikb)/((n-a)-pikb*(n-i+1)) p = p/sum(p) p = cumsum(p) u=runif(1) for(j in 1:length(p)) if(u .Machine$integer.max)) stop("the input has entries too large to be integer") if(!identical(TRUE, (ax <- all.equal(xo, x)))) warning("the argument is not integer") else x=xo } x } sampling/R/UPMEsfromq.R0000644000176200001440000000022110417201050014367 0ustar liggesusers"UPMEsfromq" <- function(q) { n=ncol(q) N=nrow(q) s=rep(0,times=N) for(k in 1:N) if(n!=0) if(runif(1) eps & pik < 1 - eps pikb = pik[list] N = length(pikb) s=pik if(N<1) stop("the pik vector has all elements outside of the range [eps,1-eps]") else { n=sum(pikb) sb=rep(1,N) b=rep(1,N) for(i in 1:(N-n)) {a=inclusionprobabilities(pikb,N-i) v=1-a/b b=a p=v*sb p=cumsum(p) u=runif(1) for(j in 1:length(p)) if(u1) stop("pik is not a vector") else pik=unlist(pik) else if(is.matrix(pik)) if(ncol(pik)>1) stop("pik is not a vector") else pik=pik[,1] else if(is.list(pik)) if(length(pik)>1) stop("pik is not a vector") else pik=unlist(pik) n=sum(pik) n=.as_int(n) if(n>=2) { pik2=pik[pik!=1] n=sum(pik2) n=.as_int(n) piktilde=UPMEpiktildefrompik(pik2) w=piktilde/(1-piktilde) q=UPMEqfromw(w,n) s2=UPMEsfromq(q) s=rep(0,times=length(pik)) s[pik==1]=1 s[pik!=1][s2==1]=1 } if(n==0) s=rep(0,times=length(pik)) if(n==1) s=as.vector(rmultinom(1, 1,pik)) s } sampling/R/Hajekstrata.r0000644000176200001440000000231412511712550014710 0ustar liggesusersHajekstrata<-function(y,pik,strata,N=NULL,type=c("total","mean"),description=FALSE) { str <- function(st, h, n) .C("str", as.double(st), as.integer(h), as.integer(n), s = double(n), PACKAGE = "sampling")$s if(any(is.na(pik))) stop("there are missing values in pik") if(any(is.na(y))) stop("there are missing values in y") if(length(y)!=length(pik)) stop("y and pik have different sizes") if (is.matrix(y)) sample.size <- nrow(y) else sample.size <- length(y) if(!is.vector(N)) N <- as.vector(N) h <- unique(strata) if(length(N)!=length(h)) stop("N should be a vector with the length equal to the number of strata") options(warn=-1) s1 <- 0 for (i in 1:length(h)) { s <- str(strata, h[i], sample.size) est <- Hajekestimator(y[s == 1], pik[s == 1], type="mean") s1 <- s1 + est*N[i] if(description) if(type=="mean") cat("For stratum ",i,", the Hajek estimator is:",est,"\n") else cat("For stratum ",i,", the Hajek estimator is:",est*N[i],"\n") } if(description) cat("The Hajek estimator is:\n") if(type=="mean") return(s1/sum(N)) else return(s1) } sampling/R/inclusionprobastrata.R0000644000176200001440000000057511502431076016664 0ustar liggesusersinclusionprobastrata<-function (strata, nh) { N = length(strata) EPS = 1e-6 if (min(unique(strata)) < 1) stop("the stratification variable has incorect values (less than 1)\n") Nh=as.vector(table(strata)) if(any(nh/Nh>1+EPS)) warning("in a stratum the sample size is larger than the population size\n") pik=nh[strata]/Nh[strata] pik } sampling/R/UPrandomsystematic.R0000644000176200001440000000032313214454370016244 0ustar liggesusers"UPrandomsystematic" <- function(pik,eps=1e-6) { if(any(is.na(pik))) stop("there are missing values in the pik vector") N=length(pik) v=sample.int(N,N) s=numeric(N) s[v]=UPsystematic(pik[v],eps) s } sampling/R/rmodel.r0000644000176200001440000000104111011042102013704 0ustar liggesusersrmodel<-function(formula,weights,X) { cl <- match.call() mf <- match.call(expand.dots = FALSE) m <- match(c("formula", "weights"), names(mf), 0) mf <- mf[c(1, m)] mf$drop.unused.levels <- TRUE mf[[1]] <- as.name("model.frame") mf <- eval(mf, parent.frame()) mt <- attr(mf, "terms") y <- model.response(mf, "numeric") w <- as.vector(model.weights(mf)) x <- model.matrix(mt, mf, contrasts) prob<-glm(y~x,family="binomial",weights=w)$fitted.values result<-cbind.data.frame(X,prob) names(result)<-c(names(X),"prob_resp") result } sampling/R/samplecube.R0000644000176200001440000000273311706305246014541 0ustar liggesusers"samplecube" <- function(X,pik,order=1,comment=TRUE,method=1) { EPS=1e-11 N=length(pik) if(!is.array(X)) X=array(X,c(N,length(X)/N)) if(method==1) { if (length(pik[pik > EPS & pik < (1 - EPS)]) > 0) pikstar = fastflightcube(X, pik, order, comment) else { if (comment) cat("\nNO FLIGHT PHASE") pikstar = pik } if (length(pikstar[pikstar > EPS & pikstar < (1 - EPS)]) > 0) pikfin = landingcube(X, pikstar, pik, comment) else { if (comment) cat("\nNO LANDING PHASE") pikfin = pikstar } } else { p=length(X)/length(pik) pikstar=pik for(i in 0:(p-1)) { if (length(pikstar[pikstar > EPS & pikstar < (1 - EPS)]) > 0) pikstar = fastflightcube(X[,1:(p-i)]/pik*pikstar, pikstar, order, comment) } pikfin = pikstar for(i in 1:N) if(runif(1) EPS, ]/pik[pik > EPS] TOT = t(A) %*% pik[pik > EPS] EST = t(A) %*% pikfin[pik > EPS] DEV = 100 * (EST - TOT)/TOT cat("\n\nQUALITY OF BALANCING\n") if(is.null(colnames(X))) Vn = as.character(1:length(TOT)) else Vn=colnames(X) for(i in 1:length(TOT)) if(Vn[i]=="") Vn[i]=as.character(i) d = data.frame(TOTALS = c(TOT), HorvitzThompson_estimators = c(EST), Relative_deviation = c(DEV)) rownames(d)<-Vn print(d) } round(pikfin) } sampling/R/mstage.r0000644000176200001440000003300313775536365013753 0ustar liggesusersmstage<-function (data, stage = c("stratified", "cluster", ""), varnames, size, method = c("srswor", "srswr", "poisson", "systematic"), pik, description = FALSE) { if (missing(size)) stop("the size argument is missing") if (!missing(stage) & missing(varnames)) stop("indicate the stage argument") if (!missing(stage)) { number = length(stage) for (i in 1:length(stage)) if (!(stage[i] %in% c("stratified", "cluster", ""))) stop("the stage argument is wrong") } else number = length(size) if (number > 1) { if (!missing(varnames)) { if (!is.list(size)) stop("the size must be a list") size = as.list(size) varnames = as.list(varnames) size1 = size[[1]] varnames1 = varnames[[1]] if (method[[1]] %in% c("systematic", "poisson")) pik1 = pik[[1]] } else { size1 = size[[1]] varnames1 = NULL if (method[[1]] %in% c("systematic", "poisson")) pik1 = pik[[1]] } } else { size1 = size if(missing(method)) method="srswor" else if (method %in% c("systematic", "poisson")) pik1 = pik } if (description) cat("STAGE 1", "\n") if (missing(stage)) { if (missing(varnames)) if (missing(method)) s = strata(data, stratanames = NULL, size = size1, description) else if (method[[1]] %in% c("systematic", "poisson")) s = strata(data, stratanames = NULL, size = size1, method[[1]], pik = pik1, description) else s = strata(data, stratanames = NULL, size = size1, method[[1]], description) else s = strata(data, stratanames = NULL, size1, method[[1]], pik = pik1, description) } else if (stage[1] == "stratified") { s = strata(data, varnames1, size1, method="srswor",description) dimension_st = table(s$Stratum) if(description) cat("Number of strata:",length(dimension_st),"\n") } else { s = cluster(data, varnames1, size1, method[[1]], pik1, description) if (is.null(s)) stop("0 selected units in the first stage") m = match(varnames1, names(s)) nl = nlevels(as.factor(s[, m])) lev = levels(as.factor(s[, m])) if (nl >= 1) { dimension_cl = NULL for (i in 1:nl) if(nrow(subset(s,s[, m] == unique(s[,m])[i]))>0) dimension_cl = c(dimension_cl,nrow(subset(s,s[, m] == unique(s[,m])[i]))) } dimension = dimension_cl } if (is.null(s)) stop("0 selected units in the first stage") if (number > 1) if ((is.element("cluster", stage) & is.element("stratified", stage))) result = getdata(data, s) else result = s res = list() res[[1]] = s if (number >= 2) for (j in 2:number) { if (description) cat("STAGE ", j, "\n") if (!missing(varnames)) { if (stage[[j]] == "cluster") { if (stage[[j - 1]] == "stratified") { k = length(dimension_st) s1 = NULL limit = 0 dimension = list() if (k >= 1) for (ii in 1:k) { r = res[[j - 1]][(limit + 1):(limit + dimension_st[ii]), ] r = getdata(data, r) m = match(varnames[[j]], names(r)) if (method[[j]] %in% c("systematic", "poisson")) { index = res[[j - 1]][(limit + 1):(limit + dimension_st[ii]), ]$ID_unit pikk = pik[[j]][index] if (!is.null(r)) s3 = cluster(r, clustername = varnames[[j]], size = size[[j]][ii], method = method[[j]], pik = pikk, description) else s3 = NULL } else { s3 = cluster(r, clustername = varnames[[j]], size = size[[j]][ii], method = method[[j]], description = description) } limit = limit + dimension_st[ii] if (method[[j]] == "srswr") { s3 = cbind.data.frame(r[s3$ID_unit, m], r[s3$ID_unit, ]$ID_unit, s3$Replicates, s3$Prob, r[s3$ID_unit, ]$Prob * s3$Prob) colnames(s3) = c(varnames[[j]], "ID_unit", "Replicates", paste("Prob_", j, "_stage"), "Prob") } else if(!is.null(s3)) { s3 = cbind.data.frame(r[s3$ID_unit, m], r[s3$ID_unit, ]$ID_unit, s3$Prob, r[s3$ID_unit, ]$Prob * s3$Prob) colnames(s3) = c(varnames[[j]], "ID_unit", paste("Prob_", j, "_stage"), "Prob") } if (!is.null(s3)) { m = match(varnames[[j]], names(s3)) for (l in 1:nlevels(as.factor(s3[, m]))) dimension = c(dimension, table(s3[, m])[l]) s1 = rbind(s1, s3) } } } else if (stage[[j - 1]] == "cluster") { m_cl = match(varnames, names(res[[j-1]]),0) mat=res[[j-1]][, m_cl] nl = nlevels(as.factor(mat)) if (nl >= 1) { dimension_cl =NULL for (i in 1:nl) if(length(subset(mat, mat==unique(mat)[i]))>0) dimension_cl = c(dimension_cl,length(subset(mat, mat==unique(mat)[i]))) k = length(dimension_cl) } else stop("error in the previous stage") s1 = NULL limit = 0 dimension = list() if (k > length(size[[j]])) { warning("the number of selected clusters in the previous stage is larger than the size argument") warning("the size 1 is added") size1 = size[[j]] for (i in 1:(k - length(size[[j]]))) size1 = c(size1, 1) } else size1 = size[[j]] if (k >= 1) for (ii in 1:k) { r = res[[j - 1]][(limit + 1):(limit + dimension_cl[ii]), ] r = getdata(data, r) m = match(varnames[[j]], names(r)) if (method[[j]] %in% c("systematic", "poisson")) { m1 = match(varnames[[j - 1]], names(r)) m2 = match(varnames[[j - 1]], names(data)) mm = match(r[1, m1], levels(factor(data[, m2]))) pikk = as.numeric(pik[[j]][[mm]]) if (!is.null(r)) s3 = cluster(r, clustername = varnames[[j]], size = size1[[ii]], method = method[[j]], pik = pikk, description) else s3 = NULL } else s3 = cluster(r, clustername = varnames[[j]], size = size1[ii], method = method[[j]], pik, description) limit = limit + dimension_cl[ii] if (method[[j]] == "srswr") { s3 = cbind.data.frame(r[s3$ID_unit, m], r[s3$ID_unit, ]$ID_unit, s3$Replicates, s3$Prob, r[s3$ID_unit, ]$Prob * s3$Prob) colnames(s3) = c(varnames[[j]], "ID_unit", "Replicates", paste("Prob_", j, "_stage"), "Prob") } else if (!is.null(s3)) { s3 = cbind.data.frame(r[s3$ID_unit, m], r[s3$ID_unit, ]$ID_unit, s3$Prob, r[s3$ID_unit, ]$Prob * s3$Prob) colnames(s3) = c(varnames[[j]], "ID_unit", paste("Prob_", j, "_stage"), "Prob") } if (!is.null(s3)) { m = match(varnames[[j]], names(s3)) for (l in 1:nlevels(as.factor(s3[, m]))) dimension = c(dimension, table(s3[, m])[l]) s1 = rbind(s1, s3) } } } } else if (j > 1) { k = length(dimension) s1 = NULL limit = 0 count = 0 if (k > length(size[[j]])) { warning("the number of selected clusters at the previous stage is larger than the size argument") warning("the size 1 is added") size1 = size[[j]] for (i in 1:(k - length(size[[j]]))) size1 = c(size1,1) } else size1 = size[[j]] if (k >= 1) for (i in 1:k) for (ii in 1:length(dimension[[i]])) { r = res[[j - 1]][(limit + 1):(limit + dimension[[i]][ii]), ] count = count + 1 if (method[[j]] %in% c("systematic", "poisson")) { index = res[[j - 1]][(limit + 1):(limit + dimension[[i]][ii]), ]$ID_unit pikk = pik[[j]][index] if (!is.null(r)) s2 = strata(r, NULL, size = size1[count], method = method[[j]], pik = pikk, description) else s2 = NULL } else s2 = strata(r, NULL, size = size1[count], method = method[[j]], pik, description) limit = limit + dimension[[i]][ii] if (method[[j]] == "srswr") { s2 = cbind.data.frame(r[s2$ID_unit, ]$ID_unit, s2$Replicates, s2$Prob, r[s2$ID_unit, ]$Prob * s2$Prob) colnames(s2) = c("ID_unit", "Replicates", paste("Prob_", j, "_stage"), "Prob") } else if (!is.null(s2)) { s2 = cbind.data.frame(r[s2$ID_unit, ]$ID_unit, s2$Prob, r[s2$ID_unit, ]$Prob * s2$Prob) colnames(s2) = c("ID_unit", paste("Prob_", j, "_stage"), "Prob") } if (!is.null(s2)) s1 = rbind(s1, s2) } } } else { if (missing(stage)) { if (missing(method)) s1 = strata(result, stratanames = NULL, size = size[[j]], description = description) else if (method[[j]] == "poisson" | method[[j]] == "systematic") s1 = strata(result, stratanames = NULL, size = size[[j]], method = method[[j]], pik = pik[[j]], description = description) else s1 = strata(result, stratanames = NULL, size = size[[j]], method = method[[j]], description = description) if (method[[j]] == "srswr") { s1 = cbind.data.frame(result[s1$ID_unit, ]$ID_unit, s1$Replicates, s1$Prob, result[s1$ID_unit, ]$Prob * s1$Prob) colnames(s1) = c("ID_unit", "Replicates", paste("Prob_", j, "_stage"), "Prob") } else { s1 = cbind.data.frame(result[s1$ID_unit, ]$ID_unit, s1$Prob, result[s1$ID_unit, ]$Prob * s1$Prob) colnames(s1) = c("ID_unit", paste("Prob_", j, "_stage"), "Prob") } } } if (!is.null(s1)) { result = s1 res[[j]] = result } else number = number - 1 } if (!is.null(names(res[[1]]))) { m = match("Prob", names(res[[1]])) names(res[[1]])[m] = "Prob_ 1 _stage" } names(res) = c(1:number) res } sampling/R/strata.r0000644000176200001440000001034313214437040013745 0ustar liggesusersstrata<-function(data, stratanames=NULL, size, method=c("srswor","srswr","poisson","systematic"),pik,description=FALSE) { if(missing(method)) {warning("the method is not specified; by default, the method is srswor") method="srswor" } if(!(method %in% c("srswor","srswr","poisson","systematic"))) stop("the method name is not in the list") if(method %in% c("poisson","systematic") & missing(pik)) stop("the vector of probabilities is missing") if(missing(stratanames)|is.null(stratanames)) { if(length(size)>1) stop("the argument giving stratification variable is missing. The argument size should be a value.") if(method=="srswor") result=data.frame((1:nrow(data))[srswor(size,nrow(data))==1],rep(size/nrow(data),size)) if(method=="srswr") { s=srswr(size,nrow(data)) st=s[s!=0] l=length(st) result=data.frame((1:nrow(data))[s!=0]) result=cbind.data.frame(result,st,prob=rep(1-(1-1/nrow(data))^size,l)) colnames(result)=c("ID_unit","Replicates","Prob") } if(method=="poisson") { pikk=inclusionprobabilities(pik,size) s=(UPpoisson(pikk)==1) if(length(s)>0) result=data.frame((1:nrow(data))[s],pikk[s]) if(description) cat("\nPopulation total and number of selected units:",nrow(data),sum(s),"\n") } if(method=="systematic") { pikk=inclusionprobabilities(pik,size) s=(UPsystematic(pikk)==1) result=data.frame((1:nrow(data))[s],pikk[s]) } if(method!="srswr") colnames(result)=c("ID_unit","Prob") if(description & method!="poisson") cat("\nPopulation total and number of selected units:",nrow(data),sum(size),"\n") } else { data=data.frame(data) index=1:nrow(data) m=match(gsub(" ",".",stratanames),colnames(data)) if(any(is.na(m))) stop("the names of the strata are wrong") data2=cbind.data.frame(data[,m],index) colnames(data2)=c(stratanames,"index") x1=data.frame(unique(data[,m])) colnames(x1)=stratanames result=NULL for(i in 1:nrow(x1)) { if(is.vector(x1[i,])) data3=data2[data2[,1]==x1[i,],] else {as=data.frame(x1[i,]) names(as)=names(x1) data3=merge(data2, as, by = intersect(names(data2), names(as))) } y=sort(data3$index) if(description & method!="poisson") {cat("Stratum" ,i,"\n") cat("\nPopulation total and number of selected units:",length(y),size[i],"\n") } if(method!="srswr" & length(y)=3) for(i in 3:ncol(X1)) x=list(x,unique(X1[,i])) x=expand.grid(x) ng=1 prob=rhgroup=numeric(nrow(X1)) for (i in 1:nrow(x)) { expr=rep(FALSE, nrow(X1)) for(j in 1:nrow(X1)) { expr[j] = all(X1[j,2:ncol(X1)] == x[i, ]) if(expr[j]) rhgroup[j]=ng } if(any(expr)) ng=ng+1 } gr=unique(rhgroup) if(is.data.frame(X1)) X1=cbind.data.frame(X1,rhgroup) else X1=cbind(X1,rhgroup) for(i in 1:length(gr)) {l=nrow(X1[X1[,ncol(X1)]==gr[i],]) lr=nrow(X1[X1[,ncol(X1)]==gr[i] & X1[,1]==1,]) for(j in 1:length(prob)) if(rhgroup[j]==gr[i] & X1[j,1]==1) prob[j]=lr/l } result=cbind.data.frame(X$ID_unit,X1,prob) names(result)=c("ID_unit",names(X1),"prob_resp") res = NULL mm = match(names(X), names(result), nomatch = 0) if(0 %in% mm) {index = (1:ncol(X))[mm == 0] res = cbind.data.frame(X[X$ID_unit==result$ID_unit, index], result) names(res)[1:length(index)] = names(X)[index] } else res=result res } sampling/R/UPsystematic.R0000644000176200001440000000045311714741526015054 0ustar liggesusers"UPsystematic"<-function(pik,eps=1e-6) { if(any(is.na(pik))) stop("there are missing values in the pik vector") list=pik > eps & pik < 1-eps pik1 = pik[list] N = length(pik1) a = (c(0, cumsum(pik1)) - runif(1, 0, 1))%%1 s1 = as.integer(a[1:N] > a[2:(N + 1)]) s = pik s[list] = s1 s } sampling/R/UPMEqfromw.R0000644000176200001440000000067610417201024014412 0ustar liggesusers"UPMEqfromw" <- function(w,n) { N=length(w) expa=array(0,c(N,n)) for(i in 1:N) expa[i,1]= sum(w[i:N]) for(i in (N-n+1):N) expa[i,N-i+1]=exp(sum(log(w[i:N]))) for(i in (N-2):1) for(z in 2:min(N-i,n)) { expa[i,z]=w[i]*expa[i+1,z-1]+expa[i+1,z] } q=array(0,c(N,n)) for(i in N:1) q[i,1]= w[i]/expa[i,1] for(i in N:(N-n+1)) q[i,N-i+1]=1 for(i in (N-2):1) for(z in 2:min(N-i,n)) q[i,z] = w[i]*expa[i+1,z-1]/expa[i,z] q } sampling/R/calib.r0000644000176200001440000001762013214452762013536 0ustar liggesuserscalib<-function (Xs, d, total, q = rep(1, length(d)), method = c("linear", "raking", "truncated", "logit"), bounds = c(low = 0, upp = 10), description = FALSE, max_iter = 500) { if (any(is.na(Xs)) | any(is.na(d)) | any(is.na(total)) | any(is.na(q))) stop("the input should not contain NAs") if (!(is.matrix(Xs) | is.array(Xs))) Xs = as.matrix(Xs) if (is.matrix(Xs)) if (length(total) != ncol(Xs)) stop("Xs and total have different dimensions") if (is.vector(Xs) & length(total) != 1) stop("Xs and total have different dimensions") if (any(is.infinite(q))) stop("there are Inf values in the q vector") if (missing(method)) stop("specify a method") if (!(method %in% c("linear", "raking", "logit", "truncated"))) stop("the specified method is not in the list") if (method %in% c("linear", "raking") & !missing(bounds)) stop("for the linear and raking the bounds are not allowed") EPS = .Machine$double.eps EPS1 = 1e-06 n = length(d) lambda = as.matrix(rep(0, n)) lambda1 = ginv(t(Xs * d * q) %*% Xs, tol = EPS) %*% (total - as.vector(t(d) %*% Xs)) if (method == "linear" | max(abs(lambda1)) < EPS) g = 1 + q * as.vector(Xs %*% lambda1) else if (method == "truncated") { if (!missing(bounds)) { if (bounds[2] <= 1 || bounds[1] >= 1 || bounds[1] > bounds[2]) warning("The conditions low<1 bounds[2])) { g[g < bounds[1]] = bounds[1] g[g > bounds[2]] = bounds[2] list = (1:length(g))[g > bounds[1] & g < bounds[2]] if (length(list) != 0) { g1 = g[list] t2 = total - as.vector(t(g[-list] * d[-list]) %*% Xs[-list, ]) Xs1 = Xs[list, ] d1 = d[list] q1 = q[list] list1 = list } } t1 = as.vector(t(d1) %*% Xs1) lambda1 = ginv(t(Xs1 * d1 * q1) %*% Xs1, tol = EPS) %*% (t2 - t1) if (length(list1) > 1) g1 = 1 + q1 * as.vector(Xs1 %*% lambda1) else if (length(list1) == 1) { g1 = 1 + q1 * as.vector(as.vector(Xs1) %*% as.vector(lambda1)) } g[list1] = g1 tr = crossprod(Xs, g * d) expression = max(abs(tr - total)/total) if(any(total==0)) expression = max(abs(tr - total)) if (expression < EPS1 & all(g >= bounds[1] & g <= bounds[2])) break } if (l == max_iter) { cat("No convergence in", max_iter, "iterations with the given bounds. \n") cat("The bounds for the g-weights are:", min(g), " and ", max(g), "\n") cat(" and the g-weights are given by g\n") } } else if (method == "raking") { lambda = as.matrix(rep(0, ncol(Xs))) w1 = as.vector(d * exp(Xs %*% lambda * q)) for (l in 1:max_iter) { phi = t(Xs) %*% w1 - total T1 = t(Xs * w1) phiprim = T1 %*% Xs lambda = lambda - ginv(phiprim, tol = EPS) %*% phi w1 = as.vector(d * exp(Xs %*% lambda * q)) if (any(is.na(w1)) | any(is.infinite(w1))) { warning("No convergence") g = NULL break } tr = crossprod(Xs, w1) expression = max(abs(tr - total)/total) if(any(total==0)) expression = max(abs(tr - total)) if (expression < EPS1) break } if (l == max_iter) { warning("No convergence") g = NULL } else g = w1/d } else if (method == "logit") { if (bounds[2] <= 1 || bounds[1] >= 1 || bounds[1] > bounds[2]) stop("The conditions low<1 EPS1 | any(g < bounds[1]) | any(g > bounds[2])) { lambda1 = rep(0, ncol(Xs)) list = 1:length(g) t2 = total Xs1 = Xs d1 = d g1 = g q1 = q list1 = 1:length(g) for (l in 1:max_iter) { if (any(g < bounds[1]) | any(g > bounds[2])) { g[g < bounds[1]] = bounds[1] g[g > bounds[2]] = bounds[2] list = (1:length(g))[g > bounds[1] & g < bounds[2]] if (length(list) != 0) { g1 = g[list] t2 = total - as.vector(t(g[-list] * d[-list]) %*% Xs[-list, ]) Xs1 = Xs[list, ] d1 = d[list] q1 = q[list] list1 = list } else break } if (is.vector(Xs1)) { warning("no convergence") g1 = g = NULL break } t1 = as.vector(t(d1) %*% Xs1) phi = t(Xs1) %*% as.vector(d1 * g1) - t1 T = t(Xs1 * as.vector(d1 * g1)) phiprime = T %*% Xs1 lambda1 = lambda1 - ginv(phiprime, tol = EPS) %*% (as.vector(phi) - t2 + t1) u = exp(A * (Xs1 %*% lambda1 * q1)) F = g1 = (bounds[1] * (bounds[2] - 1) + bounds[2] * (1 - bounds[1]) * u)/(bounds[2] - 1 + (1 - bounds[1]) * u) if (any(is.na(g1))) { warning("no convergence") g1 = g = NULL break } g[list1] = g1 tr = crossprod(Xs, g * d) expression = max(abs(tr - total)/total) if(any(total==0)) expression = max(abs(tr - total)) if (expression < EPS1 & all(g >= bounds[1] & g <= bounds[2])) break } if (l == max_iter) { cat("no convergence in", max_iter, "iterations with the given bounds. \n") cat("the bounds for the g-weights are:", min(g), " and ", max(g), "\n") cat(" and the g-weights are given by g\n") g = NULL } } } if (description && !is.null(g)) { par(mfrow = c(3, 2), pty = "s") hist(g) boxplot(g, main = "Boxplot of g") hist(d) boxplot(d, main = "Boxplot of d") hist(g * d) boxplot(g * d, main = "Boxplot of w=g*d") if (method %in% c("truncated", "raking", "logit")) cat("number of iterations ", l, "\n") cat("summary - initial weigths d\n") print(summary(d)) cat("summary - final weigths w=g*d\n") print(summary(as.vector(g * d))) } g } sampling/R/HTestimator.R0000644000176200001440000000036210723545414014661 0ustar liggesusersHTestimator<-function(y,pik) { if(any(is.na(pik))) stop("there are missing values in pik") if(any(is.na(y))) stop("there are missing values in y") if(length(y)!=length(pik)) stop("y and pik have different sizes") crossprod(y,1/pik) } sampling/R/UPopips.r0000644000176200001440000000066511022247510014050 0ustar liggesusersUPopips<-function(lambda, type=c("pareto","uniform","exponential")) { if(any(is.na(lambda))) stop("there are missing values in the lambda vector") n=sum(lambda) if(!(type %in% c("pareto","uniform","exponential"))) stop("the type argument is wrong") omega=runif(n) switch(type,pareto=order(omega*(1-lambda)/((1-omega)*lambda))[1:n], uniform=order(omega/lambda)[1:n], exponential=order(log(1-omega)/log(1-lambda)))[1:n] } sampling/R/varHT.r0000644000176200001440000000157312540550421013500 0ustar liggesusersvarHT<-function(y, pikl, method=1) { if(any(is.na(pikl))) stop("there are missing values in pikl") if (any(is.na(y))) stop("there are missing values in y") if(!(is.data.frame(pikl) | is.matrix(pikl))) stop("pikl should be a matrix or a data frame") if(is.data.frame(pikl) | is.matrix(pikl)) if(nrow(pikl)!=ncol(pikl)) stop("pikl is not a square matrix") if (length(y) != nrow(pikl)) stop("y and pik have different sizes") if(!missing(method) & !(method %in% c(1,2))) stop("the method should be 1 or 2") if(is.data.frame(pikl)) pikl=as.matrix(pikl) pik=diag(pikl) pik1=outer(pik,pik,"*") delta=pikl-pik1 diag(delta)=pik*(1-pik) y1=outer(y,y,"*") if(method==1)return(sum(y1*delta/(pik1*pikl))) if(method==2) {y2=outer(y/pik,y/pik,"-")^2 return(0.5*sum(y2*(pik1-pikl)/pikl)) } } sampling/R/calibev.r0000644000176200001440000000174112140456166014065 0ustar liggesuserscalibev<-function(Ys,Xs,total,pikl,d,g,q=rep(1,length(d)),with=FALSE,EPS=1e-6) { if(any(is.na(g))) stop("There are missing values in g") stopifnot((ns <- length(g)) >= 1) if(min(pikl)==0) {ss=NULL warning("There are zero values in the 'pikl' matrix. The variance estimator can not be computed.\n") } piks=as.vector(diag(pikl)) if(!checkcalibration(Xs,d,total,g,EPS)$result) stop("The calibration is not possible. The calibration estimator is not computed.\n") if(is.data.frame(Xs)) Xs=as.matrix(Xs) if(!is.vector(Ys)) Ys=as.vector(Ys) if(is.matrix(Xs)) n=nrow(Xs) else n=length(Xs) if(ns!=length(Ys) | ns!=length(piks) | ns!=n | ns!=length(d)) stop("The parameters have different sizes.\n") w=g*d wtilde=w*q B=t(Xs*wtilde) beta=ginv(B%*%Xs)%*%B%*%Ys e=Ys-Xs%*%beta if(!with) e=e*w else e=e*d ss=0 for(k in 1:ns) {ss2=0 for(l in 1:ns) ss2=ss2+(1-piks[k]*piks[l]/pikl[k,l])*e[l] ss=ss+e[k]*ss2 } list(calest=sum(w*Ys),evar=as.numeric(ss)) } sampling/R/getdata.r0000644000176200001440000000322213026226467014070 0ustar liggesusersgetdata<-function(data, m) { if (!is.data.frame(data)) data = as.data.frame(data) if (is.null(names(data))) stop("the column names are missing") if (is.vector(m) & !is.list(m)) { res = NULL if (is.null(names(m))) if (all(m %in% c(0, 1))) { res = NULL if (!("ID_unit" %in% names(data))) { res = cbind.data.frame((1:length(m))[m == 1], data[m == 1, ]) names(res) = c("ID_unit", names(data)) } else res = data[m == 1, ] } else res=data[rep(which(m>0),m[m>0]),] } else if (is.data.frame(m)) { res = NULL if (!is.null(names(m))) { mm = match(names(data), names(m), nomatch = 0) index = (1:ncol(data))[mm == 0] if (length(index) > 0) { res = cbind.data.frame(data[m$ID_unit, index], m) names(res)[1:length(index)] = names(data)[index] } else res = m } } else if (is.list(m)) { res = list() if (length(m) >= 1) for (j in 1:length(m)) { mm = match(names(data), names(m[[j]]), nomatch = 0) index = (1:ncol(data))[mm == 0] if (length(index) > 0) { res[[j]] = cbind.data.frame(data[m[[j]]$ID_unit, index], m[[j]]) names(res[[j]])[1:length(index)] = names(data)[index] } } else res = m } res } sampling/R/regest.r0000644000176200001440000000470011004364650013741 0ustar liggesusersregest<-function(formula,Tx,weights,pikl,n,sigma=rep(1,length(weights))) { cl <- match.call() mf <- match.call(expand.dots = FALSE) m <- match(c("formula", "weights"), names(mf), 0) mf <- mf[c(1, m)] mf$drop.unused.levels <- TRUE mf[[1]] <- as.name("model.frame") mf <- eval(mf, parent.frame()) mt <- attr(mf, "terms") y <- model.response(mf, "numeric") w <- as.vector(model.weights(mf)) pik<-1/w if(!identical(sigma,rep(1,length(pik)))) w<-w/sigma^2 x <- model.matrix(mt, mf, contrasts) if(ncol(x)==1) x=as.vector(x) if (any(is.na(pik))) stop("there are missing values in pik") if (any(is.na(y))) stop("there are missing values in y") if (any(is.na(x))) stop("there are missing values in x") if(is.vector(x)) {if (length(y) != length(pik) | length(x)!=length(pik) | length(x)!=length(y)) stop("y, x and pik have different lengths") } else if(is.matrix(x)) {if (length(y) != length(pik) | nrow(x)!=length(pik) | nrow(x)!=length(y)) stop("y, x and pik have different sizes") if(ncol(x)>2 & length(Tx)!=ncol(x)-1) stop("x and Tx have different sizes") } model<-lm(y~x-1,weights=w) e<-model$residuals beta<-model$coefficient # variance of beta, Sarndal p. 194 delta<-matrix(0,nrow(pikl),ncol(pikl)) for(k in 1:(nrow(delta)-1)) {for(l in (k+1):ncol(delta)) delta[l,k]<-delta[k,l]<-1-pikl[k,k]*pikl[l,l]/pikl[k,l] delta[k,k]<-1-pikl[k,k] } delta[nrow(delta),ncol(delta)]<-1-pikl[nrow(delta),ncol(delta)] j_start<-1 if(is.matrix(x)) { if(all(x[,1]==rep(1,nrow(x)))) j_start<-2 xx<-as.matrix(x[,j_start:ncol(x)]) s<-0 for(i in 1:ncol(xx)) if(j_start==2) s<-s+sum(beta[i+1]*(Tx[i]-HTestimator(xx[,i],pik))) else s<-s+sum(beta[i]*(Tx[i]-HTestimator(xx[,i],pik))) est<-HTestimator(y,pik)+s } else est<-HTestimator(y,pik)+sum(beta*(Tx-HTestimator(x,pik))) V<-t(x*w*e)%*%delta%*%(x*e*w) inv<-ginv(t(x * w) %*% x) var_beta<-inv%*%V%*%inv z<-list() class(z) <- c("regest") z$call <- cl z$formula <- formula z$x <- x z$y <- y z$weights<-w z$regest<-as.numeric(est) z$coefficients<-beta z$std_error<-sqrt(diag(var_beta)) z$t_value<-beta/sqrt(diag(var_beta)) # number of degrees of freedom is number of obs-1 if intercept, and number of obs otherwise if(j_start==1) z$p_value<-2*(1-pt(z$t_value,n-1)) else z$p_value<-2*(1-pt(z$t_value,n)) z$cov_matrix<-var_beta z } sampling/R/varest.r0000644000176200001440000000141711270334236013760 0ustar liggesusersvarest<-function(Ys,Xs=NULL,pik,w=NULL) { if (any(is.na(pik))) stop("there are missing values in pik") if (any(is.na(Ys))) stop("there are missing values in y") if (length(Ys) != length(pik)) stop("y and pik have different sizes") if(!is.null(Xs)) {if(is.data.frame(Xs)) Xs=as.matrix(Xs) if(is.vector(Xs) & (length(Ys)!= length(Xs))) stop("x and y have different sizes") if(is.matrix(Xs) & (length(Ys) != nrow(Xs))) stop("x and y have different sizes") } a=(1-pik)/sum(1-pik) if(is.null(Xs)) {A=sum(a*Ys/pik) var=sum((1-pik)*(Ys/pik-A)^2)/(1-sum(a^2)) } else {B=t(Xs*w) beta=ginv(B%*%Xs)%*%B%*%Ys e=Ys-Xs%*%beta A=sum(a*e/pik) var=sum((1-pik)*(e/pik-A)^2)/(1-sum(a^2)) } var }sampling/R/balancedcluster.R0000644000176200001440000000115611711530307015544 0ustar liggesusers"balancedcluster" <- function(X,m,cluster,selection=1,comment=TRUE,method=1) { cluster=cleanstrata(cluster) if(comment==TRUE) cat("\nSELECTION OF A SAMPLE OF CLUSTERS\n") p=dim(X)[2] N=dim(X)[1] H=max(cluster) XC=array(0,c(H,p)) Ni=rep(0,times=H) for(h in 1:H) { Ni[h]=sum(as.integer(cluster==h)) for(j in 1:p) XC[h,j]=sum(X[cluster==h,j]) } if(selection==1) pik=inclusionprobabilities(Ni,m) else pik=rep(m/H,times=H) s=samplecube(cbind(pik,XC),pik,1,comment,method) res=array(0,c(N,2)) for(h in 1:H) { res[cluster==h,1]=s[h] res[cluster==h,2]=pik[h] } res } sampling/R/postest.r0000644000176200001440000000371711022001372014145 0ustar liggesuserspostest<-function(data, y, pik, NG, description=FALSE) { if (missing(data) | missing(y) | missing(pik) | missing(NG)) stop("incomplete input") str <- function(st, h, n) .C("str", as.double(st), as.integer(h), as.integer(n), s = double(n), PACKAGE = "sampling")$s data=as.data.frame(data) sample.size=nrow(data) t_post=0 if(!is.null(colnames(data))) {m = match("Stratum", colnames(data)) if(!any(is.na(m))) { m = match("poststratum", colnames(data)) if (any(is.na(m))) stop("the column 'poststratum' is missing") h=unique(data$Stratum) g=unique(data$poststratum) for(j in 1:length(g)) {p=str(data$poststratum, g[j], sample.size) Ng=sum(NG[,j]) t1=t2=0 for (i in 1:length(h)) {s = str(data$Stratum, h[i], sample.size) shg=s*p if(!all(shg==0)) { nhg=length(shg[shg==1]) t1=t1+sum(y[shg==1]/pik[shg==1]) t2=t2+sum(1/pik[shg==1]) if(description) {cat("Stratum ",j,", postratum ", i," \n") cat("the postratified estimator is:",Ng*t1/t2,"\n") } t_post=t_post+Ng*t1/t2 } else if(description) cat("Stratum ",j,", postratum ", i," empty intersection set \n") }} } else { g=unique(data$poststratum) for(j in 1:length(g)) {p=str(data$poststratum, g[j], sample.size) Ng=NG[j] t1=Ng*sum(y[p==1]/pik[p==1])/sum(1/pik[p==1]) t_post=t_post+t1 if(description) {cat("postratum ", j," \n") cat("the postratified estimator is:",t1,"\n") } } } } else stop("the column names in data are missing") t_post } sampling/R/inclusionprobabilities.R0000644000176200001440000000145213026226644017173 0ustar liggesusersinclusionprobabilities <- function(a,n) { if(!is.vector(a)) a=as.vector(a) nnull = length(a[a == 0]) nneg = length(a[a < 0]) if (nnull > 0) warning("there are zero values in the initial vector a\n") if (nneg > 0) { warning("there are ", nneg, " negative value(s) shifted to zero\n") a[(a < 0)] = 0 } if(identical(a,rep(0,length(a)))) pik1=a else { pik1 =n * a/sum(a) pik=pik1[pik1>0] list1=pik1>0 list = pik >= 1 l = length(list[list == TRUE]) if(l>0) { l1=0 while (l != l1) { x=pik[!list] x=x/sum(x) pik[!list] = (n - l)*x pik[list] = 1 l1 = l list = (pik >= 1) l = length(list[list == TRUE]) } pik1[list1]=pik } } pik1 } sampling/R/UPtillepi2.R0000644000176200001440000000111611121454624014400 0ustar liggesusers"UPtillepi2" <- function(pik,eps=1e-6) { if(any(is.na(pik))) warning("there are missing values in the pik vector") n=sum(pik) n=.as_int(n) list = pik > eps & pik < 1 - eps pikb = pik[list] N = length(pikb) #ppf=pik%*%t(pik) ppf=matrix(0,length(pik),length(pik)) if(N<1) stop("the pik vector has all elements outside of the range [eps,1-eps]") else { n=sum(pikb) if(N>n) { UN=rep(1,N) b=rep(1,N) pp=1 for(i in 1:(N-n)) { a=inclusionprobabilities(pikb,N-i) vv=1-a/b b=a d=vv %*% t(UN) pp=pp*(1-d-t(d)) } diag(pp)=pikb ppf[list,list]=pp } } ppf } sampling/R/UPmaxentropypi2.R0000644000176200001440000000053311714742667015516 0ustar liggesusers"UPmaxentropypi2" <-function(pik) { n=sum(pik) n=.as_int(n) N=length(pik) M=array(0,c(N,N)) if(n>=2) { pik2=pik[pik>0 & pik<1] pikt=UPMEpiktildefrompik(pik2) w=pikt/(1-pikt) M[pik>0 & pik<1,pik>0 & pik<1]=UPMEpik2frompikw(pik2,w) M[,pik==1]=pik for(k in 1:N) if(pik[k]==1) M[k,]=pik } if(n==1) for(k in 1:N) M[k,k]=pik[k] M } sampling/MD50000644000176200001440000001634513777557156012434 0ustar liggesusers56cacc4937c807e361212a56e4f17553 *DESCRIPTION 8741a4e05231fcb44c4583179eba6161 *NAMESPACE 9da2c0433ff0f277f4dca4edb4e4cc38 *R/HTestimator.R 08c4d7114334d10a0caec1fc6bf71968 *R/HTstrata.r c9b1ae0be6fe3df9883ede499bb10339 *R/Hajekestimator.r d1fe76f0337a7a83a6e902ef57541ff1 *R/Hajekstrata.r fe4f3c4849c77f39e23f698eca641df9 *R/UPMEpik2frompikw.R e46e4d37db086ced1aa7be52a49cd99c *R/UPMEpikfromq.R 23780f67aa119e06e017e57affdd5076 *R/UPMEpiktildefrompik.R 0dccea40f8c13c0b820558079c6049ec *R/UPMEqfromw.R 545df0ce43ca06cfb0c7fbc9442a15a1 *R/UPMEsfromq.R 102b1a3871bb37821dc7ad8ef53f22df *R/UPbrewer.R 18d63d5af3691ef430eb0129db69e2c2 *R/UPmaxentropy.R 593f5cc0fc0acf8705657d50c172cac8 *R/UPmaxentropypi2.R 7fa457ee403a0b911d8d189811d2fcf8 *R/UPmidzuno.R 0002b2eb0657eac34889d4bb8f75bde7 *R/UPmidzunopi2.R c6af0290109363c3d31363b94144cb4e *R/UPminimalsupport.R 78b55dad22fdeed69d97cb9ee11f237b *R/UPmultinomial.R ad2fb1e97591c9f3854b746daf439b35 *R/UPopips.r 695bcb24ea0da460420aec129d36955b *R/UPpivotal.r 367109233af0ba4fb12deb6ed85680ec *R/UPpoisson.R 3e614b0d70ad5ea13ffa93131d421f31 *R/UPrandompivotal.R 1c9ace9f09024f5a9a79dbe0e8ee0df9 *R/UPrandomsystematic.R 524efbe9b151122e0e390002d6c8e6e5 *R/UPsampford.R b687f9fee230d9dc101f05a2c63a1fa9 *R/UPsampfordpi2.r 25806b316c79131009c208b7827d7301 *R/UPsystematic.R 925deff4870d5ce2203e418ae99c655d *R/UPsystematicpi2.R c0eb4ec2628625425f6210cdfbbb6fca *R/UPtille.R d002737a0f285f107e31f5a12aece8de *R/UPtillepi2.R 16d498b8d595d0160ce04705dee1dfee *R/as_int.r 9ac79cb69b3ffd8f96984f49ede89d84 *R/balancedcluster.R ff2082de62b9741eece459369ccd1fed *R/balancedstratification.R 59065fbcb53f0015bd7990735caec82b *R/balancedtwostage.R 53e62760fea98e7c30cdc7eeedc42818 *R/calib.r 28d3d2ac6fc3a6008683e313472c6b90 *R/calibev.r 999511be362810b6970f43f50c9b2196 *R/checkcalibration.R 7937c838f969518d281942465939efdb *R/cleanstrata.R f31a31792ede02a3c86e2a492acb5380 *R/cluster.r 39c9d86bca5f4e38e3130c3a9325a74b *R/disjunctive.R 9c2972ba701bd6a2cc3988d34c45554f *R/fastflightcube.R 4685754109fa3b574f94774ed4b62ff7 *R/gencalib.R f8f217acc40d29baab54a330c10bcd74 *R/getdata.r d25c378c17416caa65b913522b929a06 *R/inclusionprobabilities.R 2fe76fd3a0dfce5268a28997cbdaf052 *R/inclusionprobastrata.R 6ee3f3f14a53db1df0a458d266b55980 *R/landingcube.R 0a103aad8de9560a72eb9cc1851c17bf *R/mstage.r c8d2f7e09c4074d3dd323b3248ee6e6b *R/postest.r 1aa9e564d16d64b1e616ea09838534e3 *R/poststrata.r 75769b91b99bcc971e5bf3808fb2f013 *R/ratioest.r fd2544a8cb4d5217ee747cc35aeb9bea *R/ratioest_strata.r b22724653d0e7ba80c4df99f242b793f *R/regest.r b122c6f4e381461121006625138345fa *R/regest_strata.r 6852035727c0ec3c9ab6d2d85f6aeae3 *R/rhg.r cc40a03d7b7fddf52b7d2790d0513797 *R/rhg_strata.r f5a7f5e7fb324169076bed95f2ed2397 *R/rmodel.r bf4b40ee7262d8f14af763eba89a76f1 *R/samplecube.R 3d3548f11701d8a50858b15db0fa2682 *R/srswor.R 968691ea093c11bc866c59c6920f25d6 *R/srswor1.R 2a3f22e5754f8fcaa0a7cf656fba9e06 *R/srswr.R c14b989cae91ceb752f857f044bda7b6 *R/strata.r bddf8f11e93733f4393e28b8a2462d1b *R/varHT.r 65c054c0a234bddb75b4684cf19751b2 *R/varest.r 6820788410303d82df42fd8260c7c324 *R/vartaylor_ratio.r 369c55286464ce3a9ea558c8ef0ba02f *R/writesample.R 8bf50e09620f850bcc1645a4fc6dc5f2 *build/vignette.rds 2e07b4f45a90838a0f66bf366bb435c0 *data/MU284.rda 4134ceaeb1231bf2a3496f9afd74ccee *data/belgianmunicipalities.rda f0145264fae36530f1fde11d39353c12 *data/rec99.rda 04160e33b7934beedf9e42b0e58752d2 *data/swissmunicipalities.rda 9d7bd4aa988be067625998007832c322 *inst/doc/HT_Hajek_estimators.R 3dd623036a9fcbc5a67bcccaf3c3704f *inst/doc/HT_Hajek_estimators.Snw 5d8ccc9d36d6493017131188ecebed89 *inst/doc/HT_Hajek_estimators.pdf 6d25f79488022604ae103e034babcda9 *inst/doc/UPexamples.R 35f8db39afd2a556ee99d4501c7961df *inst/doc/UPexamples.Snw d2e84b157303efd1ceec29e53c4128d9 *inst/doc/UPexamples.pdf c4a5a449c9aa4be510841155de373d23 *inst/doc/calibration.R c42ef902ae0205fe971583d8d95dfb7e *inst/doc/calibration.Snw 67649f4f7902fdad01ed9d5722fc7756 *inst/doc/calibration.pdf fdd77c07c3293e4b43a5af9b4869dcd5 *man/HTestimator.Rd 31059113db9574c6e23a2d601c220414 *man/HTstrata.Rd 9003ccb777444503ec2fdf05f8603aca *man/Hajekestimator.Rd c4b4cf1a62993319ad4fe8fc0c6e34b7 *man/Hajekstrata.Rd 73adb6d709be2360841e69e9fb0df6d9 *man/MU284.Rd 2563045435c6eb648363ae693cee7ee8 *man/UPbrewer.Rd 56ba40465646056cff8ea940252ef39c *man/UPmaxentropy.Rd 099ab538ee3a988afffce5d710e9c13e *man/UPmidzuno.Rd 17b1f8deba7aa7bd0b9f4434abe1b4e6 *man/UPmidzunopi2.Rd f0ed9896f97357fd9fdd83bcdc79e443 *man/UPminimalsupport.Rd 5110571c0146563406d436b3348640f5 *man/UPmultinomial.Rd ba7efd8e0f16225430c64057bba9b227 *man/UPopips.Rd 3c4a475d5312f8f5637a1664518b019c *man/UPpivotal.Rd 58507abccb1b7b18bcb23f3ed1397403 *man/UPpoisson.Rd c29e65d32e8f80b544e82ed134d527a0 *man/UPrandompivotal.Rd ecaf67dafc273fb2c37c7582c9fc1a7e *man/UPrandomsystematic.Rd 2572410944ded9140f39f1804789ac49 *man/UPsampford.Rd 593be39827cc6d7ae26319f0ecbda5d6 *man/UPsampfordpi2.Rd 2f27f2227d9a483baacba391950a00bc *man/UPsystematic.Rd 518634b5186b123d758b1df7de5f8469 *man/UPsystematicpi2.Rd 4a4c6fa3c80eb66c1a9ed55ff533f08a *man/UPtille.Rd f57a7caa62817f7e87bcc374a8b29c09 *man/UPtillepi2.Rd 759ba49012f43aa328f0edafa81a5e17 *man/balancedcluster.Rd cf2ac1050213108ef29e7c942e6b8619 *man/balancedstratification.Rd 76001b85741fc62dcbce4764d26deec2 *man/balancedtwostage.Rd 659f97a964a181ff80e117289b4c8316 *man/belgianmunicipalities.Rd a945892669d27360b4229ad66e4393f4 *man/calib.Rd b219ca5976e1bd2a4a5af2ba95a3f0a8 *man/calibev.Rd 299e8c737fe8db3b36b415360b1c724f *man/checkcalibration.Rd ac12eccf1b6a8c59cc1485db8d551ded *man/cleanstrata.Rd 71ef37cd1ea18672adc2581fc994a58f *man/cluster.Rd 2331d0998cdce42acd317e15d8baef44 *man/disjunctive.Rd db506e56428e3209d387179631a08ca3 *man/fastflightcube.Rd 7348774da88a6e884ad150365fdc7a42 *man/gencalib.Rd 4219f78ef007f0213ccc568f7863bfe6 *man/getdata.Rd 555b9bbc8bba576578f548f4abc69644 *man/inclusionprobabilities.Rd fd98d1326817f3b87a4ed74e97b952b4 *man/inclusionprobastrata.Rd c76f9175f88e14f71e83c2582874c22f *man/landingcube.Rd 536ac93d3468243668f452c161a7e44e *man/mstage.Rd 5cdf5dd9419c2a777f8f68a38587479c *man/postest.Rd e1a87ef127f6295212c8df268715fe36 *man/poststrata.Rd 42dfc3a813b4c69a25b3a1c75c7136aa *man/ratioest.Rd 604d9e9c4b5aaa79afe02c4850eeed32 *man/ratioest_strata.Rd 596ae35a38927803c6515a2e3b7cc1c2 *man/rec99.Rd 626434f7d8ecec69d6231def89591af2 *man/regest.Rd 2fe8c7d49390edffa81a238b664f52f5 *man/regest_strata.Rd 4935e94c5a852add6aa238ea06ef5251 *man/rhg.Rd 3dc8c4fc0d3964616b1b9c629323b36b *man/rhg_strata.Rd 2e565348cb69144d1c2cc80ff71a96d4 *man/rmodel.Rd 0750590dbd3573ef427111e860f24adc *man/samplecube.Rd 63664b8889802a37267ab2d2727b77ee *man/srswor.Rd 92481bec2d6fca6b5dff4e98858cc11e *man/srswor1.Rd 0585354006fa3c07204be567972010c6 *man/srswr.Rd 9cade8207cfb07a9dc47c889a938a295 *man/strata.Rd a364efc8434566bc73a71218ca5ad9cc *man/swissmunicipalities.Rd 0caadbbd66e01000d024fa70769abb7d *man/varHT.Rd 675d6dc9f27f167493b6e203931c6a9f *man/varest.Rd 1836a01803a1830a5612cc38827cece6 *man/vartaylor_ratio.Rd 66c43c684a2acdc00780a3ff3c498bea *man/writesample.Rd 1a2fa79cf90ad39905a943ccdaa1b9af *src/init.c a5fccd459d68d965fb6f694875cc5804 *src/str.c 3dd623036a9fcbc5a67bcccaf3c3704f *vignettes/HT_Hajek_estimators.Snw 35f8db39afd2a556ee99d4501c7961df *vignettes/UPexamples.Snw c42ef902ae0205fe971583d8d95dfb7e *vignettes/calibration.Snw sampling/inst/0000755000176200001440000000000013777316644013063 5ustar liggesuserssampling/inst/doc/0000755000176200001440000000000013777316644013630 5ustar liggesuserssampling/inst/doc/UPexamples.R0000644000176200001440000001142613777316641016037 0ustar liggesusers### R code from vignette source 'UPexamples.Snw' ################################################### ### code chunk number 1: UPexamples.Snw:21-25 ################################################### library(sampling) ps.options(pointsize=12) options(width=60) ################################################### ### code chunk number 2: entropy1 ################################################### data(belgianmunicipalities) attach(belgianmunicipalities) n=50 ################################################### ### code chunk number 3: entropy2 ################################################### pik=inclusionprobabilities(averageincome,n) ################################################### ### code chunk number 4: entropy3 ################################################### s=UPmaxentropy(pik) ################################################### ### code chunk number 5: entropy4 ################################################### as.character(Commune[s==1]) ################################################### ### code chunk number 6: entropy5 ################################################### pi2=UPmaxentropypi2(pik) ################################################### ### code chunk number 7: entropy6 ################################################### rowSums(pi2)/pik/n detach(belgianmunicipalities) ################################################### ### code chunk number 8: entropy7 ################################################### data(belgianmunicipalities) attach(belgianmunicipalities) pik=inclusionprobabilities(averageincome,50) pik=pik[pik!=1] n=sum(pik) pikt=UPMEpiktildefrompik(pik) w=pikt/(1-pikt) q=UPMEqfromw(w,n) ################################################### ### code chunk number 9: entropy8 ################################################### UPMEsfromq(q) ################################################### ### code chunk number 10: entropy9 ################################################### sim=10000 N=length(pik) tt=rep(0,N) for(i in 1:sim) tt = tt+UPMEsfromq(q) tt=tt/sim max(abs(tt-pik)) detach(belgianmunicipalities) ################################################### ### code chunk number 11: up1 ################################################### b=data(belgianmunicipalities) pik=inclusionprobabilities(belgianmunicipalities$Tot04,200) N=length(pik) n=sum(pik) ################################################### ### code chunk number 12: up2 ################################################### sim=10 ss=array(0,c(sim,8)) ################################################### ### code chunk number 13: up3 ################################################### y=belgianmunicipalities$TaxableIncome ################################################### ### code chunk number 14: up4 ################################################### ht=numeric(8) for(i in 1:sim) { cat("Step ",i,"\n") s=UPpoisson(pik) ht[1]=HTestimator(y[s==1],pik[s==1]) s=UPrandomsystematic(pik) ht[2]=HTestimator(y[s==1],pik[s==1]) s=UPrandompivotal(pik) ht[3]=HTestimator(y[s==1],pik[s==1]) s=UPtille(pik) ht[4]=HTestimator(y[s==1],pik[s==1]) s=UPmidzuno(pik) ht[5]=HTestimator(y[s==1],pik[s==1]) s=UPsystematic(pik) ht[6]=HTestimator(y[s==1],pik[s==1]) s=UPpivotal(pik) ht[7]=HTestimator(y[s==1],pik[s==1]) s=srswor(n,N) ht[8]=HTestimator(y[s==1],rep(n/N,n)) ss[i,]=ht } ################################################### ### code chunk number 15: up5 ################################################### colnames(ss) <- c("poisson","rsyst","rpivotal","tille","midzuno","syst","pivotal","srswor") boxplot(data.frame(ss), las=3) ################################################### ### code chunk number 16: UPexamples.Snw:164-172 (eval = FALSE) ################################################### ## b=data(belgianmunicipalities) ## pik=inclusionprobabilities(belgianmunicipalities$Tot04,200) ## N=length(pik) ## n=sum(pik) ## sim=10 ## ss=array(0,c(sim,8)) ## y=belgianmunicipalities$TaxableIncome ## ht=numeric(8) ## for(i in 1:sim) ## { ## cat("Step ",i,"\n") ## s=UPpoisson(pik) ## ht[1]=HTestimator(y[s==1],pik[s==1]) ## s=UPrandomsystematic(pik) ## ht[2]=HTestimator(y[s==1],pik[s==1]) ## s=UPrandompivotal(pik) ## ht[3]=HTestimator(y[s==1],pik[s==1]) ## s=UPtille(pik) ## ht[4]=HTestimator(y[s==1],pik[s==1]) ## s=UPmidzuno(pik) ## ht[5]=HTestimator(y[s==1],pik[s==1]) ## s=UPsystematic(pik) ## ht[6]=HTestimator(y[s==1],pik[s==1]) ## s=UPpivotal(pik) ## ht[7]=HTestimator(y[s==1],pik[s==1]) ## s=srswor(n,N) ## ht[8]=HTestimator(y[s==1],rep(n/N,n)) ## ss[i,]=ht ## } ## colnames(ss) <- ## c("poisson","rsyst","rpivotal","tille","midzuno","syst","pivotal","srswor") ## boxplot(data.frame(ss), las=3) ## ## ## sampling.newpage() ## sampling/inst/doc/calibration.pdf0000644000176200001440000062061413777316644016623 0ustar liggesusers%PDF-1.5 % 3 0 obj << /Length 1500 /Filter /FlateDecode >> stream xXKoFWDj>|8MH M*zHs`$ZVaIei~}gvfKzy7Kh'jSD*Z$Z\E*MD.M¨4ZjVcu ݇iToN)[a.[ado ; !sKMpBS,Ls_!x3m%9% xPP(P'U+ LymuIY~6򣯱7_@2ExEoc5R@(=ňTȬ0ҵOuBF .k㶚Do\#1`0CX/Nf\[u]=Y¨$㣉#"^+9TF[WK"c{tǜ5_/L]PYiMP7hw49 |="Ba(|]̓**yHA8=FTt;>v+wk[$xE 3HvHiݕIGN#[a\ H)}?6NhzICWMsTeۀ}zGYl 1iAhw^o~C:ҷe޼z#'_78t6ˑ ˠm ^-ǀ_ҧ8jp2`@I6yacTAs'O0]Щ;4AYM's+\!Dhǀz![ sV ,;_|Q}T%LxȘSħ*TU O3 endstream endobj 2 0 obj << /Type /Page /Contents 3 0 R /Resources 1 0 R /MediaBox [0 0 595.276 841.89] /Parent 12 0 R >> endobj 1 0 obj << /Font << /F39 4 0 R /F19 5 0 R /F46 6 0 R /F8 7 0 R /F53 8 0 R /F11 9 0 R /F36 10 0 R /F55 11 0 R >> /ProcSet [ /PDF /Text ] >> endobj 15 0 obj << /Length 1381 /Filter /FlateDecode >> stream xڭXmo6_a*o*Q^e  +bˉ[$'Yww<gA_;ʛͼo߭.޾,uHDv{ҕQ@Ͽ4yxbRBHP&Jܟ$t2g ˪U:ýؼ7RDNu@w T^^ ۛ+Jj(n #);=jHOy Oc}t @~aLK=6%AL{#`ir}{BPX ޵gs6zBGr2!%xb*AҡOOkI?edO "MM4scqLpƜH7 d,M9+Cx J> y lNԨ @)"qr  %WNqTXA 6Q|󄢪 Pl:8Bpۂ!*Ȝ X 1S&TCT uK9ZGw"RN"WV'9 t3j$_@V+>WJ n{jv 5UڕC'm=F=s+NT ^ M^޴Qcvb#Yۜov#<7S+S)- h>l‰K4KW$ާ晈_S5#-dBX[\FPZW;a8w)QH߷d&0ˆ $Av!MR: z"*7rY Rŵ O"$IIq!}Q3PTC+]0h{i)YǷU6ǭ 08y[>\#tV%pƮ`3&{"Ȟv,nqdaizX,/*PL(w75ٜ"n-Ņ%إUӚ ]0I4JB/O6&Q'<bO{)2uȞ S6Vu%gw C &}o$2 UWZ)T]6W yeؠ#|`Snl'`-995рqicu2hU2HlɆ˴ݭ -bmկ~=Wm)$o^D]UkC 'VVѹׅ鯁ƪ{iWShFpiWSbyXo$}O2F$ YDu@.xTFh .*~> endobj 13 0 obj << /Font << /F53 8 0 R /F8 7 0 R /F55 11 0 R /F11 9 0 R >> /ProcSet [ /PDF /Text ] >> endobj 18 0 obj << /Length 1236 /Filter /FlateDecode >> stream xXK69AChR@6p+ym#kyG)RRoKr%͋7CEDӅӋUTuhzI!RQ)T:u<]Nd<$:!3goHk6Dqk8ͦn?$O c|  '$[Ǥ`~HqN\Ȝ#F>H&h}O&lbs?r6^t%SYC)H;PI? K&Ruqجi.8*:OKmu(z-+4>T_2O8I +Kg>!x@0QkX@:,:M\{$aW;e+9ǥGI,0fq ;< &/iFLj@Ֆ1 9F3ʽ(Q|I>()ל8 ?GC.ᄯ`Zfh`܈\ &Ɠ_/H.:eQxUy߽_gezE`_(WYIsh>sckv=4fѼT).?'cj@W, k!!˫Ȋޟǫx FOq'sޏԃ5_:<IRIAy [kޡ D=}76aiUEԯo9Wzuշts ti- RCtͥ<$5Kza2m\6_1L!\^0vcD;QMysn9c'ETsؿ%xD8;w0x3bOÙAO|H1R Wf][k(kw8;[ :BkgWh_eᙍ"U7,DZ.]9٤ @p}ߓu3R]8ԁX)egtt-nUQut31h\M9MΔr1d?at HAzcM0tȗ23A=ܱs6M!VƑO{} h Sa !> endobj 16 0 obj << /Font << /F8 7 0 R /F53 8 0 R /F55 11 0 R >> /ProcSet [ /PDF /Text ] >> endobj 21 0 obj << /Length 721 /Filter /FlateDecode >> stream xXQo0~WXjԾ!Ĥu4mĀRPn?8!Zd'9C kW;c ێl 'l`ڠ=hEo%8hOGq8kC` Ğ#ZZ-Pp6:Tg"q-J ^)m@ r k ;&}wDX8 pmV^8 c\rzLBJoZqySG% qWhnD /ĺx}=0i_KOnƣ+קA1P>CAyAsTI'vAUJk>g4{g\:>gQ3TITĕ\ =[rdX="@" >S92s*dqBܤ>vVwlMAgѽ (0%m O:rGYK.;im)Ӧ5bC~Av]Ѩ~[ATB96xP"ĠU~2ny^$ W{)p~ <@9PEࡲi > endobj 19 0 obj << /Font << /F53 8 0 R /F55 11 0 R /F56 22 0 R /F46 6 0 R /F8 7 0 R >> /ProcSet [ /PDF /Text ] >> endobj 25 0 obj << /Length 2543 /Filter /FlateDecode >> stream xZ[oܺ~ϯXxe'8Z nPڹ<ȲlJk;'!H^}E237Cv&f~!F?8= YJf73)@j$*_>?))֝el $빏8j!=)2Tj^u[ua[ͽknα|EMiGB&#Mk(~χFo`;gqȶ$ne@f)W@iBk*zE-EQh঴Z8u cH̖RyY(BddٗƆKQo:;MCFwMHq5kxm:k|ɢ"l2DE. Bo VdB+ճvqӠ Kc;G(H䐢&"JK@(hfҏfRT@.Ɯj p/ϬkM()ȼgx2""^Χu4<$B/Aoݛ^r=G 4N`c<ր-ywhp$ju$ iT$1Oi^JR%I/z:܎%?ܵǫd (zXgm Vva/d(T@AP_lZ,/ZK\d U?јfe3j o\?o|ִungP" yQG=%tO^#%O4֓eOokdv%?=m\WDbm15'QWTI0˝ܲ{xUCc]h脤 *3[o0ݶza/4tiA~=+U7k=U@;E05Xlt1~e8.z*-+ ݛز# qm546vGI](sP=վ1[hOvV&da|Fpt7!ݨMb giwڼ #^l@sA ,Ը\95?dOw^^N`'l 2yrd?M> 3ߔ \\; Oj,dgz"]Ej*Ct~kvi 3'ɜIx\x>55m8L%a8w Zq֥̱t%\qؿ|+R39@:NZ?@BR!TJ%sCr.;פj7ߦ2Jr.Ūwfs&rkz >cOoؕ [h6oLsC#\Mj -b7p]+z{0~yxdj}M$#?9V7+~ S>gw$Q6q׳o/N?'۫#cħgx=߹;&{f?:wkyCI>,Ne??ޕe'x~d4j W 8|E8ZuOZxc$۞њ!שG_&[|~GI,PP&_i{l;4prk |EҔ.dկ0 ;tdu;W0zz/{gWYӍ KBT-;~uwP' 'zTX;R陭p^gm/ϟѪ|:[B s+!(3sK'VѺ3x_4-~EF[}$fHK#͒yaYF?(ƃo_a]$( endstream endobj 24 0 obj << /Type /Page /Contents 25 0 R /Resources 23 0 R /MediaBox [0 0 595.276 841.89] /Parent 12 0 R >> endobj 23 0 obj << /Font << /F36 10 0 R /F8 7 0 R /F53 8 0 R /F11 9 0 R /F13 26 0 R /F10 27 0 R /F14 28 0 R /F1 29 0 R /F7 30 0 R /F55 11 0 R >> /ProcSet [ /PDF /Text ] >> endobj 33 0 obj << /Length 910 /Filter /FlateDecode >> stream xYKo@WXi!㵱HP)iTC#VAq Ox^?(5wfvٙa,O]M߳=;2eN3g27FZs8CSӄӐgN}NO1P]/bSNwff.YHʥ= &PT rc >a>Q:ߥZ)wX̙%J,CM&.*j# cN jnG<_6T,v'g&f6V6֋jQ$ ,$! BƬ乽Ȝ-!fN S (ZVsiP*]d[{,D퓊 g'=n鏤.*qM 9BK4A޼ҼKo2֒.mh"024O*imJo/ W&ωT64r8x8x4}L*=J U)r䒴k0oz,$\IJ iԟ?TqQ4e tD4k4 w&!U;!h h[ ;Ů ӎK+7_EI K ,"G!YnA$c9o9aQ80:]M/5iahlYDBWr]ӻpW9ꢳݪ*jhTS[e+8T%K~PjnRs(  rO(Es붎Rh6=$ShMP!SqYS'iI|ǚ5/H|?ߣ4+JvvhQpB*( sТO6Gb +Ŵ ur:GWibAoǹߧ !$!0T,3m΢6K2RiJfLqT=3}D4k *?Jq=ן5'+D7 :I/HpЌ?ꮷ(]Xk_7C긣8?~Wiͺ"'.jI]m<%%֬L%tkgF幎U3#yVfjq-QlOM,b( !D^ .XC x>F~Q ^1pns <Fl7FJesd,yq9sofp+ 0*H4$GɈr##i"i߁i)|i3 3\ 5 ɒ++ +-fuKw ˬE,`DeEQq'A.6bg1~}g㰭GaFØz)%R9׊HH^hK<=Nb0W$CB%T5,۞q@ke0Hw+n{nthAfC=(/kT˅lh5J1I+dTB%i6C(u)袪yk6'x\1M~x i,|}H+5^Xb^[}U7M5~I=,vJ7X2d3z+XdZc AJgt"UJ^^>%lHCP[@4Y]g endstream endobj 35 0 obj << /Type /Page /Contents 36 0 R /Resources 34 0 R /MediaBox [0 0 595.276 841.89] /Parent 38 0 R >> endobj 34 0 obj << /Font << /F55 11 0 R /F53 8 0 R /F46 6 0 R /F8 7 0 R /F11 9 0 R /F14 28 0 R /F10 27 0 R /F1 29 0 R /F13 26 0 R /F9 37 0 R /F7 30 0 R >> /ProcSet [ /PDF /Text ] >> endobj 41 0 obj << /Length 4042 /Filter /FlateDecode >> stream x\Ys#~_UǸuUDT$+>(:"%)k_n3 DDr4 \M7Ŀ''zb #]N(!r,(3.fޭ7xa fL…m=butWn^͹I o~:Jc(-ѓcdڑ ! MJX#)If.^h%˜ IbaϙX n$SmReQҘTӷyU! Bnw~YGH!rBxx4N\,4ME DhFd eaLD⥡Q`b%- O?NjJ BʦaD.-ȂR(ѐJġjqHxVCb:YGCЌꇑwaL8˃^"# J"1DɌBO]|?ݭE_j8oi'[wu.xV˅k [3Upf8d^u~r%J\5Cf7M3Ɣ)54qۆI4hrNT Tog_B~!qB;^,G Y!MN )aLg6?TѨ4ubA#8Gs69FZ4q5Z<_>}<d+W+} Mj!b8 Kx5!~~BluOn AQyA%‰bLHj4n*OKg*F9S Tb~.[cX Q`s >sbHҜ!CJdA!\xgZLw;|çkoV?/çiigS6Wy>`Α]$< ʘ8Աłubܖkͯ1Nx^mB .!-㶶^1v 4ʖL0,y+,xa9~tzy@PB2,SHy\)(އz8Ryq 5pW v[ )X1  v ˮƓgs-J$K:0R}^F͋9q d uYo Ȇv3`h`I{s>3$=K 3oU9 !%lc*#W@˃KVġE_=ԝ߬.B;ϊg=n9'f\_ 4^@/֢ {^|FZޛ UvAԫs7+p׮fP&hHQ6Q̞ؽ~'v/jkj+?2J]S+@(qvAĸ8Uk^A|av+E8fcJ jNwTޣ^QfIC^=$9'c M e`u%ZRx Y÷.L&UQ攖8,^>G]~7ķd-w5إ<3r.2nFґdy`] }ual!*w{],̸QقEͦ6:Il^CgRdd%a ^Ou^޺J(֑g'Խ=7Q +Z^y묠5Л0T%. uImRcNmݢ-1m+[]21"Jg+k7(G6vF w-V+M.,aHb}@#Z'Sm1InP,. W]aO AWv at%7dw 1M*l` +6JzQpQͣB{#..T%gg2Yf"4ME}e4%%XQ]wcs%Nz(_[8xKIxW)dSR͛҈.G)X 5x=SrT77KR,i,)IoJ|s=}RKxm6ғQT''LH )zsdӪDV;T 3x_pL/5O G))NVJBߛ z]Q[W |f] ! jҧ/hȷmPWUOEJ4BUaJJ@OWɑ;d7u_W8!_"#Sxo xS0S5jQcH8V58@(qtSӽ,T3PLɸEP +X/(v7РπcR=-o=6G en\j+ݎX ˲sB.h33h&$~|=4Wda"Sst ٝT)>x?w}fˍl{G~ MfQۛTuy}m3o{fX PbJaUݬeYk5 zEZD0VJZ:=h&|;9u[Uܛ}a5Ff^r2ǚ2,Ô=v70ƒ).iQrJ_@pǃX|[rZ5_^.L{]3FE|Dw\ۇ5)h~_b:70tC2F9LTlSih˧gO ېz ܑOAqඡEvϮlG{~eFٳC``ËVk`[mkڎ]WIPGRrpQOK2WB}œDЮp.8uAӮ7_"8x7{#igtwnŽoMΊ9n=s2JA @!TuxCw1fS'1G?Dmj1c*W*cmu%{bOvU7MHK-aMaqo` V[7!±5A\IO21AAO7(Dvת,yםiIDfi)ۊpכKl$g2! ~mPߺ}0nQID݊q>ã58<eV&QIQ89PM@ fo,ҿw]86%nsABv\0֟Q w(vV}u:j6̞yAbVgfŃ5P">xTl-xZ'yŎRb3DxtTDϵȸL0hETjCl(Jy;[_K22ʓ(G )L> endobj 39 0 obj << /Font << /F8 7 0 R /F11 9 0 R /F14 28 0 R /F60 42 0 R /F1 29 0 R /F10 27 0 R /F13 26 0 R /F7 30 0 R /F57 43 0 R /F67 44 0 R /F36 10 0 R /F53 8 0 R >> /ProcSet [ /PDF /Text ] >> endobj 47 0 obj << /Length 1665 /Filter /FlateDecode >> stream xXK6W9ɚˇDi@hiТ. Z6 GevdIp曧gB 3Zv 8g*Ճk&gfv"gWP$f8:Vy6 3^Fm_Z4=!H~;'L + >`Y.Px݀U aˢ:fO'}g9&|=BW52"oʬw1f:7E/;覾I#QXcL*,5>#I)E$mu F!|d> .]bP$7h9{J'"d@oSDJ~m`A\5#Lyq_y3Y USͰ%%jm#H4gYAcn O/*Oǩϻ/2f K|n6}06Z pILW]ѽ%Ť,.Lx%l{H.\,)R0z_(n:zCRUDvu jrrOM#oD»\֝1DRsz.DBh^y:KqqE{q{J{ ?˖JG}}\OUgu#v|J7Ru,}~֦Ǵ8fa5jj񈶟Znds*{;i9rT_̂tVMiTy~ @% 6XB!ҥ)]ZJItig"v."Z&TA~EE+ ψ_m~/+}aKWAUAvv坣,X$QAVO:@ʗpۣsuDyh?/U75üy5|;2v&cFe(ˊj: ? p endstream endobj 46 0 obj << /Type /Page /Contents 47 0 R /Resources 45 0 R /MediaBox [0 0 595.276 841.89] /Parent 38 0 R >> endobj 45 0 obj << /Font << /F11 9 0 R /F8 7 0 R /F36 10 0 R /F55 11 0 R /F53 8 0 R >> /ProcSet [ /PDF /Text ] >> endobj 50 0 obj << /Length 708 /Filter /FlateDecode >> stream xXMs0+< #Y;i:CO>ʄG/J 8!dii,̬Ŭ/OayVҕVhqIINcỢ:\ɕJ3aI y>;¦3hej= (KṾ#:J+q=5d-C; D]"ѿ+wJ<;;P2[LS7%um+b='5]l5!4hzJJƀ{Hw0e#f'qMk $N=:&zS1 ^+oM]Cz>hW&=L-(G@qTŜ8^ēE;fhuE3PO9cΐo}Ϥa qoގT.7mjE»$yiPn:4JwNnTfd &.<~Vn @u$q1JdŒE2+z;2i=ks9?CsG-IOHn> ɭ xL0E@bG'Κ+\iZ/b>sGv'8o3Ҏ9m699!wMTիCG؅۽` "us|&>7-3yVCkrf9;B endstream endobj 49 0 obj << /Type /Page /Contents 50 0 R /Resources 48 0 R /MediaBox [0 0 595.276 841.89] /Parent 38 0 R >> endobj 48 0 obj << /Font << /F55 11 0 R /F53 8 0 R /F8 7 0 R >> /ProcSet [ /PDF /Text ] >> endobj 51 0 obj [511.1 460 460 511.1 460 306.7 460 511.1 306.7 306.7 460 255.6 817.8 562.2 511.1 511.1 460 421.7 408.9 332.2 536.7 460] endobj 52 0 obj [638.9 319.4 351.4 606.9 319.4 958.3 638.9 575 638.9 606.9 473.6 453.6 447.2 638.9 606.9 830.6 606.9 606.9 511.1] endobj 53 0 obj [590] endobj 54 0 obj [670.1] endobj 55 0 obj [569.5 843.3 507.9 569.5 815.5 877 569.5 1013.9 1136.9 877 323.4 323.4 569.5 938.5 569.5 938.5 877 323.4 446.4 446.4 569.5 877 323.4 384.9 323.4 569.5 569.5 569.5 569.5 569.5 569.5 569.5 569.5 569.5 569.5 569.5 323.4 323.4 323.4 877] endobj 56 0 obj [1055.6 944.5 472.2 833.3 833.3 833.3 833.3 833.3 1444.5 1277.8] endobj 57 0 obj [777.8 277.8 777.8 500 777.8 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1000 1000 777.8 777.8 1000 1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 275 1000 666.7 666.7 888.9 888.9 0 0 555.6 555.6 666.7 500 722.2 722.2 777.8 777.8 611.1 798.5 656.8 526.5 771.4 527.8 718.7 594.9 844.5 544.5 677.8 762 689.7 1200.9 820.5 796.1 695.6 816.7 847.5 605.6 544.6 625.8 612.8 987.8 713.3 668.3 724.7 666.7 666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 500 388.9 388.9 277.8] endobj 58 0 obj [674.8 778.2 674.6 1074.4 936.9 671.5 778.4 462.3 462.3 462.3 1138.9 1138.9 478.2 619.7 502.4 510.5 594.7 542 557.1 557.3 668.8 404.2 472.7 607.3 361.3 1013.7 706.2 563.9 588.9 523.6 530.4 539.2] endobj 59 0 obj [892.9 339.3 892.9 585.3 892.9 585.3 892.9 892.9 892.9 892.9 892.9 892.9 892.9 1138.9 585.3 585.3 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 892.9 1138.9 1138.9 892.9 892.9 1138.9 1138.9 585.3 585.3 1138.9 1138.9 1138.9 892.9 1138.9 1138.9 708.3 708.3 1138.9 1138.9 1138.9 892.9 329.4 1138.9 769.8 769.8 1015.9 1015.9 0 0 646.8 646.8 769.8 585.3 831.4 831.4 892.9 892.9 708.3 917.6 753.4 620.2 889.5 616.1 818.4 688.5 978.7 646.5 782.2 871.7 791.7 1342.7 935.6 905.8 809.2 935.9 981] endobj 60 0 obj << /Length 119 /Filter /FlateDecode >> stream x313T0P02Q02W06U05RH1*24PA#STr.'~PKW4K)YKE!P EoB@ a'W $o&| endstream endobj 22 0 obj << /Type /Font /Subtype /Type3 /Name /F56 /FontMatrix [0.01204 0 0 0.01204 0 0] /FontBBox [ 24 27 35 52 ] /Resources << /ProcSet [ /PDF /ImageB ] >> /FirstChar 39 /LastChar 39 /Widths 61 0 R /Encoding 62 0 R /CharProcs 63 0 R >> endobj 61 0 obj [43.59 ] endobj 62 0 obj << /Type /Encoding /Differences [39/a39] >> endobj 63 0 obj << /a39 60 0 R >> endobj 64 0 obj [525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525] endobj 65 0 obj << /Length 149 /Filter /FlateDecode >> stream x3135R0P0Bc3csCB.c46K$r9yr+p{E=}JJS ]  b<]00 @0?`d=0s@f d'n.WO@.sud endstream endobj 10 0 obj << /Type /Font /Subtype /Type3 /Name /F36 /FontMatrix [0.01204 0 0 0.01204 0 0] /FontBBox [ 5 5 36 37 ] /Resources << /ProcSet [ /PDF /ImageB ] >> /FirstChar 136 /LastChar 136 /Widths 66 0 R /Encoding 67 0 R /CharProcs 68 0 R >> endobj 66 0 obj [41.52 ] endobj 67 0 obj << /Type /Encoding /Differences [136/a136] >> endobj 68 0 obj << /a136 65 0 R >> endobj 69 0 obj [466.3 591.4 828.1 517 362.8 654.2 1000 1000 1000 1000 277.8 277.8 500 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 777.8 500 777.8 500 530.9 750 758.5 714.7 827.9 738.2 643.1 786.3 831.3 439.6 554.5 849.3 680.6 970.1 803.5 762.8 642 790.6 759.3 613.2 584.4 682.8 583.3 944.4 828.5 580.6 682.6 388.9 388.9 388.9 1000 1000 416.7 528.6 429.2 432.8 520.5 465.6 489.6 477 576.2 344.5 411.8 520.6 298.4 878 600.2 484.7 503.1 446.4 451.2 468.8 361.1 572.5 484.7 715.9 571.5 490.3] endobj 70 0 obj [525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525] endobj 71 0 obj [583.3 555.6 555.6 833.3 833.3 277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 277.8 277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4] endobj 72 0 obj [562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 312.5 312.5 342.6 875 531.2 531.2 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 675.9 1067.1 879.6 844.9 768.5 844.9 839.1 625 782.4 864.6 849.5 1162 849.5 849.5 687.5 312.5 581 312.5 562.5 312.5 312.5 546.9 625 500 625 513.3 343.7 562.5 625 312.5 343.7 593.7 312.5 937.5 625 562.5 625 593.7 459.5 443.8 437.5 625 593.7 812.5 593.7] endobj 73 0 obj [272 326.4 272 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 272 761.6 462.4 462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 611.8 897.2 734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 489.6 272 489.6 272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 272 816 544 489.6 544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8] endobj 74 0 obj [667.6 706.6 628.2 602.1 726.3 693.3 327.6 471.5 719.4 576 850 693.3 719.8 628.2 719.8 680.5 510.9 667.6 693.3 693.3 954.5 693.3 693.3 563.1 249.6 458.6 249.6 458.6 249.6 249.6 458.6 510.9 406.4 510.9 406.4 275.8 458.6 510.9 249.6 275.8 484.7 249.6 772.1 510.9 458.6 510.9 484.7 354.1 359.4 354.1 510.9 484.7 667.6 484.7 484.7 406.4] endobj 75 0 obj << /Length1 1400 /Length2 6424 /Length3 0 /Length 7374 /Filter /FlateDecode >> stream xڍt4\6 m c Faf 5J B]= zD$os{[֞}u繮ʤ-g*#hn>8%o@ v'`5"Q0\? H(}SZ8 ||"  D Ep(Uꍄ; C8>11逜  u; G vI4UӓA 9OЃH-ke@+`CGء=H(ppApu;jCW(/_.|<|*'W!w2A0=`s5y^h. ;`0ls =:PA\(׎\VQS!ssNp'o+!USvgEB HDXP/ޮA_}]Ph;?[ @apWvC @@~zf-o+U7P|g^/0/jp; ׸8G ?ki# Mtsr?w忪Dݝ?q ⚹kh!o1/#m;_kAnca^P[]3 A`>-7_kuA?kNAϖJpoD /|h b@_v$ | ?L~w$Z{yq=oC^P"ıII'Jq2-D׏GrݭKJ쇲uau.^ |1)WNOm wgtI5]N6gWE۩бRa ‹Q_XlFqxHɨV@<L?)5۽Clk/թ} DI<|7aDC|R-D~9t6 hl+|ŗtXO/YL0m|lah1l􋋡p$Eؘ |q[RNØe~xgO?_IUk31 07hY6B/Q*sʵ˼Xn2CʐARFA4@|'\jT򷶋Dԓ@.(:C,A3[-&v[#ioetwno nC"T-FZ ɼ^IGuU75sIWL &U9vōYAkJ1zZ 氠?NG] {7=Χ,НfKlS@սHTc%WC<AF#enxG* W<4&?BR4tݢ%ƞ87ZgPVSa1;pzލQ)j2͆Jk'z+zFü7DZ*7)8&#\Fz)9,DDL,o|T+jK5mIΆEwqkeȘya]೙~Χ*h-#B٪B$ݿSˉZ]# 6"ύ }t,Kr ;\D\:6XoՅ&#g&Yzzg=C5q-}L $zW/OoOWz85+k9JDʰ:3?*oZ==$~unē[3u4pXEwMɂشjӂã,ߍsRjy]6NP!67cҝ*EbGx7I-Ѵb [CVC'5XZC)WYM{ Сq]WʮQ*ͧ9bEBXO0B! q.fWP^3@f^t{39ִŠIf=,qDNb =7/Yox Iaz8"C{+/i@·$CJ cP˶E%L f^}^%V7*؉8w gdwzV%Ou{$#TK[6Ow \b|)ga+甅fqXğEڵf}Cvï".s|lAK |JOTwc#,򝋋Iߟgwꤥܯ 3YL8=i)O 4_?ܤ* i3{^Z(X-4d!C7Ӓg05.A! b;I4{ -PDjl$To [Gonxڲi,2q>5X8u`JI e#Cvq1)2ӫO6AuC&c)Ze+#xF=щ-$ XE: WR"ЖrD8o.KٵoĩAOH40'=lzR:M{8NZurX,&C kР{epׂ@zغot,۬%iUDTy:.c~ٓqLw)OI3*އds )R [D?Kv=啨"b^գ{2ZQrTHm2#jC$ cx/=}g(;i9.(M$<9Y$iR̨_-6O]dTie͍tܭw|JL7,4MMLaq:~6 oBmb7jU|{' /gZ(#ԑޅ |0u3J6bIҍ-o.%WpmqP~HkGJjpGҹ|;1l55^ujTZ?-GnX#I]4aJtH ΀X¤b߀b ?{v<4 XmU&t'FY˜7zWzr%T+,uY7p^:2<*p"zG- 6;$$QU3 ~x79eGP2SWJEs$~-O󦒧j*,'?(ŊxIw0<ёɰ \mn81笇Jݞ(yA|uJQna˞.Y -z(="kީb%$1mʷ4Y^tgy7W$D Y{$n,i[rZWHU;S6MHvVt<pGr31)okO^*@yN6 m vdzxư"JpZ)Lϐ|Mo;;Uڤ}^ _Cx3U0DʻWs Iſ{]) >Z?JAxìHtlQB[c@c0KYBT{ŦgخD' hwݾs%N&:挳(rO'ť[ǣCuE+$Xقi ޑ;,J+Wf1Yp-EB n9+lHb"ju.{W}ZSSZ-"TAxǃCo=gIǟ6(q g ]Ψaj$OHk@ǯc&cFRmmP{j$(&-92.EJF?>s;"X i1tA Mb@9ҖϋH?=z|ʈhk!-L_^S$1!4x8@2;7-*H9򦘚{-2W>N|c#C~ Ȣdw}KS6gn>p `ίySA{oAVBX&J[cYNPnG)\euVa0)MNIO- &ߥDhWX& p4.;j8Gnk3:nh_WH M\M %:5ǂيPRs5Y x2][~$ÑI0%&Dx_FYf %=;YĚ$)X $cQXǏN`V(ʟW7)WQf٥ؖdǺǬb"{|b-[[cIh~^;~YB9p /8yd0JFy0Xs-gGRPΓ)yplų%ZH~A F٥JXCVTd:8H= i9`_6I[cT]#PމP=I\"gÅ"zLt % K)fW<o3D)4F_V.s,X S[dM]>•1JN% Ӟ>j2k+[Ow U[$-2¾SƾiMkvl\]_v%y۶*M)!v>-X]e^vfbH{wEq!݂; xYgߎDž%u~3&< -d-$StoKrx'dZ;$7e Ԋ8܄F*e*e|c9IڵT2#Ru{ {=*A(M Ϲ1<ΰ4WyJjL&=?&=^{ܒ&A:̹2[cht͔/@s ]ޣ(-E5Ͻ9yv &E7"IcWC#kꝗI Hat4a:dQ>CSH=; ΟɼՅ`K*Zxݪ_5kux9YoZrw [7)jJm_ᢌmEPhdPS@ډ2iHH1T>!7q{n€U3S;{`mDńZὉ̾sCHbQ̔:IlК&hsPCFrG-%vCۻkmP{eWjlr%foH>;qJy-I D`]VL}tMnI71EI9b !ͷg 4z7s)^OHH詒H -#b?혅d"W۸Ql`Z5q=az߳³=}^c2zS@//*ibj6:>6ԢJ 3 σL`RӦ,p=bvqwBĔJ X•Ի59.M#"}!Iz'Dnp[Y)?j}obnN陼聧:Gu./sH7xuVr4 \B;%L 6b<-3v:oȏIA2D~{ƹ.|Υ@-wqR#lX->Um*J Dk6T`V4hQ+vhqu#R&pNbOVk_( ~ZHN_N2HϷ(wMٳP 4cJ=[Ƴ~{y}kq|E& > L.)j~;CYӰ,.7L,o@EVWW̻%Sthd;!1":X@ᴡx޶I|ۉ;&QLPT|!ս0 P0tsH) LjP}4r h{`]+؊9j) r7)[xS VLP*$+<9vq &9O]]HHx j roKQ:k(G'MqS4t0s# tKk}lҋγEt%<А"e ׈l7K]F R<5=0)H$G<ƭgR S;قo9m 6?/ηaWn = (j-v$N#Jz6ghĕp'c$ 9 ҹƅS d훛F,V6;R\9$!Pz3ghM`uqCRS*6)3[Jl˴! Oȡ]wƟrb5%q(WX30ypo /Qrr:.8~X?|ﲀ O#))z1{8ѥcĪ$u1]분PBD@n{TOײ9 =Qfpu˒cc`8^Q_.Ha/; Zh޴<`'p~4k5"ڽsfώHr.,6SN_MqѪsw勺(u3M$oKgraIF>9yr%*^U)n,dԑ!2HTW[yu; +\Gefǐũ(j4qF͘?2]YHF {$’U7=toVZQJ(~yyތ3nM#[hmhG `@'-F41,W;yP5?a74u endstream endobj 76 0 obj << /Type /FontDescriptor /FontName /HSTHLL+CMBX10 /Flags 4 /FontBBox [-56 -250 1164 750] /Ascent 694 /CapHeight 686 /Descent -194 /ItalicAngle 0 /StemV 114 /XHeight 444 /CharSet (/h/x/z) /FontFile 75 0 R >> endobj 77 0 obj << /Length1 1508 /Length2 7589 /Length3 0 /Length 8593 /Filter /FlateDecode >> stream xڍtT\5HJt9 !-) 0C ]"JJt7Hw HH(%RSZ߷fssٙu vH[*(i+  пP; @ǔh6t ŤťB()2 nh Pwv%/ n^篿.7@PRRw9@C6^v !pZp8xxJ@`w~$^ pCݡ(/d4~v FA3EK<vP:@] ngFpb0tq#|{ Я }]h HW -A?`/( Ŀ BP}(\m?A,C"}b?%TTD @PPX .*w]0}S!l}NmOp9 ܀A pct QKl%?w;Ƀ]ξ2@O6= @]E=YP@;}pwUNq.č~ 3E=-qB?hONA%Uݯ)Q(/JBA8A}~G =% "uhT~~#Iq7D;(9D EF{7D<VFS RDsۃhߏ M#!M?轁ò&@9TO$WQ I}d k*\'癮/_Z'菭7̎RVf4qV=f{n]j>E#64 /ƁύYOg۾a2NNg0i$|.o,{>Xb(FFkFÈuB>8᯸A=_.N#2jV&uNh`deuRXdDo]﫳Af yVxu.^_W0']Oq[gfisz%9^O0oq02c~lhGp/)kƤI-M5ZHn:ulCd6Zq3\ +2Ŧ;Ji#4/ 䔛~hK.?X /+&GpE2J W?!jWhzn+'ڤ#PVe=&mGTb32}YQ4\%:)$f՚9:U]{\V]X1W2`jC3 lM^[{VD 3-Xn]3i#s_㉚֒t( Unhםcik$,3tOd3tA7uߺԭ>F&!c"\/":Pr3b颚&+1'x.5g `r$>)`R)fO\Lgg[W13`ty FG} Up DCtE+`A{"@aNc'5< ğ_ډxF%9F| ʃ)~- eAZ0|7kn5un"( ‘d3}a@᫅xKm?h1yZm:\j` 絶ewls/̀ei&ɮeD9u5فgy+)JC"o6q}]om(2Vlw ~p&tnH N_=iH<*o6i'5 PN9^)]h }EjI||s}P5$|Fvr]f|շpf7R&դ$61JAoj:ݡ%{XjU܋i$Wx|)[:Y-Ha;2")%q>Z!qYHĪV<. TYx,X}sw^*m֦\=:?R$7DerLEpE2*e8-n%4ͦiHWUq9S79H/('~TpQqGʏ''%OIB~(>4/<&Ǔ6$=wV+Y%`fƻQ|@>i%O3En{YxE*ٖߦʲBkjR.j4Hh8{df__%磳SuV< tm.L b4Nwc]B$Ypu6-1oRRW@ .RgqfR4{x 2h8۽<O%j >3U@@kzcpIp W3bRTDzɐ[iMm |wK?e#iX6h(pzQRA!{~NMlpQ ͖ Bݳ/1ogypWd`ΞHdKݺHO_t|Lݸ<aH\<W,=!=WBꎁ}MSQc|K QѨ$ֵ9/JG#UܔT_ iL/$8r=vl)IV Yߑ֠.|:=M9!&;F$ۼY\<%B6q)+Xs-&]Ӂ~$2"!g7!;ZB!.*2`ГH3\rŃ %ɱPK mUv'_DBܣ~jKx ]Fl<7M@\ՂT'A/dÃ!Uo'~8%K/Ai([T? 02fTzAUfmC\{1cgfjޡ{u}Z@,n坢3aX@]e9 H>{ӍeD2b }捘6 }ULi"x}ARtg7'q7mxDUoQ?Q[ ŕ1ZޖҀ Z(x5(ћRҭm|喕0ol?[YYSN%XxvrܳR*"]ozj6y',8XW(o*eU_Oi]l1f0c)D'"&o[O>co3=}{⊰/3:6Yr@̢vem%=$zGw&+hDm{N?KpFfM_V' f1fsG~#-)I693 L)yY/`5ޛ㾬Wv7:"?fX`AϣLXrHʏ]XZ_S˜~B'۹g;xCbkEa)XNSBvޠ:Mn,P~RxM`vlI4SɹAvU-5|ɵJE}bW:R҈|C>L&Kդ*YƖ5|a,QHU;x0]wڛ%` .!%K Tv֖.i2%O!rС̝|8'j7=ԯpczCUaK{̼O™N6-2Qvr -єHU4ӉNd&MO)nOi/__oXz}7a$l v%`1$ۉp #W"\`yYbϗaᚉ{Qc2!B,}Pf[N<\='"]ҀaOXQEf21<C,#ce=:x#aEbHpI=xKè'Vnh*> ⧋DQńa?;sߓpoKRjmru{J," 6q݀Vg]W&oqdQbX(}?l[O خ w4pv U K*s,L7Yܪ=kɗJ+f d0;ԷK6Yi0~G8tӕiGK~Zn l1R~:Z Vo^~|Xp{p4pT KN\(.U \*GgޒW ~N ws&x(Xl fXxȃmjvǜՇ"s-7oczdnTpy=xVG[rpoQS'r!,Wc,3~_L#NuAkMR]ou5(mr(:vȯls!U!+&fllI L :ֆ 1q@Xq{?>9罙(f!"Č6_!Vj}Ee"qtp[V5S)t̜%Gaډ%&p5fڇvāAk[&FY~91:#sN][r5W km8 gŬ@ ,3Fa+ʻ&FTݯ:1-ؤߕx0귱ShK+t\*B#L\h(]ˆ#T!JtM\'O;]VC)8mGBr VQ!Yai}'c$GVfP1GG mE|6$ rɅ9o3䚹/P)#|hDUa.Gu%S_7q.EĿd]O?<OuCk{ʼ"|G#nɛF_hRȃI'Az8JlA2[tА^GkSQ ZԵm?lĕMy7R[Yվ(wyX>U^#nb=-߱rbԣw:O3k؏h1{L9>l<\|u k6a෷9SS$VLwkg_Mq[oNDԄz+Y.YBU2Nx2 zqUjI{f1,?C3'YiWtł23`p'<@ܮ_KupB\eˎ~.0/v ö{|YzI?u%u s  qeB~Q~=$ n^أd-(V1ԝٶz: )s$|YDd1x_M85 .N4@{lJUYkښ fRY- RU%gTxT^WFJLb*1KꃝM%a<2WkX~s6C^GR-P< l"!hꟸAI9ԍn0" 5e|RW=}:zjQ9[Ў ޑFv;z-iKhjoE- ZU+q 5-|1 {K |kv{Z&ʼLJ+|l)LEp4*Xv6(*2B9=n 4 f2ݨtQ6Uex %>EeIcB˒@8F{jJlvMw sAa;ПB@xEeO,mKP+V>ޅit[8Ӎ!ac KhwTlLRn-[tm+sgʺ/T-L]Ox}k B5^IV .E[u=˲z R'bz&DվE+㪤j#f\sH Gz-9bwJ[=GSܔяu-+ @vYWZzPdJ}|2cg` W ė&Crd#Sԣ}=t:Hو#> o~g~:sƵEW<׬oo,yDdr}USƞܑn$<">dw8w^oGznS}l={N5N뢆y8h.^~[=gɹ>w]_;X uL3$1cL˔7KuVɸv#*&-zoLTww7 ʫNs^)~ Zf=mq{W:|@Nbk,ؙEҽNkVM#Qn/U|7)_&bˀ+*p e"QmIZHˮW o*u͊߉.LRpiND {VEؙQ7&s?%_dߖFLKtI$;,ze4M Z9`&7a]Ф:6y\^-BH(ko #J 1[]jrX(ckI+9WTE6vj9<#:%~Y6X+[qU,쫪`]?MX=$ľY URӀa]+2_r>]Dж.lE$` jzTcEƦ]a]o/?شW80*-9}цƖGcNJظNOꞅ2BsA{%GDU?`)tx#7NK(y~/X*:绅F]˽[+_QV/;)M-^cݜY]UAP XJ_`7uN&ʥ'ͣ3I1)l^fpST`o 1W>j#2{jX)\m+•6(Jrp]، ny'hJ$)*7b0)mTOPʮoc~  v<4 d^9 04]\sKoTxw_aʯQثcȓwgGf ysnֺ߀MsZ6,^ZCPYQtEHu`=?B*j0}.k(VbB)?9RVWqCg¶AO2P-iWb.,Zk0+FG.| b&A2>K/Ky0KQ=1=W| &zz" m5i: r?|rhͲ//hliMtv0VH`^7%M"^JYIa..D^x5i+&+N(l~2I-qcLr۵ zl]φmV1ǎaX2Q- OI;4嫷>r=M㩈RXiTil>h9ڽ.WS(QIZ9u8&rn<{-hI%ʊ(s>1PVd>K8C> endobj 79 0 obj << /Length1 1440 /Length2 6267 /Length3 0 /Length 7241 /Filter /FlateDecode >> stream xڍtTڶ-AzGZizE. B"E#X] MQ*d9k=b70TvD8@5p H(PU@(BeCCsA0\?H(uS8;$ IȀ$e@(7}a]!=M̥ @œ]P %~=H Q.P!`w1QW{x ! |?`"}_#? sL\`' \a(:Ewk=:ܟ_`` ';#G p_D7:  [4  AzE*D7K/}R}ÑE/fŧ-a`;>~OzIO;sO&VoU+-̏׳n,L>EQ*,`^PifV-maBNEmHM}34tC ķx%-qwC 㞅-"7>qZ~rC{s}ޭc~r3D/<, |^Tz ~ɣE;qIU*oG)r(3bI:g1{n6n&0~zDj=N{n,Z7AtH?t*u`y{ [,ul o6 ,;dz#h4ڱ3檬@fA0^+n˚ŷ$ LBµCR9_"nK ~tV-&/o/:V8:d! nO^ސw`|ϹER״ڃ8j ODBB|ŀUgo6l}cwg>qjmW`H;6Lݻo_oUn.gt*-Y6ZAUpv'I|}Zguc7L^Xwlt2]CDRNTuZA UV8a.O|+MMT;DӔW܌՞u^YzU`:݈֮LZ{95} ۚJ~k4;X̙7Bd% 8GܟE3_Z`Nw >4䀀V,&g"4PYyOsj Ƃ uV=;2I^1g3ν^PW={g5VgOr曮6{x :ܠ:F]9 Cw J AlzYJ_˄}^LU_qrSe!/ʚgL6MX7*ڋ ؓ%afUqѰ{1: N3p49d@3=?ȭIE[A5PG]j<-[Ge<ũQi f*$~\Bá<YC KU/*XGܲ8^Sy8-D_nA=IVK<EԻy_f`ٗ#}y)ŝAmu3"&Qk/)KLCrd&3ˮ(hmկ<87Vz!F|dY,;şwltݲ<ʕsN}HvRgYJ#v`.sF$Kz{Zimy}!; >aUD VK}{Z⢙Vg=k܍Q6%D#)qrLbon'b#d'Q_YѺQ21UOl*gɟil+ȗ˼Y^z 0Ӝ>$!mPc;XTm:Q.廫Z75aag^\V }! m&%al X0t j-Jt$ȺkM c~VBL&ETOz-x1zȂeɗAS׵f[Ճվ:x&71RevP.1c쭛yM" BăWе45PO/Ki8mcco_ph}afl22zlxRt]!p)*X@#|fݡɈQ*oP,IDFԮڷy1R܋$8v$踳͕sIl7izJ k19ñJ4QN|J8ځa+]Dw2،&6.T]k8|_f65bvr9d& 2ht|}bd"ڔ}|*Ml%[68.nTc\2G)} .:'zS\qS9uz8L7MTOm-%L"# /3}e Ҭ]:SprETZȡ$J #}Wh'6GT ~d]O~VL[j 4ͼBA=|uP[êZ+W NZhqc(v\~Ē0qWW\,wbw^ K!M->R1 :ru4JJٰH9)$!uId ~ֿ[U^,椐q7H,h$g\o˂lXSo;45>g6 } gƟ6 MA:lڠ'}ioaQkߺbBUc.~.6DQkx kgxC^9jr2DEv!Ѷݫ(%>xUݽ$;V#үV_d&{t? c/<7Mz3l[EU.cEJz$HA,7ȱ\Q8pE>^lJwOU#O(DHX~AH'$)C\O 4xߓ(ڿBJf; lNx[&R/6˫&H\t76p%aybMzUFUJ6$Ձ!6&>~B ShwXkK^Տ/ x%1`d$H)B28ZcyyEUUFzaIx{ HHmgL #Bz 6Us+}#5eU)m(5<ո/:. en:hQaayۈz]ਸw> 5PQ+sv{6?yg<#4??lԡ3V7aP$Ed69+ZL sC2W5όSNϊ-Rɪl/\ӈj3=20V9?.7<etts+abƫL^,bOdQOy8oL\*¯8 _eQΪɘѡejHS$ קR>.lzSFsk9Q7tX'Ϛ;3}"@T9gGBȾqZ=`f-gLY{.ԚmVGTAenw̜ylݼg&O<:? ?}Hf'RUPOn>H~%ΌjxnA2U|,8d08X,Ļ|1'^ ldJN^lk@Z?*&sIOܵQ)߱eM/Pȃm>̟%n:E. PT -DPŜi@@ { ͏c P#7, WۊF7*EmRlWŠX\o_-O) n4RcXɨрR^eT L@KlK.Ǟմ0 !`W^<zlEWa$Q|.&O"d.S|r*bo<.Ik+EJY׮I4JW9OammtMv9އ L(Gţ(lCɾ`*`[~TghIEJ?PM%{/̷'!B pRmbkX0]ipמjg`GZ,!+F T*,XJ1, &kSV)ԬvAS}wW\u^gHFy&f-N|gr`|z Zf<'H/}" ~=i2N춼I^vN]X,>.ܰD{<Kd?]0&<% xL\i;k-fqRyhM @_%Hݯv+:/Ȟ-P9 &'VBl/W JBDed0;;[N,r 3_~R`$0 ]ifg[@.Kςt endstream endobj 80 0 obj << /Type /FontDescriptor /FontName /NABPZQ+CMEX10 /Flags 4 /FontBBox [-24 -2960 1454 772] /Ascent 40 /CapHeight 0 /Descent -600 /ItalicAngle 0 /StemV 47 /XHeight 431 /CharSet (/productdisplay/summationdisplay/summationtext) /FontFile 79 0 R >> endobj 81 0 obj << /Length1 1825 /Length2 12084 /Length3 0 /Length 13253 /Filter /FlateDecode >> stream xڍT-Lp .` \5@ctpw nw%8 .];3Z^UT묯)ީ3AL@2;(3; @RYY ƁJMڀcG9:!vbH:gLT>9<ll66!)3 P؁P%!n` K:yЙyۂ@;2j }^hPAPJA'd mX "L0r9:[mAƂJ а;PC] l sz`gr<PWIVks,+w"@SS= lg0ۀoeXP&7hy:6@g2sd:8m~;6KۙIBlmAvP'IAZA\?xww@_u+Vw_Bd*gt(]Yw"66$@[_g~>2y svAf땇AY\,l\N2`W;0Oi=p6`;;?)3~F {CQ47UO,/U`UXUF|w ?ys?7΢7~=_.-o`?_{jO?ϕXsA羬+>S؟W쟵1"U s1daF6@'p L?8:>}72 2E ZU^W0o !\p0"C{'~ĩg/(ZH8\^;ب!ud&ٱ 7}|1qEB9$A&P 4E̢Wӓ{ ^ BPJ[Gea O5hɀ&9!mOHdOBm7q.XkCK=~ TPli). O8&bf%I*t  7Kx)Y[fCE⯜Sr]+e?IB'?(&˿ cR~,8l L[!HNeGetI4/ŲUC`6''38\n)_Ý1笭Mf". '}fS^;`ijUK J|2V[_ks#!E{Q,ae=d1f0*Y%~ 0΅~*&-xsz`E晞ND*pي.Giجu`xݮ-PqS,rh|p'g Y#^b.wݳ;vR(XE gRl6cjDU'αh,&HOM@ .# =\[#ƉuCt06W!9җV½Y66Rm6u32()}͸rr51oޘ*F3, 2#DVร[^NLx6٣oFhDA3W¡{MBVm.Wm Rי{6_Y}^/ݤhc}gq̂בVs<”&iB;:Pt2ׇ^֭.ljd}|!Bj:Be=E k!%$$pՈZ h=uzulM$WM$JwJ|k#efFsКtkViE-dum+~ٶ%H8N8ԗc1Fl;a&^'l)HR'$N #?x 7AYhez.r?xc mucH9J[ʡ)@@< +;~d%OT CgLy 2 X.V00\r= ~sLmqv[4dS?y?'ܙۋ8˫LJ`k-6HwW ObۡV%hK$kOp۩D\hߣ͡K܊ΞO9ݨ>xWg^2Tii&xtuRj&P~]ƞ k K)D՚'+q4cj/ۂ~䁒&;%aA42"PsnbnF9„Jim6:/Bž42^Ym*6ʚ5dMw*U%]-b.G>XHO[WVSv(Ŵ_gj&W^Cln5H&z@}}ONAK NQOr@A{߲J9MMv`V~X {c2 T_|5*̙:eVxUɱ0P.$ZWVA\]sտ۽mPODvH>@l zO4bR勓E$}nT9zG˘:RU\ B%/VQnk+aUor4މR,RW͠/$b`]n=j~f!~V/#~!Vhho]$=UoG߮K74\.S(p? ;|촣ۜa䕃C:!KeE hBz_• eW=xvx$V\} + XDNa7o:b};59G+{уtQ|Ī&mK3kĜ,r,y 9lL,˥CU6cn$煆ґ~DTæV؆Z8:} 5FPh4"+m9M#]+'6NX㏠H)5 Ԡh:4'^oCZ4L~.soT4Hh)9Ptu_4ƌ{NhQoINJU4'q9 dґʉvލ,L V\}Ne>S!>dd9r۩Q (ީ6Lh{ 8鮒dÈK}Yc@2O Tt+j/$(K#/aDS2oIY  8ʃVڴVl<¼˿:!.1C?~g}k"`}Ǻ鱊;I ~'Kf?:נ|"0xkEeOMQ-1XER>>٧OgN𤙆{9~ˢ7;sHQF+Xhg;~fX{)qqܑ]s4fc)o)-PogЈBo>ƱLT=?>q=Je2L&M5?570o~:靈Lz8حe9d#Z5:Hj=œEJ]PP SxsJzWpo3ʃͫG(9hR+L9)?H&$#K XU 5ܮop8ԯމZSQ7㘾osa ^^睑h()#bOx1f8/ơ`=UDVCz Z0iϞtufrm[\XqITfK8-,,Q\$=gO]R:X,G@ѕ8ZY&__/$% tu*وZl0 z/ZoJ^h/-2y@->[Xb7@x0A^h%n7{e r^<iwgB#|xK7GA!ݧ{nӒUils V/G=&{w66lNR$UODߜM^%R~y'u멀Ft.OŔ0)*%D;tdwrWseWv3ՎO|\ʤ o2y^!"BqG9;B&7M/P3 Ce}|xi¬/6#}I*v%{3T K97I7QŖ<96~a|K&66Wص:!b^xɷ^#h? 1]";K4Z;Vy"XI,noJ!DĒx&0ߎdMI)Ӆ[x  z2(dhSrl}Esʟ1# z x抖xv8B[$7ft*tNַ)@E͢ wmǪ3km{M7I~hΡcx^Mc`[UROIE/GY0ie4 NZ9W ԩIhݢru%PLnD1+^}ŦJlh;!r=^+6MMq UuCZ #-œT >V;{6Xu0t~,^pDdjxp#2͈o OH̛ɵv.>rzޯ w _:Hr謢L6=Ll8l6 Gߜ]`J'ȣeN kn}!K%5fpX>wC4x }XDjgԍ%_:4>CV&+oI&X޺Rƹnc|i$*S3:d𛅜8 #j2'+ִjl99hY8.*h-D"B`8gUs h-w"koLPO-@"|SvDy{SPơpciZH"b%\Q(iEk\'L¦|yci?KsY-N$ae`;ԲuSCܫYz㓢dU]{+xnÂ@< H()2,75BnǙ{ vp0m}fyM{q+5:JtSuRhﯡJ7\3ktRD=͇ƿK7m=iZ~6 Y\͖^hzKf BJ&& H0Oi|+Jep+2vaJweVޙӰ%`#z_s b" HTΣ$Q9&|RvQ߄7#>s7$I*?u"xf/kiO/ž]IVdti!]M4x)l!˜pHktqxA7?)! (3td&O u1~TyjE}Oo-IJ9@bWuCNɤ9,Ý;|oк $/#Y ]b訞,$Ҧ޵=tY{xs}D^n Q?z0lιK<F僈hV^:sydz29;q%>~ͱzk+uNUjטT!}PWk|U}@9N,.k$_s/[9`4[ig(iL_$>VpU_!n 9 XxLX7M lν)wGiЩ xfJ)]Rf`!=A&[)AdpcU?~hj !N1] ].Y8gGcΦluWc/P'ӃoYJER<oZlg#0{E*TB8nA ,Xw`G4 j6nee-׈ڳC~=V6&^:0ϼ[վpA4w+R=X>H*Njb.M<#yiZ^f Fdg&uJ! 48-&Nvӱ,MPh(:~bw5XB0o4LDYk8/>4`jPGC4 r@{/f e"ѕޫc z y=HyP,g҃kAI?`F:_#5@qS+TSa46(xBkfo@3_mҐQ²~wXl~?L{W7<3a!= EٴHN(N#y>ӥqKgz 2@]IءWY.oNnO=Ϊ^1!'L[ix#NJsx[U15 ǐ3ĝ(Zkp\-]/Rbck(9F<%>y5=$$_)cN igEb`'Ni-m}U(@r(2L_@>{͎'ͣ ݭoP 'VդPy5Vڽ537V@4:nMN-HioCxAh`i [pt^lJL4-5"y-c"mBke*y0n֌/YTI~;C i %&#f_k=>m􌃯kYvTل{4[d_KWc|@itɛAA1/9D()sDi/G1P)LIJ `9*ZsV3v3ۭ"a+Z,;I ,_f5lzD*ߵqU Vy1{/*mn*E+̈!v Sk[beP\hY}uJ"C(?Nޠ6T7g|p u;3WPO˔=a$Ȅ5:Y;P+mp$r͠M9F-Fv6#p<Qvg+NE4RPp?-Zd cVzZ S=(}ta9^AEߕ}wFRW aqQfY4R>y} #Z ,>)I쿸uwwQQQnT0^@Q-]]V}w{+x~l̔{r8sNi޶쫢#=hk$wX{ "=%VOXM*,jhZ/6$mQ=Р(,,F7a$,uQE;3bz1^vd\J> 6.N/UJu1jo=i6P}OuH,ÖXShbV!焹|1k<)+l'n6=v b9\{O;bqcM9 ,/b5-c#[Ds '[ݸׁ)v2ଐc9sDk6k,%%*dR]*`KJ"(uy]=-YҪe|bś ,qOiڞUnHqo^ksyaX>b?Bɋ "3T2?,Sw<Ԋ/]s$sQlY]f\'352"\L|-7m`f/ Zrsnfn8p"D!{l*%ow[RP,דLhoBCpw2fyg T81 F"fT]nP@iF :$He龿 ~0y\p!qYjNrkXtO3xR]!-SM7isȐ}G+}\caPiRKБBF(:lO1=7玄8O[-֩|yeS49Et%oFll*ѡΞWr 4'XQk^]hT-Af\\ewfmqj%ŇC&W4  1<(_Z7:q! O"QL!л CK8cqByOXy_y'`{O~<8wѿ-1D9{쑔#_Z8H?ӣBV X@&,kĔKls,F0 ѦܮE4Ƞ榃\{9y}#a.M EBܓ ֭M _'tflDqK 0|pS3 iE3}h'vINtk+d){c@vZ|Mݘl|00OHS|:wz"-d!/E4]ʷڙ7\?v Xʋ#O`fk0{-<͢ `5#ܕ{})j> y}Z'=qGͬa0_Ӵ(/`YF).SAlW$fpZ);,e$ӎJnCQRQNa#EoShsxg̢cF27Jж*CPM*u yd`BcrЗhWf,bɲ<w=<rs:DvV, 8+@+ (+|qim ۨCTh%Rk*ѝV6? ?"Ozi佚';;mM32&q4Ȩ˺^jq\RdG59$Rr )fV%8߈l5Km?vp4恹H{Zn`LѣFv3[n#JWԠ+^k ]mCNjMi>ߓ.fEP' XjyQKyWl{lHkN cUX/;d!O ʂ He&*dJ /q/gKEhH KVe o∈sÐors~jYy3U%!{O2'e>2D"Z:Whr #ҷrp(EI=) Oו™qHSA-hُqtw E'kO J+ NGt ʇ VTi'vH[=6𨑔ܧhQԥsw:8VԉfSV ngI854x]^=~l:3S"o~-nkYa&:dd 5 Rq},.v'v/A/6׾LR %BwT‘,{1kds\ʻ-~b"ڸ}|˹OܡiQ޾2.fEX`=幄:Õ/V{vCEׅ1Y3Ɂjz?10췱ouf#sݍV?"qߏMwЀ]6ցI܆S^=1b.W91YB1iS`|WǗqC[͌Vq[>.|q3$i ):HY6>2nBYRU;侉%2!};J҃8{^j {P }LE.ߑ͌xQMyGV!iCُ,a՝hw6Utˌli@Ӹ!悁h](D(Ev?a5ܗf>]BWVw[WIxG~Qt+bxEˏTOܤ]mUyk5 Ȣ\O+/U<^{ B0. J %ڧTm`w[ bO_&Mc8¨&`{_n0$lpLIIר~qٌ`9!]K;" ypq[D+Mzva$iVt]gg(mD?SSR-7v6G/ $fiRMO7H]yRߋ zJacX}=Nd_mKyzk.MKeDZ6 ]A؇F>0o3阗'VѰfXL?ЋQ3.M6ńg牬i;7]^; t>ryƧ"-#wS =6P&i{X;Ec6١Vփ*] =[Vȇ#MHy4=%!]o4%01өqk Aa#:_a e[9-udt+Gl٠5 pha\?uvbk7affCNeSǤޜpim'hQ}P*+Dcmy^9eL ug{VGRD["ĂLg12;dt TR2R)^k % -z}#Zi9YlU@Ļ)V _eIj>%$^t2P*#+ 8ғ JQ%nZubd̝.ǿM]ܗ24UPD@S %m<'J?3ڣDG7`d-`dw g~[qPZgLs59@VY D)nE^yO {9;zxa> endobj 83 0 obj << /Length1 1385 /Length2 6000 /Length3 0 /Length 6949 /Filter /FlateDecode >> stream xڍtT.ݩHЍtwJ 0 14ҝR"-4*tHJw(0sw]5k}߽<+! Q|@I XY_7  I/@@Nhxb@ @! PyC| 8 Iw:8"Pa wx@mA06qEh rm?JpH;"n>>>| WO>,'p@O˯Aݲ2N !< ~آݏfapX_ 51 QW As "@q1!q :*oFMwأA!?O7?-C0TG!l= {߿߬P\_~y--S5y?;xE( KP/ATu= -ձ_p't(B!%PhzSwῪH xsa+/EZ/Jp ` 56Qu%y̼|@?~ bE:/@a='׷W /[g?!'JlkeCPrg0[/ @ ?Q @%P;of`p*9` f/?zyxMԡMmjې>#GYG#Exǫ/r5ߨu X;}QpG\^X'|˨N=GL c&mB7P`,Aӣ#Ρǐ4k6͇k16_jQI5@46DS}uM [yά) էlo#wHT?0nBu^;`ջr{v=˜ZS=+&.xZO' TK-646~%,EDߏxEǤWy%P]A$BEUgOc3#c' ;[o<'\MeLzdR Alwvϊ{c˻ɧ{r~Z w4R ]y Xǭ_6xfz\Ppz-.:Z#tBz6;N7L!fpFdؘ,#O O˻!Y=]~o.4)gt h^!iqjY:wjAREكW19o˂ pĝ 'H*ijIʻZ95ps*lO_&=2 :"~)q`@݊9".4_jKvJ{$+$>>~4|n4B@ۦ?G*IBYft.iRK\o>} G]qU,+N\$@'ނZz{2emfD,;j l}4π1w{'npooi݊>27*oQݾ7/k&qԺmєNUXi߁qdñBʌ<''VIi W/bh:PIKG02SP֒ƴӑ"/ݥZ,}b6#Rv=s2CwزvaXv&[B|w[;iDW_;GA"oxxOZ~>(NVyX8ejΧPjb_~ DYJvS[{b͜je͆YgO xtH{Vr}.$p g9oz <٬>a_iY~Z6s{sriF8ZCHKEa k¨s'ѣ:Rl[qNsB1J"峝 kQTa}+}xrdƈ:R(x Wc\ا T<3523WFyp#D9)n'\Pnz+pQf4Bӟ{|-nf#0NgKL5-$7$)b`m&H-c Mqlx iԶT|{.𡻀0@.*z5/whZH#I ks^)ԟ ٍtpE,U>|& ]qE}?MXGІE!on r`yrB7h5ILo}+UEH Q ݎaϼ\Ue@:S%^# 65>YO,/KޒVCIf'n: ҵ^q-j^Y'α_AR,Bn y{?U\Or\#zA)`Y{ >#51A`#@tϴ]mL<(4O|qeEGn-:E$9FEHa[d&$aA3ӕWg`Q/zLȃ`웖i64kѷn KG´x49 7Z5.DGu?nUIN >;¹ qJ9$T4axLlLHej^1hЏG4Bz$(Ü ź'Q}C_ŀ/)+,Yt\?YqjE<ߜ'=s?6֘ȋߟiHY'}4nSf[C.=F2-mQmfl^ĥtrNW@Ih%{±9Rx3js;|v{,4(8Ü/s?5p;̞)8W,uA\0v|AwS,FP^yd=/[%.9̳JX>x-%.wQ~X^T1YBd %q>窅Lz 2i~@_2)hXkD]9UگkQۦ}a)髤 Q,Ic&8|3w)]WՒ(YU[& z0]jRu7"FFrX_7 Ntͽ"B Ā%Ux12*z03s{86^9J zrg|1wX,9<48XŨTslѯU5'0ÏMb*5+#^BUOC,vD2lqg!֛s3(R3cCȾ[t/I>83}R=9~~U̽. Y싍2&J+ %`z\qfțhsRy 2C#X6t)5#`hٷ1\eS=ʤ(uLCM^f*/X<i0d[a΄f'74ƖT?=W|IcDB۽IJ:ÅۦK}`w =@]%J~7bv9>uXǵdf oB:A\%D9cv+Rˋ}&N^u5~,'achG}x2v] Ȇ"E σ+;_*ϵo& e4йII2a/ːK\<_ҙYN"#w?$AUhv'Ok-;~`=LyBa:o^ NLUkɑ8'BKK+.JC5=-icADn4]+ܞS`c;nKyfͤmˇ QßE93z[z??yBe%Drf2]];sIX c&LP2-v] 5|4\:WhwE_Ŭ4ֶE97:R {tqCOr+]CEg0LS(ywb?ITrڹc|r;<$.m?P,yَ7$DJ;|[8(?ˤ &Nn%,G=֙>&ԼX)}- RCvRrzE%ki^GLr륻/DH" A1x%r9_ 8t/6ո=q@r4Ȱsx+N?L4-˺$Lʬfr₮ vϋ O22+ۊ1hvgwK4Q(T;2ݾX-Uy30lHfrObPȋ^![}i6Hӳ`C7坃]0mkT\V6[~ xP_,L!){,c#f(Eע y6՜J:x+.gh< ݼoHuYzۻB|럆EgdR{Ky'+Z(9 Ns)DI$dMR5R58wاCs"= |_ߐ8<:@wy\4Ӹh)Vq=ɫ?aQ1)]?Y]<]ɵ ͧFjP@Ƞͫ/n0Jp1iEڳ+aL]ƩxB3غZQ cU_E]~72R%ժ7Ũ~8؁I@۪vߦr\uhjas;JX$xSaI)G|՞gBw<ݐ FUB˥dO^soHZY|e=!?C(e2&}gQW& i|`nCoVq݋ׅSkK `><4tgbp#։\y; ^m iդD&_#EHbfC#"/ib,5=#)( %cUt-)SL4Ft:k;W ::Mۥn3͎Td϶?ءYp'NUyыfb=l*O) #*GvNF K7Zo ^AVҳe_f^4F'ms0jE}2W ɍoy1`~"|݁˧K7bg G4Uݤ'l&YN}5xJ#*>ț 7ۖ-IS\ jOcT>JkzDLZm G9U~r{}[i8wL8'1iw xET綞 vtcf\ Wzf yG cO{!śd0zZ"뫐0ܷ5pH{Eb@-ѪjӆL:J5 $ ,!OZ/ߕU][~iIf|b,NQe l/Qz&C6ܔK^{ rlzӆ% 1q-f n*ͪd, Z(6O7+V9n{{}1N 6_|91l cvg+5'b`6 s{HS`BϚyH{ZI]svfyisYn ގ" u$ K0UF9r8^V61wwѣxpJu ƦV8J endstream endobj 84 0 obj << /Type /FontDescriptor /FontName /ALLWHA+CMMI5 /Flags 4 /FontBBox [37 -250 1349 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 90 /XHeight 431 /CharSet (/s) /FontFile 83 0 R >> endobj 85 0 obj << /Length1 1473 /Length2 7451 /Length3 0 /Length 8448 /Filter /FlateDecode >> stream xڍwT6)t  ]tR 0 14HRHwww4*Hz=_֬5{aaX-!pȩ+xqXXG_f9WɃ8u8  @ q>>?ؿyP n8,rpgoWͿv+HLLw:@ `  B(.i@8zzzxஶRO(qz@4N?xpXzvP?v]   P+ t؟`?܀_ٿ AaVVp'g0 @!ME5Y ;`0l 9( # Epq: `rp'' ?y+ y޼nl0k_$ݝyaPw_!H6[ '*"  ^Vvy;C~;AHpg jA= ;?D8 jXBl0#?yP/3>@_L}::zF\'+ A D VCTe -ձ_`k88,G`[&|B|V/YS U7NPGuG @B :^e920[ A>?v" bEXQs Zp7请_>|Y9 7.naC_[;~!a썃z$j l/ @6pW_,*eF >$: AJn?rwuE-3$ߏY[IWWx7%1ύf؈>ix%b^}yZo3 7[z˸3ԙߟs(ن \P;K[U,$x*jwVӊ ,6N)2לb_|}eQU'޳G^ C"AZyA 9י}-*q}'ikc~gT.wHmf07Sω$m7,ݹfLEodݟQ!%+zdHv&ݟ&٫e yDE4̯[N8ۇ^=2ɕGGةW(VguLp)_+"[duX᥍!֥&)/V||s>[aӦsʞ~D {ЇXŠHOmz2jV k^~4+ZO /xz,acx/;L8$V#1 *{<]ҵ2ݬ 2Y Kli5~Ӟ[ cui<(#W[38 1MwK+ 2j!ʉ("Bv#\+WEGq]|/ byi0BHߪ^z,0.gJx$^T(oIBrEwizn"n1Z;񮴚>9{Zu;hƳ]6)"JkAQTXZ+S;1m4k-gEi9 4+H^ +)T֑gc WjcC j< AWe%&!gǗ]aL=a7}9$ifJvq7=6uOk̽R5s>?$@E},2H%^$B1pn?cG5oOν U{vnebdӴkt?D~]{a3ꬨYaS3gPR0Tٟ]̅,A9c0JIR]te䡍C#hե]fи)rn4>HJvt5+G:塠g eBFSՏ[E)e,Eg0[;geAxK!9CWIyAc)Rh}ӣ'.,GϿJy Z {Ƴ+:,hܛOVףtEOxrf>Umi+B͖nRSۇСR.>U&yԛ[QV0Ǩi^W[/CK:4e&?tlÝSe9#@yLC3Ւ0'_Z)Ca um?F\9DEn\Gȅ)C r7_;IhT!l2j:-D Y8Yz'4o}E7)M4Yku6UylZ B.y]h6gSp} ;y^P6XpADOSIgϥ|@_b蘆q 5&;oq3~-#^9*qr/ A{O6J,c #Eռu QxmKbLNHFo*b[):k,a7bJ̈G/AD#ԓl?ڄ-Q,4\;pJZ>jD'YFDr!CLa`xw\J#V|zy5MF IبN鴽Y~2 M>Bd4fWgcMhOm-A({jHOLEѝ-G u|U=V< y怗9C0x(ߒ b!t<}Ai:uTI {EGPbw+!"uyEROc{,M*k<m.ӽ˔K*W*[IقH%;$җzh^d7s BQp<j=,}SvcAQ@G\%G-cdrd3i՟=^?^qk}!)< ,5%t[*GTi;;<sY&҆+3HĈU7^QˮWolyc]/x\6;=8,z6[|d :+@ k+ʶgܱ0!p;kf1]LbYJSFكǯxHhlLiU?>tlޞ&m-7t[$SQGC89! 0dM8PTHt&| FHb52Mecz#ubatYݍB&Dkx}sT2L{gF^ܽ,ʄt>/e&Dk]ʹIMǯ:Zhֽ|A}%X=/8"UUx' ,|`Fs;'JSωbdPE^TҾ~I۵NZ2`"5ixM-=Cf!B\Oz,DY'&CN7VC4WTҚBݛ:²g=kg*R_#dSZ}ڣ+.f9 v-x&he&ݜbb/2Z0:X"EaqlbYJ srLT~ ~Gϩl~ (Hh验Yݦn8xoYZO6|څQr?%}yķyW9$3?eRnPU7w}p/nӬw7SjEdo7[.l5[(`dmgL;%s$O̪80tE[2qTHRQDQmg_Jh>eQMމ\clºfn&S–3`ޒ8z&XT9u=CͭˬUJ@ϾuMG.(=C("yz6> e6 wQgtKE\Q^.|?փ{o>Nͷ!" q^9ϖ8!:.k ZC9?,م'¥s.qL fsٯ̊_ы[Iv_acf7xz6s{QLEJl>K%ѩs.䡺p 5pٸuT[% !&"ZE'$iyUKkVlnmbʡTut_*H5F퀟OJ9"Na׀{)8!<.TZJY{T"?Kbv%=Gר\<7-f DһmCt7aq=f?] 1IWR[%uhbt̯罂wJc_8<GfD}cS9?DU&٤stk^ԖD7䵖MSg,r٣|ͮ7v:brgjTؠZ S,u ǡqد/#?lvt9,JSʡ84Ug. .Ooi^,ؕ^btOho˕xP1>h)̮som =Yfd*!}ͳU8b9 |U2Xu|ӝR}B8{:&TsͩQjj[}K$3n}h(]E% ,|}>bop/>n3_9&iCn-cT~ImV}`Ok Y3mTkYX-̹R[zoKk78 'g135=sgeF m١j j6gysZ6Y ܮ/ډm_etNX/[\GIC_1y!!h"7G>5.^&#{e.F8Scfׇ򦔩=>gxtF?L*#괐 4)ٝڕᥣ"dEַFNX>8jqi\ڃe&7v%;z&\$'þD!oa1{y=h@6~l9]_D7y%LI I ܇0iD,mO_wou_1:ʩ|Xb,HȊ}8Hʔ%F nf#0]T9x Sju+|VWO29I]Q2_6B^_S;dLyjolTX{fu_S|7sΛo{"ySndf/If NF"((${uv6/".ڨ;ոCUGx*l7fm}+tV 1hӾxEPo,Sws lͣnw_>K1dKz"~y 5GNS|\BULcTɅW3Ib?-gQ4Br WecR=0[4>:](sBCSew]O窞N?⭳ԟEaEo>uU9##^)cT!Pȏ.>QЖ@>d{'2a_kGb=[*jà0q`S{I5 ]VaN7Ugs8[/#p#ҐIE3 К˅Rbd_Eb-;d 1s>' ܾ^'73UO]_d>F|~-ۉAkCliyJҖN˚I*͸1uu~\aGdCq؛ʎlooKE ' ͟%2א-ixDĦ9s4KCX1Zo{Hc {Pj;V|z3UjJU(ѶV ݨrӔۉ7hWV5"Dnݘ|h9O*;Yi$DoPR$̏k*ٹ?;lx1&v0\Sv2oac; K3_ݹ\SJp0(2,g׾#󠾚8nq:f|ɅZ)=#Qq,noI-*iK'8.rqN[otF{{z*/M}4ܩfz7 \a8L#=D,UJ( pĨ[q8 {M, ~uj, O34G_zwQ3bZ۟&}aX̒a q=_Z.kA1Lt(wb/@G%VtB,\'F3Юif0PP WΧZ*loќNk _Xd1&aU{<[ک0tѵ/~'TdKV69DkVKJxW:_㲮]r&g6n(NgYdPqS)7-4k \&$;Y2k rj爁\ endstream endobj 86 0 obj << /Type /FontDescriptor /FontName /RYRTXK+CMMI7 /Flags 4 /FontBBox [-1 -250 1171 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 81 /XHeight 431 /CharSet (/T/U/i/j/k/r/s) /FontFile 85 0 R >> endobj 87 0 obj << /Length1 1347 /Length2 5948 /Length3 0 /Length 6867 /Filter /FlateDecode >> stream xڍwTTm6)4%fhnC:&``[:%DPQ. Fzu֚sッ]ux9LU`G&% j:`@b似fH/o99ĠCp:uAQXKɁ@ @  $ napOr^5?K `YYiBЀ>S  Wyg//w9QQ___(("' nz!̜XL1/_($xap,Kp`?BEW $3 ŸCH@A~!(O A 8!1gP,Sդ0{@0nnp'ԑX8wE-"hW#0owh7\GONE Hde:JamRtǸ\#`${zB|K`0CBGMOtCQl@8Яd0 EokZ翭? P, IX A#0.ꯚ}K";^8 mA (oE%izP" n1@7bPxAp v‘Z,!CDaFH/Cmw@ 4HbRㆈ$@0n`p4DE/ +=@`&uA~r.._Pq fKUd*,bKL>j??7vtޏyMzWK\P=9ɚfb!zb+w0' &ݾ#ׄcASW ²ggiC7DW^9'a:`Ƨ˷9&J$gޕ陉ޡ\dRYYDgK!‡XPj HH&ӸJixʚdMzӈ槄 *)ktwy* T3wǥumBڊK]1I~2Jn&?Ũfe+f<\HRncʸ1Ujl:Csg<IlyrNoA8@H&#kJgfzMr}]$oޓlMMuI$ӓ!k/sp`'ZlxW<>ng}"g[BZu3'$=||0;/c5zzeۿqHNu7JnjGe.l콓OziY;kg}D=Xrsd[DYnnEhbE*LUafF^@mZoGo/U,CƏqC˪-T+C};ӣy9/X 6NgW92X3#u򬅪,bRm?%x/ubtX!<~y GigQin Am:mR옇VV́ӝxu@d`9I vy;m!k )`qfh'fl$fׅ(3w9s&(od(ᾝ6I 﫨w za" %3ݺ*+j^Uy\AYФTjGʾR) ڔLfr8,7Xq1Sl|Y16aլd; z\g/ssoz.E+"dnR;SzKc vRW}w7v?I|H.i2Nf =L˯۩?O׸UYg>^45;va ]Mt>zH^o:le~Axv%DFU$ 2JUi> vݲ @o{dgo[{T瘛:i{ EXYjkڳ_Wd,r>͢W'Dr;ꦅH<"x30`aAS=;Zͷ:az}QVQR(o͚aKT}ӈmh^6 ~`_CFmpwNj*Kg?҅0"b[_y%f52%=F4x2ۗ<+n#Xe]SSSCGi\xO FÝ~2$TouRYjx(uu 62%,eY?lV|wDlџ+)6$3-"Spt.Wn}C^ZSv%ɋN3nCۓ/YPoP~,b橷O0jG`9k t? WZnϗ]Gr:UԺAgr4Qc2m[KKБ\q۸Ϟd"LE+"cj? &@i=9Gws:[T6 |'7TId%Җ*C*R`CqyN{|֦.*@SSH~y6&\eITb'Q侤#noVaZʢaͬmG}j;QEF @aV:&+No:FsJ1~Jw閺>ZP"JE,2*BZG­)9XrB{=⡋zHNw o)]uNě=@%g=UjM}鏍\?TiuHN(erB}M޺pMfЍ/X kx(a״#6,.IYylx14]孔㴅fŵO^"Jk#cg!"?oe@bᙑ#|JRLT1ta| vpvE\'3u,g+J>Oڦ7$9 Gr,ٽry%'Sp~)v [xQ[F(-b3KMsZB٨-l?{%jr1dex T;){CmDmН7\aoϗS8i>Cv/l?>!hv>-BVA>cM!UT4Msx2]x( 7U8G*{hUIi^,V6h #𭓚ȩ@ ysl40-r ݿ#4pH YCxUo`8sClR849kgn}2MlʧV g[ ,}/ʦٻAdH'&Z 5A4rG/͸]N)6u)Tؙ\tc Vp!o-Bv/ԫ)./~EnW nւTQw-ȩu`D͆L^'Y4o֏ Dۀpce^cSZ) MzMٯ.m AAj[Ӑ8mыKcmyBBv-s% Uh仢kEWk{;/-X ]1) bG36 Ui[/z}^H[Y`ovҬ۩v\7:N5W\0@|~o(DQW"&5^q{ڜ^eW&??OyFW#%'y].*i X 5sm6R=,轷ev.~G/(=8T%kjѤO~%"Q'?v}t>-ԙ݃eaޞ- (ŋߥ>[ﴅ}d l6`kEF;kT_?( ',G;ڵ? ƠW>H>H|ADr4)i ۽^-ܰnJC G+dsՋGOl + ̤ovg$kk5&[E,6Q2SFWk6(\gn'ң${!'kc15bUM6ZA]zc %΀5 n;mUaz?Wh G )QLPn"(bܒg+W|f*X~dpC#'9k?d8uWCBʅ۷4wXwuMxd>cqm|¹+Oks (ybuioD]'*^հвh/[xف.EwwWƍE妏~ ޠh~3 /6ڃj?naoZ;)~V9OTX%~IՆAl'GXIa챃`g&-ɦJ|E-^ >%Ᏺν4mAo_~nEI?Wڑk(oӶdT|/U?1)mVʜA1DJ?z'#&V]nVdž]*e>J|I!d5MjIaj$NzJ㻨I-RN22#IC;AE29[ז2te/QCwd_dY_L T[ӓ% 0 b;U$/R4 endstream endobj 88 0 obj << /Type /FontDescriptor /FontName /UFOYRL+CMMIB10 /Flags 4 /FontBBox [-15 -250 1216 750] /Ascent 694 /CapHeight 686 /Descent -194 /ItalicAngle -14 /StemV 113 /XHeight 444 /CharSet (/gamma) /FontFile 87 0 R >> endobj 89 0 obj << /Length1 2391 /Length2 20236 /Length3 0 /Length 21634 /Filter /FlateDecode >> stream xڌPܲ- . apw N ;]|rOrWWTW P֙ "`ddgdd##Spk#S::Yr 4tD Aqrvik ?vQCW =@G&bghaf :>(L\\lƆ9Cgs DcCk((y͝ mhneha NUL hp5:@Td @e  ?tfEdawPwvwښhhd7t564]!@\H `j-읝,j/b&"v66@[g'pd`gVvn^S [ӿ0qgdk7dm3:9X@؜/zU{N̠&@8/'CW `42M;ZA`?tAebgk;2h)I|v/:VF3#%}oEC#WO bAo.y;\yNXoK wM67.Π g;TϥXo!"ٚYGF 'q w?_hd׳@W t8VotsH1[c;3;4dbx1 %09RvpM `8 "'A70q0#&o `X R<t'S7(F ߈:8@? ԃ1hؿ~#? 3 ,Yll`MR7;h@ T)FMCP/oB'sqblT@?"@6? f? H@? H?k fG 1~3RmA;Ԝb@v5c "_ +H{k?A@.v_LLL Г $o6PH@oP= ? z.@@Pnl (ØA@u1y9꿞cG?w߿ʁ@w1¬1O叠oBnt;|Sd;iTt^ .H0TYkBɃ]([b7/^G0MJO'v1ƾ ǣSY ],IޭG½li8dvGi]l.Si|lbhg:|Xjsw)ܱ7Bx8h"/u昇ϕ UfR-l| r/i9yF"\De:}j H mLyɀ >0#ѝXLWZn:M-S&kӈG~ ^O+C}tw!MC[_zܘ̵#3SʜG :ԁRPh]9 y.?2m~ad;e|]Yw.߶>:g톦.fԞz~ǜE +2?S3<5Bn:|^ԃP6amUJ{gj0B'򁫐TSs[q$~p`p׭myƁy[`̆*GP~x_nBP$DL{#UaW"XduUǭg72)Q2^ E81o*S!dĐe.A֫]~UQ/ \랛"5Ee]󕵧iON4qGjѰMv{tpx`0 L+ cIRU"o9ق |UN:?V?th }:|?̞;.d_mQM6C47' ];'zȗ(4X#x5lwؔ etE| :BHP =?DGȻ8ؿÑwwJ&^E2!ϙ%ź]~~SM0ɛMX6欶a>ku|5/h۷LA+#Lx<(+NwE^V+>{IEdDoGO"`PΕ?&o= f_} ttvYX]3駱 T?cG~d\/~dub_Nչ@8: fA&eNj/`RubI xh K{,Q"EPt3+0NVK)Z?t.cq/X-k˦rF^Jw4:Go"arE\vk[ )j@,w|h#X>Rfوq! '?q-;ۺLQ9@MJEXa L$Gp.ۚW<%IӼ8t1l$XX]jg*嶾9Ыg;9x}٩TuԵWVDm7vzw9 LG `I?Y<Hҷ%z^V!m*ޚ<Ǣ}ߣY=wIWͫ Ǫ yQŽ[VX?_zـY,Y֪M*n]1Z*VյR^5ۍk`p6ucycC E\PG;l);G5EC OO#rG>i3PmGUx TbWSo BBDRWYm,%< 6[$_W7zJoS󏱦6^4^!j/I`ȪĄmPεVuguRdi SY{O6G7>,U^-RNTJvqx I䲀y_j7n83 Te# k3%K?bX%N'".掃)&V5ܘ"Qwq~GI `]>qdBBs@xsN9X;Ag\9:;$>v:0{sW[D&%Njzى~;[B(Na۠)R)\f"HrW 6n%:) J*g}䵢<y%8?y= ҩN"QD X|u C)qTNgs5З,xNkX+ډ+`qQ[>xi?P4!K_}% ~tY Jp߱[Bq.Јz78 CGYaI:J]ez[B9/!*d5M2հ4ڎE7'@xEw󚡊p ^Χd;f%(~k) "K-;nduhPq=癏f#|9Ф^2}A;`o )- K"c/x\e#eIJ_76sRL3!й$oրl's~''hGk aϪܐkfXhën pB"N/6p)Kfn D0p;5=Tt}.s!+g*d1>G' =j+Ia|>QY N"|Ͷp{!CE4W"<1X~ ^]'^5H:=%W(۞Uh$\<, &ޅ-Fc ,b󖳐<,mJd*~ه:̾Xho'%2¡˄ pIJ! |:B~f?]2DP 5po;n)x&PQbg cI"?J<'7v~ZV)Q61!~a_`;rܓIDPۇ8<R."8lMy1UG KTagWF|^_5L\jfu۳}]`Wf!4NT. پqXu1S&°. 4j iX[)DּLn'GÐ )Q:3C.O]&fd _Gx~AQI-' G].1ԪEj޽Ōo8*ӉmqLz-)c0AI7w@W[0Ntl<-e,WBD-[S4r ϡR^g7LYR2~oKVQ9MLjz~o쩋փ#'l;T|!ɳc7~S5釿2 L?[:o ~ɯo3 +j> GX۩Q^B;%Y2\2`l _eD!eh9fJk+Z:op_H 4sc2e*ءÇeEw&m%xsծe^Bpe>P_\aeN;l30'8SRK,Ӊ|/h2?y͆,|UG-61X-$M_2o^\)m(FTD= 91 4ofEj*{m~VKKd-0?!;3DMÿGoíg 5-32',<{0כla+n[LT(`M¥¯keuxM_;6zфFr(䌊pDWGjɰ`W7X=l. URC m7ğ ڛ(SZ,QdIuy6' D4֬MR=z37w؁nr/cBڌ>EvS'|ɶa.PdžAXhޖC #v{}ݑwB؆:Ť1R#y!U[ hz^E&E7qN>A jKȺ R NW\5) DZaB7TThj^=ݣǗ;DH<;>*Duz%]ߔz_(XxIbYU,POaNVpu5BSmvYg?@ٵh友ʓP[F|Wꔺ'P>?ړQ\a[Al> j(.ZoD?_ A5AGlB % 1.~]}  욾=giԁ9|f%)s$FB]h Yv)x[gA5'Ab.j)Fo̩:by 3O}.Y _oJ8?e=QUGp^7$)j^3q/jqCkL"4 [кt]#;SQgZ6cK,v\'~VƤ~>Y:Kgx3/6KL=Wai.Z/kǒVҞ3jWy?ujp X\0%[DyYX+><,{'l_ee[ϨTz5) ~ #"*q+Xz[| IL&,- `G>yzfWѽS:S(++kS^FoҷQQho.u_Hc֞ |ղH=lp3Ԯ Mz'vz>jTRhG^'` |x FyH$ܰ6069`__N|lEz*xiL3h@i0OBIMؘ'C|tEӒhP8x7~V܇ U9kM"Q,0 \9 M?^%M(H:~~OP]HiXA{2 *6~+c++< Ka%VI:偃8w䴈ɉeZX!vbw@k{ϘDIYǩ{NCW4$jwj,OIb+ UkcC= /O=!@3SKw.psGBJmBdD'$w|**݄K}aR 冻Hf#, =ǑQB #YZwtS#y{+hy`1z hN?sЎx4U7z#mnYjq%٤oܯGu7lN(DChؒh;uLĊ3kbt/HHh #=}'h&+;cݫ>3}jK̶(8Att t@N$*y'nҹ}4LArlO I<:I25i3ׇ=^w# kO="%Qb~}f)vH 2s>6I;޵YP6sRtӭzrաY RIJЩ'LfAaޚhSv&Jyk‹p |bG0804;2ګb CgFggrsIX )3I!OL1?nm3GgZ2]I+:B;}PG;q"T,Clb60^U0㕄\8t稁 ZAug(We$Ӣu_!vmlM͝kO2 1|iN΂\fؼ-X͝D69UgKثT2% Uե/ے2"Q G- 0ƭٽnv[[0Q+Q0tJ1xk,\ܳ^yzp~К J*?:vj{?, Lzyn vKM"nh GLƗ} 9&P(ejJ={ nd H\`0#0y{NE-Æ2 F,SezKT#KN(C8ٳ 96sB%o7Q\|6@Z?|U{M$ a;<^}vVP;~ '3LyaK,nI' <-}s3i+Yj%aOQEp˴~By(h0lξ-)yK~/O Ш`>E~9ӱ' }%' zxH2S't0K|5kYˢ6&?\;ngR{ȗ/]r/QwD*Tw ct9 "ب`[GQܘ 'a.ZiwV袰Q~MW?Z~2$Ңzq+WТ< j}C53!ۼb4zr 6tMIpt`}+[s^%?(ϊ r2CXjoޘO~B*i-[sSU|[L+W!bX)8qV?uY+yN!8]ǴFqei|oF:Qm<x ~h(W_al׼|= ɔMd|?¤^PGr>4}]ro܅jVvq5ųNX6M&G({2@}.&D0iT'sxL:Z.1Ζ¥ ztcG7ֲԄ`Bw) X2Ol$Bx/pW0n{nK`̐Yw=cMP86+A(Osz+vHTl 2{~Z*uBw:dnВ%  YKk6o{sO|z x41(^C8_ijtgM9=kcİ0*h%VNnuo! 3~7q]ѯ[<ʔ4 A Xsbz +jd: IʬMOՁSM GBjB_-8A ~<"a(1.͉.[ˉ>%G[0yQJW # cpjeHLd]ċ{d|s9eqe6zN*Y[nP>BHO:xS&dǮMrϣ/ҿU9YӶ܏{ᩰ>}.b;(C}ɍRJ/rc@2 'FVf&?wTc<\ ds cW"ڈs'i brQt*Ȳ+zXS7nCUޭ3]h*d/kÖ~!JfSELdPܶS |@xnx-*,QFF&_ـxF:f ZJѓΥԈ`ŅaCF]d d;Ua'1UȭnjJSs Dv9%+sqx? _,_iC7?FkӡyB/}{՞m+7rԽ%)& #cƾyJ_O7'9@ [sڻôڴ_278_ 7J< kd԰Ƿd'mEݚ-jJ($ԈQ4ńT_s4z|rF΃\j,g˭NKJ &ٛ4:!`br7 ȧ,V_.u>`. ׉_"YMq"P<l6< :Xzc'{O¹^0ɘub0M&f=]x*vtE֒e3$)!D~VcBBU_eU=Co1펢|7?R570XH-hBN%WGP;HtUCG~kOp*@uqh<б`c Tb(눡.-u78zNjTB|вƔղyW){Í/:9&At eP] 3\GWwǙg+>6(.;ۓ7 $`-4 I+dxDƳS81(FԌSTrQOUW/(/v:٦elOM@ܘI{qk]E-bp~= C87K@nws')^='f[_m6!Ի}kWreW+՝`(\Q] K\ YOR }*cܹh s&t lP~-\?uawE*8)X b~LxmIȕH=-䠅Mn}ٲk{.}#˺RJTJoata\Na˦Ou#GK_ARW:n?>FX=A1OŵpVQf)e2KGD^^}ܗ+ ew&E?Bk˝:yMCwbϭPOߌ˛R9<">wd6#n0e|% PgMʭ\ ,q_fdhaȒɻ>u>4^k&F!eLp'%p8ǓwOP>0jylՁ`vt=44;_2Ľ!ƺ+9^ U'XLj$ V\oQI(QX*&eXl3=QN {V-˸ei.1^_.]%%ь?2CH;.C_ƸT[+Wk+T#W y;p˛` sZ r-ķ-_YG4\d_3N1kh>Na1RhIӌ Qf)^?Mд/ |MD6e"J5-6:=y䁝BN@x`b"aVܸ`%h]):%BaKhxp/~b:G{ye1JN_|m><@՗*k /Yy0:i=f2#yrVAҨNd|WWK灾>{4)uؗö~/ RX !9]+2':aL[-b|Ӄ-FEYy,< )y& PO;w /hd"4\N 9V/WTpO4vdԕ@@GlL!J>4JMuEnWřu'_,¬A+I9wA%Rk[$XA0{v@g|T=J50g&uN7O4qF!EtjgzR%a-ݦٱݾ9捂 "Z>;em+לwisEy[ӏ6x<&_@Al5~5#FщܣGʒ׏lLs4{-^ mIA.PGkbFČOZ~kz@>GD 6V4bJ"1|` T |h3'CVg!r $$U]{HdLIhGׅl*ݎa S6^5:/G;dqHK|8rBÑ;+[QH[r-vNt+yJ^aطbͽڀCg.es<*|Zժw}M ަ $>{q4rM Y,4ƛkMV5F DRytI͝\|CgC sO˒0嗀tq)|_p˗N]Q(/>rcM5ˤuV}FX\5-jVBxra YwG<)i(=gܮo/*:d ~DdQ^v" 1ŝa>ʠQ>@ӜFbYQV y,X-ի! Tg &X؃jG&cCx/8b:bg#dG_}ҞBg|2,cV5ޘ  ߥӊ8.,w$]K[ Dwce΃p[ibocA 쁪O&DIӃh d&)B3qzȂ2<| &!i)}3,=}I1r=mi>=92k3lHH0<|A:_\W+;_$.kh}g]ZO6J s 5Ը7P/_EG"/Yjp6߈߽+?,IGX`}4jIy~Ơ,r(7nkHUq\9N3{o~#[t2fNU:0NDbYJUlSoa w/wyB:9vh)01>%]J6 dCP_zN^_,R<钑nPg\X5odL٫: ̨W$4#גCwfh;r| tEgBB[ttP&Q`;S=^m\乩\QudnTemq\ Мg!Px80).}[$Vg{Q_ ߾3̆&gY0~AbL2EN2@mFl {hȌ$Xoާjc-UODhbM0Ι c0c!a*I@ZCrN;oz:$^2ۢ-1:.c@i%}ZlY5ϸGʙqW]nc # 1M)r~w 6k}7D1@ TJz]("m9]RZ9fgrCwWq=.^-(S6Î0&Ȓ1w}DƟ%`OK<}y=)JmۿFyP>櫌:ʖgw/ HkR ,E F徘Is~VN,FAUq 3N 2C>3L7/=_ T&eSO0$R5rg}5ً"b]# 4=D8JfIQNЍ| *!d&e[M;"2Z U:e5=MzNnT8Fo߳5R@Wߡ8NxڑC$섣SXSäo)K~Ʊ^.iNu+ۅW\bqJV@3ATKRo>Xy[/u*1- .xx{dc|^!iUSOSPPCΠA)1)@;T'/ tq>j[g_T`KFS>@RГWJ@qE0F6BEL~4ht&8=,wSq`7Knγu@:~v<潋P!`9m{d*o\U4\R4}o!6GhTMN_{;T'iX{L/AA4(ίgʆ_`иp%W v&kʃ8JW;|wAmS>+\ :W%zf5~vv;R`pڢ#TdTD&猽8΃+p>cYd Uu6Ds8Q&YTb4@ȆAym*h785>4Wo}Rۗoc 󡰞ybV *%>_uہ#~#N/1ej=of,|yl\JZ%l0`'A$\6 Ixz]A^nAsBf]|Rg+|,#IK mͧkK咈~%>3D16=06 K}ju25{3:G"/Z(iSnJ꬐Y*Ui5"v ]{:26VsLus*^ XJ\vt%( ǵM7RS ۅ婤O6eNVҤr9& ͩ  /ɒcSZ%pEջ=/[tV~0u&~S3xQRCGW UɌ{7$8m U8zS?$u#ֆ(atAYI~f^!$Ch/oŠإ]+Z$NjH`3"q2^s8q;HYdɕM_Wڔ*h B/u;XY.!'!m"ec5DqD3p͆>-y#iC/%{~p^uAQ'ǿbҘ<UO,%1[zeeqz|W3rD]_خXR<:svEpyk\KZiZ KQ4/XYG!674ʠUUΤ>w|kt2{eA㣥 zZj,#vP\8aJ>VpKk4oJ=a[Vh)1emҭpus q!3=~a"0g3)'&C;m`{_sq++Z) )Rs6kNKE$a<ۋ72}h ':sVYI E 9&~APW;c^$2 Xɤnn'Ǒm*\1>\K7>5?%xX6~`]{S{D х;6|̏ktdK}Mj DNwl߯b(?ڡCD$1Az ҎDSH gr{y]a%Bv̦Q{צJ k؂pXMӀ/|uO|Q)HkPZ}Fuӊ?q M v18*9w/\hbOK싞 a )t0: [(nLH qS(Dq{oLD_pRƼݐ[^Oc6"̡3YC-2kcɄ K0c~ӈzZk6q5K?Ngz.4%!JfѲ;Iq7YXf*֜H[,?!lAy\{lGX|IH57Y}yɶc 5}EMe8 M0E%S#{Rz$#&@ޒcz9/uS~w]> vֈ1i'F"@{m9`Sjsw_|d:niS/&2e;QԬW*&r%w0DB[bFV_pd(4t5(Mi9Y"\*.Cۗ\zL Krd's!V3I]<@ ˙D. TfѲ^JV :GhQ đd7/s؝?" aqpGowvdиf m~Ҙ2;]#ϩ޹W#sM (ͅ&_l mm4unŤCW#O7V;cHTa64XϒPۿ+רfy4JށˊܥHeWlC?Ap UixĽf=Do \:kq|E5Z`㸊cUI/T顴:ȵ4'1s6%?ӧHfM Soȫ2aU4W˥Axc^u/ E +M]p WvZ^{+)6}aX-ƣB9TSK&>,z=. d<Ԣbjڐ^s"ب΀1@#jrnL~j1&s\ fV׏DX瓅Q.#Tq-2m}&Ğ'cb+##Rۺh$rk.,Qxor6o cr 3* 0x sy @oڦ68fBr^p`lʗeR_/VOEW!X~isJ<ӊ[xwi~ˠ1c_B-oo^BT!z ;QXʸ%ض)-Y5?_t~ Ƃ@tտa!Il;2R+` b(d;'i\~ #Rdb1z1j3R1ӂ W.VQbЫ^,"|!v 81!l' '#T1啅QGD[L[Uv.LH'm~4tӠRr endstream endobj 90 0 obj << /Type /FontDescriptor /FontName /XAOMHK+CMR10 /Flags 4 /FontBBox [-40 -250 1009 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle 0 /StemV 69 /XHeight 431 /CharSet (/A/B/C/D/E/F/G/H/I/L/M/P/R/S/T/U/W/a/acute/b/c/colon/comma/d/e/eight/equal/f/ff/fi/five/four/g/h/hyphen/i/j/k/l/m/n/nine/o/one/p/parenleft/parenright/period/plus/q/quoteright/r/s/semicolon/seven/six/t/three/two/u/v/w/x/y/z/zero) /FontFile 89 0 R >> endobj 91 0 obj << /Length1 1503 /Length2 7424 /Length3 0 /Length 8433 /Filter /FlateDecode >> stream xڍ46ѣ`Dމ^CaØa F^މQCDх$ JOr=k}ߚff{~Y {:JTt@(LnE  HO(._$P<]ĥ$@0(") PyC]6$`WA"NΨc Pr  8@rݞP_)dQ(wiAA$FOjrٙ;!![ {Fx$pC;'>_ _ ; ;0@_ _DqAa [Au%Ct@BQPدpsQS"!cf]_#v]hEusb@ PBJ@΂қC~Bܷ#M@O7BzAE $CP{NO[7OP4 x=!ַ#0WPSEX!)+#~Q@JR !;WBԟN?{u\7߹cKYC+M[ `V^["nTsȟ; CBn@ {POu(6˟~_K!OW/vY/"Cjp׆ @H$ȗx+$a11*! m{G׍J~[RAߖ-vnxA?)_mofA^BAI ? *O 8,"d]»|Mogr/ .IҸksCWߕ޼us{^TGa珀+dNC?+527Q `ݎ٫^%IbPLq3nX6ܩ!7{R6^d7CxM:}}`Y; KHpŌJ+:6:KZFS tm9Uh uغ3!.߶9r 4 6Ӹ2\ѼeU7v{O>>LQ̈Pjﲠo'ș*/ňYA]4|O6);5 7#mhMCbwgFg*[בVJ1T;}6~}O!g4U;rIMkWSBZ۞+;FϜ7\xQ7)E? *ќvΤ14gWw~:1V?ë:&9bW0.AOX@:0C_!"ːX~`A#5`90͝q>pBJ|}^K$ͩ5Xr-8xZy/rXa8ũ raf7T:[L`ף%+Y?xhqix[I=ʏš3 CǑy< iWډFP"N'5.d1vD|MFwQVUٌ1r?q|iNܟ}vuS$rlH@i(yFKYi51Wa웮Q`]v]0HlO Vh.UZnfO)aᚓT[ʁ@3cx^<_[Ig6}~0VZK6*>-c/ r${em6Fv1WHN."XE}nX2ڐ@oZ/>Д6C9#QE/&*x$S8g#2檌&SQBP(W.9̯1fIgNM^tE`dQ2Y2UFP梩$v#y:j] ThLxdl;ͬ \lRX|W~WLuZ5ʗuīIL-i0ZԤ멞 Ɲ6mS0ƳMQ bv! 3&zoQCt{-(`̍Kޤ{ܵn+.<띹=$㉏cL!m?F.(tFSvG&F'q.Y!F xD^TifQ3ŰSS TToD* H•U>iR+%9 ~ /7_ES^dqvG"PI VTX,^Jv7=:oZ=,V3{e;WbFV}\j_YD<$鍎tU)s0_H&t,D29)H |9ԳX|d{0u NӾ\V/Sj(ڬ(d#IЗ;x6>ĥNd+4v,Jr{~0O-jt MEѽKA5Мc7PxQQA/Y߱u^lw}۫wVn쒷)#.JarCMHX2BK=b Y",Fry qCzv ikU)lufGÑ6t@g1HMhfV)~+8Z)892 &RO"+V$6'W+vse*~w9uܲ@K *"qTՇMbjвZA&Dz{NcOр*Wi3v_=pH#vJqQ{;)֬ͥ1C0'7Sjt{10Xq% ̻Wbn]%'{3=Q6EfOS݋T:f 79  5bU9R k)Mɽ+'$<Ȋc^|Vt'PQQ-o3xVS!ro'%w;6$X=U '{T @~`wB(Nش^US(7݌\G5Q3.btM W`MIoּ-ݱ*K~p2;{@/5:Gq8fBU'-o/z\W9NΪՀ|ѝH5xgMN#aP$qGK´ 󍤴 WVFQ".f;tQIJaE /y?䢛j;zzXjAA4z-ܕbEqM=e1J;Zuͧ%|/~md.UVAB=ZsJ", ~;պޫx?Q4FpxĽ#`pbǣR}ȶC\ 4630ɦJg>Vta>R,(nV AIX ~ֵThG5){cAe<&laCW֖ߖH-G1;E#!:}*zJ/hmc\8萦| E$ͽ@YշR2cz+K{YBh`} ~`٢N;*yÄ́Bx*5RD <丑2kaNo0Qd{C\A6P,e@B-:/V, H1kֱY[vP-$4z =3NB[0?tz'.rS{70 {P‰ehlEjXɌuwJ:;쌍uۗ/M=.Iq=F7骠 n*Pב>出#~j|&=Pwt <,,fyl'F_  F)lj+;F}f4zdmu&,dp|E ?0){R+KUI. nFnAu}݁tt_5gNn4(怊7;ٯ)셾U&cg^܁'ntcB*^|h:t8ѻ\Er0Ex$1b YvYx!T½R%-aeDsWĭ`ŏF}7 Vn _%@;>; o9w65I9`6& WPűXOC-:=}b<2pϼpbvNh>yhF?~NM;cn ;Ý^wzޏ~pW*,yXF^VHxԟ?|"T9PIXUL ،g}X'G=I8`R貕.a襌e`Aӓog^Vo\',ֶp b2Q‹8_^X RM;_-Y%ەv3ip }3ԦICr^cgcp2=0H-Cֶ,X Lxuc?%b0W&]s.rBvfΙJf]n6xkj%.2$@~Z?gz|K]Dr(Avȶ7水! XYyQ[͇/YI~uͤv/.4~2A 7*.~6Gy2m_ĝqR(*64cRN4 4ѱHL&+`z&V46zHbKI!FS~*Q Ƴ;k&vWv!CɹJ9lVv&bҹϝ\VR9Q`R)"myBmzٚzAXrRVKF"J¼za61NSHMY酪20nLKWL~Q^l%ՔN&rT۷0l\E֯WX>/PS`+)5x&w]Q1#{wJ0w)7F̛%TL[eZ Q yV5d.CM EGvTd,!_i[ۗLl9)ٔJM] =q,s\kD_n^KvpWw2F'lq bn &,$Xo*{ ;X_@+!xeD'n\B>UʱD##{2JNo) OP(\Y@(,z*| 75|o\?)jƸTǗi7ojnvw'qU}r#DSTK}Cz bww6 '&ALM(':. : j"'Ԍ6}٪Ҕn+n>ŠPW%$LG>I_ʲ5wa6"μy@բ02#cB|@ߥt3Zi;3] qネ]8q|NP>mըL/m fop)bd>C2EBXgB^mh,D *߬}JT)Rxg^VrJI3 c˖lgc-zU`Q#X;jQHm$x!JF)):xтN:>X4EDGsOYiĵ_]CiG? %#`ZJp_)XܻD 3 ReyT{Qf8Hɔt:C{ ș| @lL@^Z^A&+ :K´`^:aB(/f!&+:=Q̳a/e2y?R )=Jӿ+TN.K]4y94?<޽Mcdfed"̬ 6gHntBЮ];e pFߵXbpa"tPL߹:\MS+e.B0 k}8) Z짦}JNRʥ4[2cK[a<\+\"d]{qթ2IX1`zsFkVӷPI un>.pE<+6e2S--flx.m.(m#a-wf3X~!첈/ cUZh)6C'vEmUBm{C]~~}⌁֭(j",Qx nsI/J)^ffhpAjSO=uKKrRϬLWaC2!ƘI6f9}I=͐;UEa)z_ZQRg@qsx.,S [sȈ}]Rc;[,5:ZY ib*u3n:FX%:d[؈#*#Q[ob8Xu4ܧAܻd{Y$?= \#c;xTXҽn&tuGŭæx.獷_Tɦ~Ar~#+ZH9a "^7^>,)۠r% V;C):|VXϝqB'R&t,,Mi:%*v9e#܍nK l~nV! I5aV1н']_\?S>JF,mae [ 2A?N;N4s;j_P7 :[Tcz~o5muEm0dBHVj(ε"zM(_ʦ`Un;`\xlQEC0{!QƊ: ZSOS7ܬwD' ix! endstream endobj 92 0 obj << /Type /FontDescriptor /FontName /HCOSKL+CMR12 /Flags 4 /FontBBox [-34 -251 988 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle 0 /StemV 65 /XHeight 431 /CharSet (/J/a/comma/n/one/r/two/u/y/zero) /FontFile 91 0 R >> endobj 93 0 obj << /Length1 1554 /Length2 8019 /Length3 0 /Length 9038 /Filter /FlateDecode >> stream xڍTk6t!1tww4 00At"% ݍ(݂t" ʇzZ߷y]^CO&i al@!'?fu_btz= 3A&c`  Nn''cwX%8 N/ wrڹ>O3SP;@ r[Yv ÉV6 rW&;WWG!v ;Vvh\@ kjPП:v`?rm3 @075p8@[Q1Vc 7NvW 0췳hl6`. Y2-- ߙ[$5U3Յ U"ǯ0]YKáPW~2`gC۽8ܬ  ؀a6vsЅ@2<ق\@ _r<8~rVr?Tw<ۀ^. #tNN5`   >p^poˡOII=l6.^ @#w _YvU}v fcH 0qc /]+[[Q[@ 8UTgfUA`7j]-@f o.r`OYu  i] dY9 o$/+? ' pC`<@>ߐ 7W[ܜo>?)C ٟ|zYy$ g,˜]vtp'cˎ0"Զ=cpSV;657Mv;@ ao:ݴgNq÷f(G0q}xt_i YY Ə„8(Q78 lb I4D[ᦚ(=[%~Q/ƃs|z: o7}!] =txR[Dbrf/㙁n!Bq1V@\ROɏVxۥ8^{wX~xuQE 7 X)Cc)z1(xw}nPhl getR0C'ϖtffrF٠n.\;)m#+^^x/?04q@*j4T@ԑ֮m{kCl5KrGW&j%l6ee`gJڙULt=Z`S)7BLk+?z5`+;i}O(JGn>g'즤br!&Iw 6 QO-{ZF2d㢦,E DZ8%^޲jdۗom*"ƥ_/L_egUY#E%ʼnhQZY0T/?IvappSt on^r YT)Bx{{S0~y}[dG@4`~Yv~ՁVn.͊e[}1#b>K V #ƯnH4IT2-GR;zk5%D)SBCM{E*1y *&.J/bE\fjf̋PvV2+nfpl_hHIކ|d_*`ЯgT- u(*\¬"VR2pvޣ=0(? HGLWA3?QQnW;XKm͘z%v(7qn6fZ<>gd>L?A`qf@*)F*IjjkƀCóq^:-Y0@e[$e9C<2Ԉkf8TAuc'^ l՚l7I.5!yCYЭ͸}Dx<[vmpY=wpPB?vT#=ӷ|N9mu7I0q":  Ih)~gأY/+rsй!e5{dDckC*@øȍ2t.պqK?̃{R'g]wKixHqJ08ib<Z{2 ,#όKUTAٟgbmtP !C*v w||U&7O-> -}+Qa_S5RLvػDm52 NpY0#_tvO$|<,aFA>WT!HRdq$,:`tN|rdEfF%曂$$h^"ÿ"՘>3gvD]5+u'[+NP@Nrd {RϺAK7?1ط{<˟}ܼY@N tDHy-2 Z,Nh Q$sX+ 3F ^zg/tm.V) P0_A_dJ u#>gjМ*Gm [);i>O TlCBλz!we.NG'hFrf!phkγᚊ~hd%L DR| gp7*rvs+IlG">_]fEc< `E[ CDnC%R5Ħ4ww1 ]B\=۽/eްmt9U0NƇJ~h%NabCGxAD#ؖE0i.,9~P[/aHʱɱa x8R<-YO, OBhD>GDMFz7$&ݦ]z#䉒a2Ф3yu]{:k22 d!\\eZ5Z/bBggg{ç)7~ ,A>NUbQ;gXGWr ߋ#`%69I==Ж X ~E3`KI_.y N#Hѽ#(# osw4~{I*o|zno]=͝s7JUGDn`H+M3IJ'F}G UXLsF6V1\-xYZeM3I"ZNDdP5n}§_~qf@`T},fď3WU9DD~VPU/=RciG-!2#̍`M'2-,rc'K?i׿VELF8ѓi@B茕|6JEk]Q8}rQc_zg+ΘA&?,]C<_̫ǺX3,ڋV)pN/_P%M×J;):Yϖ/9<e_FcC]&mؽމҫT~1+|QljْE꾳'ӑM f½H#T3?ʕ ۼ|O9}yVXL4v譧LK^L;TښۻmѫkA%2ĸL kG",Xs#E1JTͧ۠:APTIѳiϻ_`).GQ:ŃtNCSY--/HIbj:ah&_7hѡ+KvqO,RoTD}fj-28Qj7Yos:+(P5ڳxΨyPEeeov"M.,V#D[ذ4Ѳjf둔ڣX H2hO74ϫ+zKc߬<[rf[{yEbIwTIuKX[ϳdF=]J= ~1w)v|!WI#D% A~}:= >&4U8 ][whJJե hCG!"'D(&H0$[wfd;6TKr /MgY[&E܌~nAc`jR_-TĉP/|ҡE*'jͧGNAmn'J^{UC ;E_dTA0G^OzFoOp`ص'/ugp!3+& oZ N2՛Y(v>SW2$72TMɕ,zVfcbuolmjcy% 5JSHѲZeXQ=B='{ eP:ū@V"p"9&WdHN~iRP),{{Ф + vwFܣvȦY b)h]I āxרteU'O n73nR)D? ;/k#-bş~P'7GOU˃ 0Jw225p\aONS[5 {KFahbIhkYʩ"( ūwjbњPwi[5&Jxj0,@Zڱ>ݺPs]fͷύγ! <ƝE!EbAcZ^!k>*`y@>+LMjz[0 ]Skx(k͔pY7c4U_,<ˏ}VlR2fTu)k㔊Dep//k@1]~Rۄ0 !NKk'w崾Q&67iJ2_@EFK;ׂ)e W;jAY#a)%'YEt9.:rMUQOon=sf{$4PvSTi0y(.zj*Vu)8ɜXЌĬ[)c!u#AÍst̴d :Pdxiʅu0,c}SXi/eakeÿ % HDP"$*(-DoD\JY"ahV:E8$?Jr?`ľ(.ׂ*u%ח...ARv5uG FB^fWȸ@\m=\9 ['(6f!bd~> ʜH<e&%YZ8m?epG{OtߚSJIedO3<П rB![pvN ~MJrKQ<9t5ۗHM.fGѭ˘~UP,~ h -Ϙ#68Ҁi9C]-swAn_xяq`#/Jρ -ϻ}g=սpbpݾ?9/\{9uϾ}AoGTfVmgy^8}Y%崰 Qs7M2tv\}XI޵:1|in\{ 8z @zhzt BJ=msm AB7 ]"e%8Awq"" Jocgz`Q=-eY|P߹t (?TkIΘؾn6TJ&瘉[ D]2ݧ G 0u!z}+[b9Mt_=^A(;"唓3 :8ӱ(;&dy+>F%7%dPΊ8`<[ҡ0j$e4D.!+<#HoBET-- z}c]]+n'mw`!k򁅙US=3rχ^/?tگN1J2{+ qAeݙ{^!SJ|6Haa0JkPED7]rS`f?F{M*O$cY/_vo*0EUJ;DfM Zw `j}FƫcMBfvoJʲ&vŘ5hB D_F tx2n՜Q D]Vʭ#L>aۏ%%Lڎ/_nj)դ#ǾH~8r$o=RG}tzb=Qs 7 &(t[%WGT֧ F/u)" endstream endobj 94 0 obj << /Type /FontDescriptor /FontName /KIPKVW+CMR17 /Flags 4 /FontBBox [-33 -250 945 749] /Ascent 694 /CapHeight 683 /Descent -195 /ItalicAngle 0 /StemV 53 /XHeight 430 /CharSet (/C/a/b/c/d/e/g/i/l/n/o/r/t/z) /FontFile 93 0 R >> endobj 95 0 obj << /Length1 1411 /Length2 6234 /Length3 0 /Length 7200 /Filter /FlateDecode >> stream xڍvTl7%1eHAN16 " %( Ҋ(]"%!!!H(>s]q_3!>S 57+\I@$@ #sy ,- K,8o d !1h¡8 ̌0h7" )B`!Ԅ ݀F@} c8-0 DAA^;P "aP47 @ +uG $1Xweq` 4p7rPwa!lAX8x#ap w- &>pc?ZHB/_P 򁢃hw  hJp@(!C@PWġ@m53 P_HW_aMBi`P(8&  =V/4&sF n_%H__e`ƒ`_-}࿕_0!0 C"0V[@ @7$ t#р`8L<&Hlլ͍~:&JHɂPpwS(,Ÿd ];ဿ/bC`,(` M.7v [+Kh(w_z_qaoSu5!QA ;vO~ )C?կF?(KG*# NX_a~mB$Y BXC7xoAh $D`_Ap_B o@ 2Qo?U (%,or[pxE{n:T XTZy("6QȊu0|\S=ů׿mH5k<=qN1YnL_|3t][Ru%7i=qPU:|.w1f+/ OK$Y%:*s}2Oe e:Om$I>kg!cz7r_R8W0_/Q'|bJz02K^RO?7Z:qOWNoVȮrzo2l'xʘj^<8xuQ.>B_SIi^i^] -6nuK4yG8Yڞ0eV.8rKw*A&3Yec|/EZ,ˣt$p ՎegG`S*E6q"٩wx8yH:W\6>޳`NPI& `٦Ӓr:k;Ҍy #rPvq)r6WJgvr+ jjOucĝ(>IPg/ i5Xb&Qgs[ ehֲK:>͏^?ILr_̳&6Y,u6z0yefѹHi8}S=* #ԡ5 A չ,fy}9JjӕZ1 s,`x).}&qG^78oz3A4PI: MmP3<ےYab\'9Qi=UXȩ$eV&R;D&nR`vZKC.x]o#iC &xP/y _fLR9}Pj`tx76mkH~ؼyJ{44Qֺ.;B`w/0oK*!dWdaqHxǷJyF]*_o{z㓤rn* -LJIE1M*FڍbƒGCqqWroswb5|БR*ɴg:ޘ[)ы=p[ *gĻm ΍!S(㼶 xMvAi0|\Gj?VdQBރgA(Nޤ!V<*JpE=γn)K=cBlAhS :jp1 qY͇ᴇt9ֹuW? N;Ŕoe9J9~d69SMqNg1WV0O1t8 m+p٭1{ϷLsA rs:]n.ſL;P\N+sR[[*YBPQĞvL=:+}="aԙ?vb3 +mNTzɬ)3]!Q9mRqc63sƋZ2 G[=ƇZ[񎷒G_+S<孡о{xMb.[G}UnWDt7QْLk7>:/isݫڷȐJ|e⭨F +4ZTQ1 2oze_v) gyǃ GYUQ~Azmk5۲[7yt4"w_i3G9o?DqdT-B7rP3bJe]̺6 CIr}P-Vn5Z8zoXfoI_hm ÎۅfGLW7 F1Z0 Skڿ9Myאҧ> G3l +|%HHjφhG?'"Iy%MbYX ~P4:|Kr< ϕZ}y}>kH9 ^*}mG$}/NEB}@MTbK1iȇuS_4.j4VX~7ӆ:62}Jeh9ꚪ8OLh2$ʼ+vQ$relݮf1yQZ^J yk3@M[iSb__pyN1r[|_G#ֽd!`$~MWYL,Fag@ar[sA;&l< IcgKKU_UgjtzK, 1W,1$iMG8z]1#w/֕goM-s5gR ^m&yŸa+6wsP\@Y@TiUz_Q*۝я;NG[2ǝ=ߌ\Zlŧ1$!EhfcJ>iXN;٥!ͷ5/S4*-a􏣿,J`g Yk8 z@Go 8bȡyDkğ2QDn^Vh􊗲]`x#?յ7aRl v[L{$6t_l/Фø%Z>dW?*ocע37i_ҙ(v崅GUwiE!t^Ӟ@IA/hB{,2tIxS{u,ЗRsXu#۽y]FvX]4V "ХDvJ@9veBDPt,]aIZM$2yч:;B\;ae!eRQhr?Y`/JH?(uOK'uwH W"&ϵk'Neliq,H$^§op?ZGͭzzmF I'$|p tca 경-kU5tUjx{@Lp'>E'bΥCtSjE[7\G6U}.%)ġ`='$dW>7WJ`8N Pw5xKw#TVm^X'+Mo*ta[ECmǵ* Nn0bTp57TEcEX6ϔW"],Kn@Tr|>Q'[T JKh?q蝬у!2뮯ˡ?CbĘ^㜇 =iˤ&m(=ü,y8]bl95nl[*$S)f4K d';5 W/8u Hb%C?%+1!=.20zSYxRw{gi6q!vxpdR25WD+bRL(Dox),%`޸Ѫu>yZz Oj`h6Y¢9w<4!gS9A(&Kȅ0X |ex(㖿Fw'SMUHpxTjϲF7#VD 3(x)WgL!5z;Vef9`cFE☹Tʣf=R[LkX[5AּBv Qr$MKft9$z3]M? ͱܲ;b `,_vOn9M2?^4Z*/:C- RT2+PǓ8Za@8/lz[3ods|5-iG}z;ǭYLR^Kc@ԗu\agt?HDi56m3,D"ἡ,hw OS1 ʼ:(̼92GBpVǫZ{^+CQh/\d=ARϖ\Ӫ#N];e7Sj<ÒR^.Y=D:'kځ( n.T0繑&_s"35QBd0w©&'im!uNU2# ~wLwF/e$(p/Y0PbmPFɡSW^*YysT6+ALbB6&I*֔ҤڷGoe) Sn7VcQYqcg҆VݳTe4\}p5{F\8ʒw68j @!ߡtpC3yp. CFo#3$IކżDW4S $Bم&F-رY^|Z9cJnBhfs:ȪE- MoDڐ3u#V.;-\%w7n!"# Y"3C82M,8u>. ~%Vq 0]p˓qqﮎbb/y^\f6r$ZHtZ19=&Y8wy-@7ܚ$wjĪ~SwҠsdH˥2e-*R`) }{i9Xf1[;SQI$4ݯ\NГ0z`͆<&yG>7>oY W +:N }j  $lwuU h,Ӯxa KWqø$}ns>Z `2{sms[ɮ і<wӦo%oZ4ʻ<.fGSWo>߫ .`3m}!a^9M-VZ?CqbfŨ\dzUD'#UjHOQ`uN; W GGL*eRoJ?*iYrI:3)!DDͪ {F|th{eZ` '޷<%1Rf?MR|~~?EԈ endstream endobj 96 0 obj << /Type /FontDescriptor /FontName /XAVFRM+CMR7 /Flags 4 /FontBBox [-27 -250 1122 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle 0 /StemV 79 /XHeight 431 /CharSet (/equal/macron/one/zero) /FontFile 95 0 R >> endobj 97 0 obj << /Length1 2686 /Length2 17418 /Length3 0 /Length 18964 /Filter /FlateDecode >> stream xڌeT\;w),{p5w'$^u:o0FQs%s>(IUDL ,̼1Uy55f33#33+%- 1g+H&n RUpȺX,,\VffStp[@J1G/g+ KWP 6pm:[]-vƶUS+tuueb`4satpxXZ>]@3_i&Lj@ PrH lL. #7{33*#Pr,=?0?9`ne (I3zR4uq[&o QrO.V..VeP%.r*om<}~cs+{3R1ssdRrrʈG $B-8A:LQr}# b:|~#k(ob|ZYZ9+gaρ_9;_bXv nTLMm\l],ph 4wC?6@aW?ME Fi8_;ߩ5LfB6PfhXΝ/Z \G3rmױ۟A*=-zT1]7vP},-hdV@s? 6@P)~3lע>Vߡ8@A Jnv&]P]LI|:aJ1(#l_egt=P[f}:ں-PU\f&$,~{eA_QgMT`rt1]=0p= :8YDP' z,ȩjo O@=k ߏD% h8`by_'B3ϩ~FŽc Uצ=;%G\yRFR<,@"ÆG#B:_z₹?!7-@i6(j?ѽ޾ qea5 cЩG^nqf4Dٞ*YĖ;.tٹQd0)׆sr.G.9n^T{WCw)T;n_K%NFY(;zІ![Û{[Jzr pNKSOXM4"߁Sď/C.5nq *zwf#ə``؄<<躎#@MVrH $7m$g[HxK7A9/1QBRM3yjpt`]_缯j+q\a.\xɟ}M?H﵃B UDb|obZXCeѼٯrtrmZܯ]B'W'` iZ2{]L=|՗T4nqf-%YۘE#Frl_ebZȳq*8dfF\h) dC5_Һ*OM$] ŤTM;<}((CʼhNLkQY1"Sͩ 19<!%5E]iQ?Oz#QJv+(52)7L3?(qUfl])һ3Q_ϸH+Gh"nJwֽ-08:, Lowj`J} 9pkZP=)|N+Rrʏpc&OLA`g ~ӌVgK@|+m >`5 +]( ? 7(< ]fV@3<6UjTg5Y݇U 9J h`x?YKDC"UJ3Tv[OJ߮; Z^+8J"]ӝ̻~Z~Bq6[~3㪡I9&$@V,@ m…R )V%rߡ5bf~.w\k!Q톨&EwLhUϱWf2,b-\vi#]i#/#pndR["?セ~܃2z8#nYE̺ruaK檥$qCQ Zh+o'$S7;h 舷X-;G'.I_OP.HW_O}m #qS?eztZK24Q;SS dz0,]I!ev0݅x MKJz#e 'BM,A4<(6 8ϛ2@FX`۰̵^Յy3XU]O;IiiHdއU>3y(ӜD7F C!b;FQgIRist(Ra^?gGb0.~^.Js<@4xDLX|(I=mW4 kf=eYѤ]jdU3ZcC[/a~Gփt7ɁB6WtU.ewQ]ƴYVno]_X{g MF5l"Zq%|~gJ<)fLNu:Rbՙ~jt|\K mںm/\1f/Dv5'APb'p@[䨿b 歠dgbQ"j,֮:3LO1UeYÐy-8nЁ-T'u I@ UM\zeyqa[UnZ9ҜF1Je k38C {_OW#}QX7\'bv($u"Wy.)E>rPb]>ZYqAjd#DvBP&g۴AYL>~,4^W o?f\ ƻ3a34a#VQ K&3Dn;䗍ggD#YH2*YwʹH?36fW\?"׭;0 -o뫺қu/įogp^\ܒ= *Sg{oѣm 0K  9A54 d$:-$YAkdB"dˈ=僃#=ۓl&C ]CDiC.z\O cOzNT&E=׫ChRKە&Xor*rIrfWuX˜p*n>N-h*"}J `bBdKHg+=F40eL `s&жKYR)M QOdIP':D7SjN"mұƍt+F{@ӡWRW(D`P_tؒ+<ցzL2i8J&S4 s RtPodaƢ$~™MG< ]H+﨔&O:EW:ȴv"N/Olcv׬b Ru[<#8fFDI܏U;'}޷$ˤu;awʙ` N_UH^dz}֧{<NH A1:fӳo U=5  E/@8}O4zv&2%l!#0;k 7(#Yz{A&&a$WׄegÌ>.d% 8WP\nBállˬ}9[6=G8ȁN|t刉LxrBt·`.g`v/N :G>4CÑ< =-\&[kiBzn?VBe=ְxR% Gqf͓=yGZ4?¶ _"8֤`|F u=v[9.,Sћ >P?gBjt .IErA%xw-YwHAE9uS%U^R!+p(Xp't^4(m넓"g @THTQ >0V6@bz;qӱH4gBZVG1V裫WW[ܻY-׶breuUrFi$ ˆ+ -uGY9W~%]@h>D3^W2豚m\LozӰ#%,3<~0|m˽jp a[•fH\Se<2 (zN3cb :(It r1vBW"nk1N *`?PS 2e6PUFP;䫆o kJR?2ɡƠ"Nx]u6rZ{v_R ~duN2FeC5+oLTvtȝ %w50Ci}hTo^j\{ Z}*T)4LU΁V"Y&tپӨ_ ԸA{rV,:|us|J5B8]L eMq (2`Iu>(9SV_BQ4ÊRqE 3" fq]Tfd`3 'dΝ5' qr(C 4mNSgk1DƲMD}_~ɶ6;,2)b1tXԎ)HS0^OK7 1B)j2ԡpARE]$h\V1Scfh 1(hקB xrH `sQPPBy$d It֢2?{x7Dp>{=CUUlۮ:I'X?64|R,<*3wƥd% h~hڍ|n"F1瀍+ݰSww.Kjd*Dq|k?iq˭k fLL!{ W|߁<_4aBşFm'^7qC/Vg.kW_f9wg}$HKCuBUNӷ%?}4,tc^ тW-B.AU-b}'K@!eKb L]m%n%`({়\ee@ǹ xZ ^n$lWGOn(8fBdDdX"]F2Kۄ6DiR* /;BKR$YI/~"[Q^͌ 1k,VKu"vM!ϖFx}cdLeHe[MLuuWjCu_cPޛs꺙{ŵPLk|Rn"CJoknc:Z`ʒWp<+`/[WDu'"1#IKRSQݢ\$$Ea Fܮ!Iw=ֵ_V=R$!TnYsf ̘yqmą*lwvs4 ZҬGмW_6_c]/ U.3%iv:ykᎀ҄X겷|; /b7xG+H_`/098E{ ή"_n#p'FBѱ5$Y@U]Ћ |xԀGz*ZT|Xa>x'BTxhY5x3:++yn"xv0RDQ7 6_aN)&uzc!2*aVF;^ezɥ?dYonnzRm_u@iC ~\YJ3K lS_H&4ՖIClș Z\0üB.EԨ=ѨnkP^3=#K· IՊALDvXc|l町>b4Ѝ$QpsO}XRSd9H>߂c~m~C^QB H}{p2cᘂ-R*.|h P?)?})@%2W|N'`w>sH$&0~vtPS Yiʊ3Csĩl)_H|@a>*\ۢxk$1N&I!<_rر)~K<t3 ؜Ycs FSwkV=|ڏluh6\khEkgSm{‘ػd5Zg̨//҅H %1BnE5|5B`afsM_L\K!/]RC&ߝZ.\ft;^`PF2lN{S6{k^EY0:NZ/SO(] CO%&o!<:h9NXfQÍL*Ϋ39n5P/S^O*"#! -[(p׭Kw =gmGpu?J4 r$J` Hg=ozǟ>E⯟Z ˭\AXќ]]rpQ3(SӐ+:`fN9SM pJFQK7MFv~==|yXmj%;Q]]~؍hB Ajp}kpWM_yhC> zͧM@`Scߧkݍ2Z&ʰ6V֍wԔF~/;FYuT#gO;Xꏯ/B-dӴ}na4Q㙐gcMnN>3=ej|Q^{^x~!TvQONy!k"Є4 &a]Î{:r~^ESys 5+"8SQtHgS7HILm5dBcRܰ(E1O{|Yԝ`~3W~GWC`o]@]leIwsF!]$IxF9`j)D$2SbR' >s],٧fDr}Fb 0h_R\aF\}ͼW|WY0>7FʯGIMe4q1o =`b~HQ de4qm$n834f-M2IpGC7⼭%esEDj_ͺoV>ɗ?A+VZڝ5%8Z(dU934I gML=%l^ =l&a׽t*EmT/vbrl4X4_fܕ2Yyڪ̘S˃}> se.}D"Ee)h1@eƧ$q>(͗qRNp)] 2<8:? 9#[^ ɎLuI{K0LWw ͢VZ>qv}Z B:M#U6as-:"E$PGGP LxNypcAsIJa6z*_6y&gs5n1RƯY֤j'UxYv{EZǺt]6qi8yϽ:x9'|A5 sKfE ͵@[ay_ -E%vL Wif9`* ̅sq#; K&{ڤ"|"&&+}n]grL uijΛ-A!Bn8,c䷧{f#X;iuϑƻkx9$H⟌3#w:}V-Gw$\?-c K3TȾi?›D_S N;-aI'>}ݹ!E3;l;oLra^;A>=H=ó=P[3#׫!SUg߇!"MbQ*9Hc;4 j`M琛$69㭧WOzn-wi#¯lVyS1ν¤PLk@MgZm\E0: ǹK}[[dzc cA2Ǥ 5-\LM̾oa}/?Tાx s@>Ж [g;g Se"-L#¿eofHT~(yM;oQO l#?=±K~o?x İHa=_Pl 9fb9|eNnΰz#s f"lz< >u^҃xTIP&&E*?ZxC'gcYN/ٽr5 ޵dQqe;xrssl aqtm[|1yOV?d)PiX'1'u|x/$Xp8!0P8pCl7L-NETvt7Wzm G'bdqs);}2& ɛaPL:ˀˊ $g W qϨي%7`@d=&Ƕ[,jadHM3TLF,PDK}*U%f`})U_XUi~>}t)ׯ?`WnZ z7i.$ћvE3K&Q y1KO{0M-iy@.e^l佅jضf@ޒ~ۈU #Yv@Pl/x}d` n)Z#yd[5(KnlV\=:5pB؝V;5Sj&ؽ`NbO?.#-}]D°RZ&,sdwm:=ti$Uкyc|fQhoVv%[c 38`z:f cвԞn%NΪzk!d%SuFrnl_ܺ-|΂<[5?h ~HQ{k@O7gE3s+B\ʖWISJKw1ub 1&o X8Gҩٰ) >mke<t*{MX{3P ]b@(M 6-#~ؘHF?p"]2xTDaꝘ=ܔ!`vU;8%Nl;wk[N;~:sХB0aBZjjNU;PP7u!.h$5+=, 0VAD9H{2rԀTy]r) 4srL.y$boto܀n@$W.[{i.})@43+dh/,W>굄jՃJ BzdvTΒ <7#twq~FF"P]ri5l=W/Dt@WWQ- X 6`bRIוKCW85~N\XlI[:ķMksozc=m;8N`0ʬe5[ EWNfI=$\5 !QsO8]w6`8v}wߎ]iMs;EUbzP +Eƕ_ v2~җ<0t她rD), -X!pxԍBvhNIɂyǹx5)QMlP7gg<*atbCXV[_k$>RM7e֝]9Zog2]<&k]&a.:3_eVZt 4SѼ(6zkjڜjCQUWoE#cUiY"(m֐c1+6cЄ򾘕 בDK!0I4nod"Gy/;rRvPoH#+u s%c2d/ˤhZ\[\rnME,ѓˀ2˴Dދi`N_5 bU]&3LltV_ /%3U2N轲6?bMF/D F9)ۻW5-8II%d;d9l7zLN삻$Eূ|r$O&ȪSqvrL!ya;k*Qb/yN/¿ ]sTV!wL'Q-tO3x6Πq(2ZZF٧`9YnVT s?PӮ\fd-U|1NsK5qC? h^F MWx1&On}ig]Eѧ@uoM3~A:+$j">}<:i7Oj@@(7Q _RՏX>fqrWB E;^Q5LQW=Tjc r-B8*u K~R(<pfsannѝ]FА돦ߟ}( ӧxk>\B1!e"?99$4kS*dB0jѮlL}X7̛} pEA$6H{K%vKp!o̐\5eDZˋwC/ u0HT[|;>tZ鴽w@G;P'>.\F>]X6D $3'wo^<4TJiraH{kdOۅސc{=옻 ӹ:_coȽvY C[m ҺvIYݤ^u1/XAAgnL/} mt0 vKLߞ; =՞kn/m*W4y*w3VD8h虽DgO7;J͌iȓ~&zVgg9L#mZ|%U' ]yT.p $W<7mRto+xځ|]d46t)rfЬFFt5J'ymXD#^mMABFPmyZtêr|d6^FD\tsJ }9kӵwIlK'>xùQBr@QiwWP&Nx}ƻ"}e͑ռ""ŕ%6eb5- i#vz& dJG&L / JT>SդPqf4NU/یnatcF.+Ƚ 4Wvd}& +ܢII2%h _㣋~N1}P~k)1,?LZL9vlpp݅g'H8YP"(98p2޹k^"xa7l{$?(Vӫ[)䳯:;Oh_ lڪVHk?bjI̟ L/ΛBfU/3Wz&Ԝuk5[ޗi+ҽ$+'!`MNSޒUiێrG 6iIUT@[?R2’S@Q'T'Zʰ[1'合(宝 ,&ҵo>frb@}L*Ř.GEGԑdkC8p.NiLs 0(+/Q1) ;A|ĆfhZEB.J.Θ5skyRw\CʀGB>8Uh𔿮>SM S8/>ҹ…k!EG/:Ta>jF@U8" yv_CsB\ &4Ҟ{n,Л 2^FR= 1}V^74ٵ0ņΤSs(醪n'CU *E!8U+,3t!۝BH\躦A!2+y{͕}wxWK[gȭ'Ϸ紽?.%RH^=NyHoUh.voۄ=aṄ $Tt\}Iy{|_;U^18~h{n;oܒjhMʿR 3sxi |:^!C>yQ#ַ'Sd:nHNxkTy$^)U.=OO'MȘ /(M-!Wc8YFkULi'Me;Q;m(j`pV&FͿ6!{f|]]l@&ۗ$Ý3a(lvlu<7E"e+/8W|o F2Qמ)԰-2e)0UyD slO=n}K)i _嬃^ܜ.!"JrlΜX3qKq+}G#NrG~aRx[[0GrgToO>lQ,vɄNھ쀤`ɓ~md稗K9ea>ɲwAqoLm/U'edS e (ӕcj .Hic)DK~zE/XL*@*f&Ǘ u#tN'FI?%d*kȻv$o־>Y͸PIi PћFOeE6:P`[0l~*ymYLnGG;F$G |2,qA-Nb[0)n^suQR\ jHze̅ "7;.Hxk:KȔO__w+,L^KX==H?t1ʯʢO8te}鶑ѽ;OO6\sRީԑMϬCݞ-9OREⶨԽ{ţkAOܑF%k X/hw鸴EF B{yi.orY6Tɥ)٢*e )@שa.]ǡE5;hB程)ѳ|!tK i[؁f@Qj< 2=di'ĕ$s<&6%1W657}Nq6Z,RV;Z[_oW(C*c?Ob6} \gErQKF;Qm + ID0:uV tOA%;ZswhÁryfB^M^KԈmdt*ug!t AƴCt엨 kCfwt~5 Ð۰N%5ADᔟѦ3^<k BuoD !3/tXrSt ʺi73JeE1r﷍da h "%#D8#E}@w’6ꜣ67m}-ݠN)ktT&Dn嵀N}RƉHJZ_}=@`xʅyaksk[]:y= g[H[slJ1]g  7<z#6Mroo.Ϝ,9Dz6~I&Y:V2iqJ$-5IsO] {_Q88q0׬,YW.X5X]nzȶ/Y®0$6OYenp ES?]DY45!#4<3CITϖv{FeNa$~~ϱmnC`+{Q{GqaJ8 A%02˘U% M,ze75+[z3ca:Ʌ7ZJ,y[DfsU iZg_(Bik8#RMt"gn01Fjwye?ẃmS;8D[դ5 H/uŗz,V52ؙfLhO S 4ZL@%'FJK heYQ=Oa?V7ev7Fw$PS Kv@8;SDL]%XX+6'I nAb88ά+ KβG歹 >V!XEhC9`0Px ۓcX.-9 ۀJuIP46k:gR<)@/"݌Py^ UoyͧK_fJ]"@k6"Q(Tɹ,>덊2u%k O[R2OKbGh 6ݩ]֊6`8Jɀ1S( D񸝉42v;2AB熂h'T?L֢NDz-`2gn526464f:Уum.iq U  'L5Uo:G6r!K䒒$ԃaLsdq(.Wyb.}8"IL 5(C0-U >.SD^8^u:wN ժk*J ESnyt- MӎHD @]yyGW<yb/ *O|LIIF qvBfѫGT%Iv( 1Z:$CݝJݙ/Ipn ƽMGUm؂azw%#Ȗ"~3$m_&~7t\&Qɔ"kg! |t RNˇ|&O)*E)*YK =Hq+/E3sBX}&K݋Ґ_s1x-i="X-0fyHx!7c&J`0/%˄>l4*SjZgkE/6ud$(;:Pk2 endstream endobj 98 0 obj << /Type /FontDescriptor /FontName /PHHPUH+CMSLTT10 /Flags 4 /FontBBox [-20 -233 617 696] /Ascent 611 /CapHeight 611 /Descent -222 /ItalicAngle -9 /StemV 69 /XHeight 431 /CharSet (/A/B/C/D/E/F/H/I/L/M/N/P/R/S/T/U/X/Y/Z/a/asciicircum/asciitilde/asterisk/b/backslash/braceleft/braceright/bracketleft/bracketright/c/colon/comma/d/dollar/e/equal/f/five/four/g/greater/h/hyphen/i/j/k/l/less/m/n/nine/numbersign/o/one/p/parenleft/parenright/percent/period/plus/q/quotedbl/r/s/semicolon/six/slash/t/three/two/u/underscore/v/w/x/y/z/zero) /FontFile 97 0 R >> endobj 99 0 obj << /Length1 1614 /Length2 7807 /Length3 0 /Length 8895 /Filter /FlateDecode >> stream xڍT6L&Uґ.7齗BIHޤ " 7M"M@s=w?=dQ[[nVP<|y =~> ! >]8L.` )Qhx  E||b.x ,p G;/&&;@a  (Bݝ䁻?xp`$ l U2@ S! @ˠC]40$f vw詪`_dO?޿A` yB`; RRAy0_D  G݀(M:$+SA t™)'[wo׫ }$7TFU}[qfNfgh7)Kʈ͌1 WH$0.0IFB_LvLxTPThCLX:]oYٸ [e:Xj=E=]məLL/f4(3϶yZ{m,[n Hj_z3Djs?cl-yC!̀xSH>.VI~2rڀ5dWw\Z rVqYLNpm湘jF7Q7; i]TZm*wnjEC$yeYO@AJnڂ_x?x۫v6-)i4↛<^*< m 55Vk#}WIe4,#׫EB:aZ!5e|",$ B~$z896fI0*띖"<=w6 )`&⹸RivA4 F+-fS-걓Ri@B<т6\"4Ngfs?Gf&AYO-EɱkF֐N޸KtF@ٱeV=ح+WK BY4a9)ϹniiU-Lϋ),xq}{e'S^O`^#X՚/S%ĚA,%_5 Fہ[SmP9T2p.B\ݯCbqzKl=F9AgyyKD~iV{ 'y UJ'BV* ёf?sLP7Ģl!KY^%θU2,=żQ(~5FV-[Yz;wc ^Qol;]<5 +$ѠQY uMj'uYeq} 2Ln$斩c{Mv9Z5vV+#^2ġ`6 ~IӨ֤cOiFrKη:Sn%=QK2>,٫]fүP`4:M!9(|c9fxX n;Awo=j9 8=tV[櫛&/Q.>^vE-,u\GTf%ZRrQT$H͎עK՞ԥ27[Pc @{/Y nLܤߗuz?Ndë?,4Ȯ%5vmU#*9f\56 w{ *"E f>5݆Ґ;w"N6E{{|8zGv:m\yV8d/?@0є)uy]?\~џ=ʯ)'5V!sXTccN# .wGDݪPSl:mn帕Mr̤u ̽{A-ũ(mQ<&B Ol%/{Ʊp7&[5/Ǣ=j: шLN~K W#];UD~n.B#,wwy 㚋CӮ!:zb XB<'rm(8Wu*-t\/ŧyQ(_~,>vXl+dw3y](UOmoxp&F%>̣Vx1(P,-Vv5i;# 欠5ֶ%]sxQk8[,(EMF16'`]ƹhօٰkdH~6zzJ%;-ӝ㯖 kCq.ƣa?|20R~2 ٱ7~{~5#u=%ݍL;*d][O$G<|)X* D.$m( }2JEtt|)(H,`"Zvig0xLeJJ섿`v9S?C1&8G)ҀҭW*H'۫KZؕ-* 郥ǵx ayqco}$(;y4ד-|rkBN7/D-Uԧ7t!ۣ<9#ꋨG۔Ӓ@UAR;1pn㾏mb}E jhdUu~1dрiP^eG'[$,fMp;'YU0j R:܍YX-mP4.nZke }_<Htk}HO6qڽ;7۳%\I :?O6]d@1UVNܷ5 嚃[OHz;-jN^5 Rd9b㤺~f ;FIME9K 8pd ڝ6V%/^x>d_f.#+dlacE.y4mʕrM8P\:0Ckݏy]/A2meAd%)$S0X85|UwӦ}ϒ}zJS:[=IJSf;_7OiBps̴zNQ5##Famu^7ֺsuAM:uSdw<iB;/\h35rLE(Jٓ!tt5NxbwMT㢠oKXOQnnȎ᫈׼}lBoßXҬܧki2NC5RcCZi1ƻڋ,JRA]}ragg9j3~5f 8VT^v)IQW֏ʊOZ}u pI͋W4r'pק"ɶkݖO>ygjL. J.8.nD#qAs[+B$DSh/JHg3xn#v ,'HG} Tz)Uʹh#gI܊ꡓuʁ]$_`dW NdAH\$ϝG3HԻr0}1:xxMޯZip3oO%ߓM\Sy5>q#Ž`SO%CWZ ^JZ̭=ۍcc8?Zw62K=[}Tڼj Du8=Dn,*@ӸA`H&K!(7)qW[x*WSOmKpmvjZ@+<  'kWPc£ `q+0L2ۉWTVЭoE+m~׏u| wme`exy&L1>;M Օݵfy.'uIaړ2=7?Э"N9)2z6ޒ)xmumkk)ugKh7SoqLq{k6VjM -! \]~,~Z9+S 4K*Us\ӭKQ L`r*{ w>pcw8QtO֕0U t~YhzF[Mpwz;َ=g8Z/<7 ŀ? 5/sͻ9!WTxVRp ܁OA}_'h fDڮc:XxcN-&PÉ#(Ԅji~ff"vw[jGNɽۏd`KJɼWCi@$O&Of,se!>_0K=e_]ھ>-dP xYn.mm?s˦yAڄ;4O8L%"1z!24'wJ՜OvgS3Xo2-m/UFvau^U(Wi2#E2E&$عW<49jttcO0ޛkXz~u"L/|Q̄WKZ-[ud6NMnu]/^&<3m _M7.FW)MQrL-Kq,6!~fc\`r3\c<6rRaU8D?{o3bMbfѫ1ٓUL@9L0r xifYEx_] }5EMUG&e٭.1qۜ^IS$!.tUW?,ng-b7 HWo- R}ly |w`j'=3fupfq*v@'5hfT}J}$_+ڡ\=&oG]@I̕aWP}]N}f][^W#SK4/gנu+غD-ENתylaXW[ (\ pRd[(M)ʵ$+/VˡStMč{72u£ J_~7wEۊ~\Mn{}@EJu Ӽ^Ssgw: ^+&h|TҒ<'QۄHǾ'P0&8;X6XwO{hD_R፜<fu5Ӱ9/$`9+Ϗ!kpQdY5Es\h n]R9(Sa$㚣lP,O@^<9D5-_` ֡K>Xse'",r`xW\>g .ʷ0wY֝y,T;T|iP*1%o,*4L? &$םO=5L+R`MDMAԹ8XLL8dz/Hd<9X2?$;URkBԱh_,֒WYN23BqfġL'px[ NW7 2Dr]:[ e0/Ik=YZT 6/2e =_ٳKBaKP7̰ōC6/a=)L(/oǞzJ(1:#."KxK9"LLq[l"vK_$W[-Go!< sު >_wW<,/T OL 4%i-X=_2oQfx$qPcL/kCp>KN endstream endobj 100 0 obj << /Type /FontDescriptor /FontName /XDIDIO+CMSY10 /Flags 4 /FontBBox [-29 -960 1116 775] /Ascent 750 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 40 /XHeight 431 /CharSet (/R/asteriskmath/bar/braceleft/braceright/element/greaterequal/infinity/lessequal/minus/reflexsubset/similar) /FontFile 99 0 R >> endobj 101 0 obj << /Length1 1423 /Length2 6347 /Length3 0 /Length 7322 /Filter /FlateDecode >> stream xڍtTk6(ࠀ0 -H C0tw#!]*eRHt ]"(zsZfg}];5 xA|9 =cQ? ?;>  &b7"]a"!`<  @" Qq~~?Hq<f "PW"v9fkBoW' zPt 0v! 0(_%8%P(gq Ãʇ@Jq=xPv]+ vos!lP`$a("z*-g(Y௳@+W!w2A89^0-h)\ܠ*Q?-(""$;^A/=3`|\P ߁@ 5 XAmapa͟50O)?Z{ oOF_cE?Ex|xAއ H6WmE:vK ZjDn/A?@RS*/wCnÜGs m BVj ss 6 -f^ZkP??e5Gp+pEwϿUCֿ|& ,#`/"~> ! (t =$uh5uAW]PG/g!'o3>_ȿ!ߢAO MM B+C0z -,5E%wF 8&_ةg*ZZi}>2Ƚ}Ӭ5;h>U9й"{b`MZ!?Hamicz?pghFzUk*#*N&i+Ƙm klFO4MwWy2t?mZ1蝛L<~^4[5/3=ubj+77) w 9汝*ALLlNb&>X$fRPu}HGOo/)Z`,p(UܛشtT0>6fˉ|H׷)7or|KS2zq5#^6Nɴތz%4ɺ3 :GF듙JG;AL;Yc(l.iX\*kGP.YM;.X( 7#fV{_*-Ϛ]gO^g#!"Edtc*|*`VQuU? {|Ru ˚tE/60R~NaLnn{4Ix'>#VRV H)~?Cc,Yѫ^ò>#wɉ~w:^u+ aC^]췭^]y,} ɠV]i%Dt@LjOل x L97mq3p_|-Ee!A .ƃ;1BԴh&Zx2x9Ί Ӝ3ݟ q70? ;uq q|dq5q(L&xxVG!xHrӇ8 gQ\scȞn \k tZ/#1%[E*rO 'v}xds|)4'IJ|AWd~ nIԔ偷+ P_O h%{9PkDgyp*eaiMJ@OT3LPǜqcI.0CK3֓ON u_o;=">%L vdɽjũڑ)w>hc !ϯ6c}s ,hi5w&m34}|͝Dz[5{]?n\9uV=klDӋJCw ЌYTSB ߼t}<Ak^^EyO\{lo_oG}E3ެ}~3Cܿ:aPDKv~jـ`^'wU8CUaiu۪k.B⟔Ιf~iQ'VO{V5O?<-owbҚA TѬɸ{wYrz<:-CɅ#|rhV?` al90|\Irϗ~h+ o$RJ|*L! :PDނJL$1N2W׃L[[5ꓘ^|y1?GCYꚇ”lL#̖pBNui<*p='C/cn qR5cip+OdíYtv:MXD0w?X)E} !.=؞/N< &q#yȌ4k.o94 ]JPcUU:xuƔ/p"+۵I[,=6u=Sw M6'ګW̩F(^?MZuiۢ/cF؍cBsCHuӘ郕ãqLAkv|-"?&/:(~V^Qf3@`A@XJT5m[h?gBג/ F\l*_Җy&I9 ?d(cr捼O K˛pܲŻ:7%v< U*#2RIc+GSd CڮۄM6^YtE17TpXY_ nmEGi:øDYwHW:}ǵ* HN,y8ݺ,"\RᎳYv [Gdo'.$BI~+6,P֚.& xb'  "nC1}#5 s'vYbYx'<6,|!GGZb%&T;&ᛃ>Tfw E<-^@5HUJeҝ:9&n'͋i̬O+?au.mOnV ^}lpM>FupR0LΤ;MyʕWf!tHݻ2/ˮןҔ @Y97)"wj؇`W'1G}߲|ƐlqǷKgb"&6T2x8cpE@_\xU҈HTVsDnrIW|})ITIzڶ',n `r\3Do3 `Τ3yBc&Hk}C47ria\.}DbdSݖiQs@JcL!pٖG"ɯCz޷rjv]-1_DŢm-ž]}dJ\ lg[8[c3%uR<z'HxL_iCdDD̒@U3c1frx8pazzvmKI%z^yICo560"T,r,ny ~M.OMX穿N?_%)Rv·a)b&tN[vS~^zQsMe-+Ác~q%X2NܹÇ Bx̜M'o{@ &9M=vBE琯tL%_6C=jc/γ|?V>Z jJm8 :|Kz d<+2qHfרYm3f5|rR~ђ !VR4/Tz(Uyueײ5GqδO<&baޜPg!$:J;u a;<SJE-;]٫ӟ7MN2ZU<|"dt後2&YnMy#} cފq%hNV~aB5Xan>D9IڀH$T+0~ O3Z0ɇn;P˩u/n*a.S7d}{Hf[a;*% ٧@z 3ޏDg0EEs0rl DQ&)G|ΡqB7FMC^F5;]…AmFUucO$ur6TÜ⍧Yʃ룍kȋL>F[êJ$ kW7O:J̛kѼ^r!]ς uEu(Bք2>j\4N{cхTpJ.ФWQz|? ~jCp%)c]p׭I{8ŕ\K$~\6uMعbwBFðhz:cWYnq͚f%J~DJVbd>&8k:Dd7ϒN7sr)sJn,|WTZ_?h(~ueRo2bzlzK+O ىv`-!^i&TT[InK-~WS̨OEҩ0Y0}{R/v5a3>uegN*yVZ&{V,ʰt> f9Xf.4PTjZiLi޽.NPёaa|tٱJ⋼~fl }GDI 4UQ4ƤTg!T3թ;J쓟zg]b6ohW'}>f.UK@: SݎƇ]W1\r;xߊ Sb vꋐ..-{5=QK,y{m@gȖvD55#IAIvE$[Ɂ0Q7{,bTYHՎ  k@o@*m&UKfyS J;ӏrgA2P%[mޏOb[r 9 ,G$pkd}xecrt'CH&dVd?::ޥ<VzG,#7 :%:Y_1qÚ:$jBfv+_R-Kj2:a|%Z{}^ L$&+ ̄P R*bsU6_'N"ԉeyȞ|g'[MbNii'GZx 9;7TԱTP&5յĠ*RHco棆3@$r0"为z~ պi;Zo+c*-)iaeY;8閷3"VVxCUH0pfYC^2” f)?C1 v!̽fRDq],έ#} xߑ 2% hϫXʆ/3Ya%Tؿ!{KC]vdXTU<#>[15%*}*֠ ĩwaOnm̻o70[wE^/7J9z2ik)ǹ ^?߿q~4AReWX ҢZEL4w3%{#=\cBt]BG0*-El[sSn|'|C!u/r0ABܥvcwHR&%Ǵ#>j3GZy|"[IFzPzJ<:}ޒJ[1JkJx|i lk*Eb9BwtOz`@ޝ76ӹg1OWU)'GIӅ-g*ŵ&qiE)BxXPBa1=3pdM@=e{n|pbaM;4Ir>I+9 x|C!e` oY3B RSm-\9pa#n=xs5DB~b`p@lJ 0B&֪O_ B*OKoZUjj*30J[e4 ۛRT!@nӢ^*bZ;˝P,#jR+y`K7u&7._SA8Q'w6lokzS{2~K+ YBFCgy#8^4ӁJ@Vf1m 悦pafQCR;r )Gs E&KUu7޴WS7)Xw QNvX*C4|r:{NV1o#I;gpV<^f-{P=~6F,۝uO8~q6ӣMفyg*rd&)n6agHXa-6ѯڛ|i~py\dO"Z3 endstream endobj 102 0 obj << /Type /FontDescriptor /FontName /ZWLUYF+CMSY7 /Flags 4 /FontBBox [-15 -951 1251 782] /Ascent 750 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 49 /XHeight 431 /CharSet (/R/element/minus/prime) /FontFile 101 0 R >> endobj 103 0 obj << /Length1 1540 /Length2 8951 /Length3 0 /Length 9968 /Filter /FlateDecode >> stream xڍT6>t7 2twt 0 03R")ҍ ![oγgfzmg+|#Ws03Ðq .0\ y(`S#8Pp*a@MnuaG8ylk dyEE :B]`0 FAvz lvH vtFJs=`H;.2P 5nf/v 0vj;A5"p> /7G"`0ptý`p[  |Drp?`WC< s[=, T:?W sGiYn-pt‘8ԧsB p!6ݜ@pTUo΃ ?6[((#':;{9Ata~ yh>ݡ@矎F8@k 8` | ?^ f;x55L8nN99'  O(<`u#VnU9d5;AP n#y?ϐ?*HO?_s\7h"fT#_ 9W ~Y탢 pe*<0$/e7c`p6 ?!?"}WAX1l|B@  Їa*#!6?.VTa AVFA ?Pr|P"(>rE>l'!n..}8?( F@C_U6_T>xsO8h]}S'X^?'zF}r#rdޘb7%ZbjwDjUÍoCԒnmKqYǩ;%ϩme 0YqDcR㡆ȦUNL2 %-[y/zqHSӆۊx[M@ ݢ_AY t9I~\}*NUS̴j8Zu28ĻhP1 oOpqFcqw鄍{Q}15S7UzpW^'IRv]?YgJî3T CԺ1=gEu[,vƮʲ 5k̛q=C cvMu$vIS0GFx(Om'giB,;(U.Ӟ5(0W~qLֻp{έF WrL 9 Y>ֱ Dj-&Șq[ܜFe,}U$bx#q :ˇepM' $rak8arvSWYڝzg(ig@@)?8C;`rB(jfM-bNY\m!A5~VPh'Tw-n8R9> kuv,! :b"⊹+@B(\ -:3$/0Cîbo܀*띮^맴M(pz?XSgx(T3mX?d8$+rhz<ѵ r<? H%jiΚ5=2u9yv4;4S$VDz6,' ^sռk>$uK_'kCXbڲ oU~2ItQnOjVMtڡ@ҷjuKL2"٥t7OOkj3C-JD3Yms5[þ ~ri-y<,N'a:bnV7 Vn,4nsRIhc-JQy([Q+H%<U݆>9|+e,~L{eijjlo2Qk^?ۦ| `_y}+DhW%%`乧NE- \h|9Au}Hұ?X3d U*B-߀et[of:<[w>]<ҩ '=- Mѳv>¢u bWrSAlS6M1va&Љ̫ϒ/5d~{tj~4om,ݻq0Y eYY= P$OMs^,! %j΀" EzlbZpf' "_#ꏮV$%:Qײ@IC8gj~FއWtJ;x4F~OS6F>cC`ܲ|p=_K ͬ 7bpr&:u]x \nn*Ie#p-+ؾ_.Qo5Pp({ezDDveED;^ O]Z::91si u1Ujq$UϷ[YKf)oZULJ++ĺa`"雂_<^V:TF×ȹǾ NPhz3}d_B֜~,~HG IOߚ' )FvS!޽gK)K&]W8#$*i V$ѽX U7&jZL-dߏtyipU|1_ZE;lX5%dƂCc[ElKKN?|꠺663|'1Lɓ}Qg4;$_3~A %LV%=zU>l^&0#-a@-ZB%eB!ΊafⰠ7U}E-LV@A $_a,^*^E VJ!K6rȬ2e:<% C ʴ;NQq>.6kc7"-?^JFH,iXNQ-bDK>Kx5xZobuujm{y7b8{s[%֖SgqtWwP ٦c9 |40.~Bu,7Ɗ+_)=1OE.c*nT`|?&^ +7~uVC89'kwsg̨S˜hBxW oǨn*=*=#?-h'IKm)@ُߛsG\tGEE-{o&LR.Draz (0 ئ]hcߏ9h;V?:+vsyt LS u{j֥Snpbܐl73nڵRM=?I/'^6*/o-ĵT 1@ Op ӏ<^{f$R? ?]m*%jhJZK&~{a] ,Z`38bPerEff=5s~?/p%3[Pt?1\O]!^DuE^y%{پyT׍ZrnXk^HQoso y﹥;*&A/X6hH^59} 7T01Wq'n7`@wF<Iqj£3I_BoC  b7gB.J iVeGpFJMOw_C! h,\=0 >ɖw~Yc''tPcq )+jajsk6c\''^$ x_$SNi͵y?FqѮanZA/PcRW,<+Ab$JʞNaYVtL>Sp*ɆCCݹ|)FO|qœ0ƀRhj/ɳc{q5dR&+~FXݯfF[Σ΋/FvϜFҾEg+@7V-m9jce7l.Ε+bB>Yn ŰC+8t/6bòVffzvx<|hS Ɣ=a5vGL}Iu뷱vzd|~eyn{6y%gX%M ?&}ֽG3)%N=; C@,h޴G֑;Zuzr**h]ZN1*̆όDzN߆{!<=3,c52D@(bn+Z|pP/L5<- ~{-{@L>whI=$kNg]9+?(RX zDxTIȻ2Nb j2ο)FPK({J=kX3|ET̄0i#Q)__ Ob7c]Y'h,TwiQb|%Jp'橡WQUy֨"9GD.DpUڸO- ՁYp y/~FS]:}ȠpibH *$`akjzdx k&ƼX;Ќ즌7 Gfn"k6syν1{ƛ+)4u"NİJ'JRnPq1Y?bWdar /|a"z+e͞c66S XQX˒`yg~-6qfm'obb||B9F4)or(zUJ[FDJՊ{0p7lƭYԴ~.(cwT}}@dU4qLQG.0<ح]t`WÉ=Z ڣ_U-ܲZp`׌ lwu)1҄/n);ͫ!8b\q41~7/SgȄZw$tb6!^A^8#*)Hz 哚0)&`G3yFk=U'{띣]\}*8omdA9{-Pjꅲ`6:{,֍T顛II]4-cC+X\cJj?t-2hd\n؆")4Q^C3(I{NAB!cb$k<ϖDg)czų[($fh]XEuZ6P32|9pv.{\YU}ϥ_/D4GjCؤrrHyF圙r.aLht+?& 4SSk39ޥIyO^۶3֣<5!Q\^v/aj z>%RiDV{L.^BhB)kȊ$ŇϚOs1SUTjہ W;KnLRNI|5I 6EAN!WU1ai*8 74!Vf3yՠNΕxհ[LBc$$|gՊ$Q3ʳ,ˑg6T-j9Xgr0&zֆoddDK#ʾ"бj!7"w}XI-+mE.)nMUCfQQ2 ISpK,nt{Gկi@):n~˶qhPKB"[_šv8gy>'Qjԛ_V9Bg?gdGyLӘ /yVhRςG'o^zbvcYuŅuROrR(îɅ$bnKH%kt?GlzNdZbHmglΰWp;#%*jeN=paNOM2S Y%m:{=6"ooϒF˜{`u(Sr]&\jL'Ohsw[~iqj9I`'Dw!N?,Mcd#"3=krLD>5 7Ry&!FKUvnSՏ+;MJޢRsYmfŒS pM),/xM2Ԛº`/tP,'yx5p $pV^yᬕe[e\ٗ@ۼ >=e6dyȳ>2j!>5Q%faKcb @퀊{,z3W_"Kp u,q2a9no endstream endobj 104 0 obj << /Type /FontDescriptor /FontName /PLJCLY+CMTI10 /Flags 4 /FontBBox [-35 -250 1124 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 68 /XHeight 431 /CharSet (/a/b/e/i/l/m/n/r/s/t/u/v) /FontFile 103 0 R >> endobj 105 0 obj << /Length1 2250 /Length2 15729 /Length3 0 /Length 17079 /Filter /FlateDecode >> stream xڌpk Ƕmkbsm۶m$۶mN8q2/fWS]\׺׺j2"%:A#[c1[':&zFn2#L?ro6v0w;}L,&vn&nFF3## m".FYz# g<( L\\ mNf֟ JNɎՕ^ڑ - hhbl2@NafR(ٚ8;>V6.6F%IͿee@ wsLL oohhkmonnc 012ȋ;9m2Էrw774t}W's4t0srw4#_a>,jc$lkmmlW}"Ɔ}wgZغxEَAXR6"?2Sc'###' 3`fhWew;㿕L?9x{L>i{x:=_027t)66<s7&1IsŒlm} B *4_@`cs7-_~v?{(T%g9?chyv7E[zͭm9N; k 6T_+kldlN hcjF;);=gV6 ,:&F\.Cs$Vf15kɘ0dF#c@ocd 0uH  BA0q0$O??O SX J AA g>?`}f7p74MY+׈W3G!1|27wgN?!>-'_z{a?.ř#_j[41l!ǧYg}Q{57ϳжį/^񊳇0+3CEgxtG^o^-A[9 P\+'BհKþVEDi.d/bC8CQ\!.?̣NJxG{j0^جRfv&G%"YVͷHE=1H5Mt)#h%>A^ugG]gwEc*&^ R2s4 @c$ )y v~v/}vQ71i ,)j& wwUdYNóbnMsR(9 (l4*t WV/(:;EF􋇫+^Ut$J3azBzm"Gnh'ubǏ/F$4ug|?E-hd4EݣEH3j ,L,"ϋcuefgi&YE!::vS#o.]^>ǫ4[Uw_9ן]K61߫>6RUc_\D3~(m =XwWvwTtڸaQӐkl3>8eXJpcɄ<=͇}4ME]6%X:SCexJlUù32 9g% 74WA ˞.AaljkD]Nў=m=@>'.ͣƀ 8$A%$^ӗ#PzH ݶ.ınc4F:o[D?isʔ_83zdqol$/, 2Rʗ5n\Y`A8o`l|C!^eX!.5 b`?O z*= E8 hRlOWOWzyVS4:Vw3_~#fͳkW8H}Xzep$vqKީI+́nher;Y5 ^Df#sB-q5 k9^\Ã9EiP*PTgtNLDX p/Ƕgr7*2Tݟc,AʶE6ެ_5>Fj=0{U4>D+rĿ:dzr}ѳŶd(9ApKU 2"\Qwr37}wUy N,n225}:$Bѧ.\ }v!hrΡrnx;Y D j"8>q\5TYmKMfh9lƍPm -{}5 Éu14(BX##x(0mF,rjA 4p.r\'`9m`8簎Bs y~ ֪ITP2X~vk<;YIE{FL򻲥UAD=%7Lޯ,<T";/U_tNѿRkό`Št!%w^7ЇNn"',m:&G.]"ySZ%$ ֕nΜfp3rr7 |Fڞ]~ ZylP.ߧn=3h,7T0ZaT2遻/9_MXA:O[LPvΐS|ϟ\4 >}UU15uem6kǼ$T]oxE[&N69ۧ cw_HxF $U07WDm|9;d[[^٠Qy'Y%[A%vD. q,>FQL.|mTjj/y7z Q)#£ {욍jnGL2HjbY 4= .9I-!hMD:Ĉ2 轴56裯#߉0qDB(x߃0!YcطCcS~s)_q\,2Ԙy(ftJy)>s"OBXU*{8|_(3H9 0 6eHwkϯWa1D_Fb. ){0kQ0헢!92abQΙ^Ӕ|XPD샲'2$وa\\?8cRŻUCZ"Ir_Q:XuU&԰Ճe(4)|8Vsg,X[GeVȜhgIxU+%m܏tCv^=7!VX#N<)#`82.&bRW6EJX፡6[9 b`[Ҿ~VKĔL%]k0p6/CxyҲ5᱕Jhh9k`)(6Knu?(m߯w&w{0r`{T0c1gu49M(ó3{3I\K^u(ɸCoޛx(+Mu}jN t1{wԟՃEZHM9R2[lfQ({q=qu%,A%ќa&~%Cp9!c's;9NHjx5 hG,_?t x {>B(IIP|ehv#_*nVz,~dIR2)ћ9 +ԩN 9s" r=[s Kwn:Nڂ< 7u'HCwC|A05i$08mDŽiI?amJǮ4,Xg(=4Fs ts$o~ǍN(ү$x^0#}cixf?h"^kVhwSF/ L'%ZSUMpJȣBQ .7(? -]H:a:K< Ow> 2[f+0.7xLkFQvNG;=){(,|W=q!1sJI_ߜ܋˂/] i-LҖ,2$ݗw$K P#,)KtX`AӘ&Cv!d`j 1UYiEutjcC~]SYK6 M9P / +gaHyUi i+zar zvS{'eNД ^<%@jA- ‘@@_ʎtjvJOP9xFoqedgt'Jc{JgJ̪ٶ.߰$.F{+v#_UR<#+=/J.}\6_R6h=^VTSF!(FI#1F2_w7Q gZ.FԐqͯ_;_hp4l2Yg&(ؾwH76oT=RIqZT0%4r #b su/'cx=?ˎG4={8gb~Ӝء/ 68-#uzc:o]5}xxCZ:  Uzw)֢x䴋!Cf:5L/zZ%Q2?Ίb(S~zphz2HO,j7KZ|wW[}5$ pBnu=52,J9QSkmD.}y9F90n -{} ` CG|q"{q{W1C'h>j'Lx67V#cen`3퐘rzl=ap$_-̇dmx ~۪MG ܃b“a 6 PE(Ilj5l@7/]xYY i X^ #k蹚+WV&^ -l{cPJu۬Ƕwu|]vGB,1e򒈞"tx%نH`VJas{m'T9vst?&;y{YֈY34Q~oG -Cx$79+Uݦh  YrLެ?Fnl&7*9#/RRk@mv+( ;<ʱ35æ K/(w%Ş̇+l1-MNV|4SZc9J*e*St)GZrIf1nklbªA%[׭T jl8` ~wI#W`ݫqUIsLx"x:.Qn-DgL #ȏy@c(M-c*cORib՚';P;C/gC0`-WrCJ Ճ/(6q%8ϛ#i`&\:F u$ۧ;ߧ"\W}δΚJ.)$ )r[zۉ.ǂ)ZK,܉N ۏo9oRVr*Bd7[ FҎ`qA Ϊ]؈=O/-*Vo6H,LDr.5@}T DdC<r`7XF!t<䃸2隱LV'(F.Z'oN_&(xFmNY)u쉃I lbEH+axu;B_SyR ";sW'@zK#~SmQ0h,t'ġV&RMAwk5/KlbJHF̺`++=j(pʙSh[gWwW+\*%.jcY߈@|49u $| .p7u;GL/1?pI3N/h 72,f-wV+I#IږNc0 չgv9aP,k>p*sadŮ" (OGdkvѯxG_,?.uP[B \Cy=yƿJg9O1&1-*b3?Us(a-B'z(N3h?ñ24jyȈ:hDIqcC j6ow2_5  : ۴l1A"Dszb%m/@H;⏾ٲPۖLK.wЧ9{je#6ғ=͙]&V!%}^T?1sD1<1y18o382'o5cI-`) Cqxs҅s&څ^b^k/_'i$c69L~p YkXFbe%0+̩Ni0/[x]t(" N&[mmHW= Um_HPTaGaV,a}ǜ}E8~uKKD}Kwr*{P0]x뎺sנ I ,7~^NV96/7)UЯ(-6ꊜnVj 7|% \j{uI,QiYj5df!`"vII[mMwv)m?Oȩ' NSŻjXIgEaa2_0yݭG96cYRJ%SntE8Tu'@RkA 3? n\S )eUlհT>@O,CavD[F%1j媥7B+q;C+,G_~cRvv''Sav+:KA* Sr\MT- ǽ^B̎51Quj;[~nUv0d/ßj@69ihiU8vܥ,jnY)J.U LكU{?>ḾohDN ДWen$.@$x:ųEQpaTd Hl$B톿^pC90cӹV%>K˜ߑhG2<HH=; $X>T3PjK8r"8> _yՠWsZb:QѹX(0/ٖ`"Mh8gBLBȔ?>D&0} bx&eK}2(S}u}^4IiK;񡹦/:rgKi915~{.%=$Z&gOƄ5k%{R>Z ^ Ī g Irqn^# dY*H5qR2o1a7FM<`hg/RP{m[ }dU*1;V_51fZ,=gQĀ~sй81#pKmsa9/ %UҤ QgvB)TO`{^֟pQ< xR=܄0d_E|]ZgEmNVB2+SŊ+~́aAlG9X8[SU;6芥\YEZ>cNP4OX.q_(SyQ]Bҙ-9YdiQ R2FYo{(yALlpo.b(v~UmW_g Ց`u ͂A[W*S)At781%TIz{[Yi1LKF0M]]PufZ=5Ux D*-YBn-AOFΕ] ;B/i&TVAK- 6%Ht}ZpʉN'}#ipxh%_7QQ!aX-!  h-V\[VXDqJOboQD~^ܚ&GC>_]LKT ʓOdنJ45׽4Q0%LexNZrn6lX+8 d DX+З0?JeAcO9-'{XAp`?`W4hF`zw34SS$"=nu8zL}4$>FR] @^*-.4! āBWx)g~MhKWP +zR޻Q8PArVe80noھ|b:jmzq zo S5tfogNab>-M)]Ƌ1`gPP⠵j2EQbLEݼKK|tZy{εK& }sUG'%ޟ*]q _}uf~|L$c=jmw/?G nO F/P():%GoHy{6E1ddg~OX|10;?"łVB lŠ-529a]ŎҬ8XrP =&2mHA?-2J9D8u{ywQ5.\ "*6SхYvd#AD^W燴q>䘨ҙM}a+{==[VO $LIabAuRL=;011|:^4w±,i]t@,]HM^!y k%n$QqW }Fj8# F.:foAGm2<PMw81T[P7OA}m0 Bߟ rhsOG`mkay@8}!3I<QCP8ޯEmU_bE+ιJ_^*.S%9~qηD#`O7SvypE# cQ@u%=\d|.ɜ L6Z'Hj9xr)S iGLjٹ)*=7;\l=̚H[20Zc*#c[EK$DpNJ %˳Yd0];M=$K:U[.D0]c\x}4,>:])NgccNR1#0Ť1V#ܸ(Ù%"0״<8^*!Jm03-,S[ߙ#.f?$mY,޲o5ٿIş5 RP]]/yiŢ4ܯH-:9P˜mjqͦW;)y=$}ڏUbP iF@3R&4$]ay%Mq"/R;`#jq؎ nBܶ[4WV ?$VaNK #ֹ5KiZiwZpt: ̂{EAܳ!2v`<ĖQ)5욼)KִuOGs˒g]Y@-Jn _Tl(JFw\h/0?py!&[x8\U!ۢC6ki#t)eiHA]U?_!K6LWsnS$\Raa>HSF[Aυ]8jȢ x!jl*p.BҥSMK [y 0Xy꠩-*0! KTF3C$W:U0XnUsЈ4QNDykOc (_vѽ3y --x )I_Iqy5]0v>~ϖ,=I'q&q,/$S,9 s|{7 >nrZ+>Di'f77La*'soASp@D/ t+n(' !nmx"`yo} xgZ*m+ o͜Z;ʺʭ9z$Z﬜jgFI9dȲgI)Sn}cds~I܆ E~BHZGVS}?]7[$#Jy[~Bfg:E ƊMOE3'x-Tm|V(P .IXM &{To|QRafjf]e30lSU<_,PTaL~Vߛ Jl endstream endobj 106 0 obj << /Type /FontDescriptor /FontName /TBPIIU+CMTT10 /Flags 4 /FontBBox [-4 -233 537 696] /Ascent 611 /CapHeight 611 /Descent -222 /ItalicAngle 0 /StemV 69 /XHeight 431 /CharSet (/A/B/C/E/H/L/M/Q/R/S/T/U/Y/Z/a/b/bracketleft/bracketright/c/colon/d/dollar/e/eight/equal/f/five/four/g/h/hyphen/i/k/l/m/n/nine/o/one/p/period/plus/quotedbl/r/s/seven/six/t/three/two/u/underscore/v/x/z/zero) /FontFile 105 0 R >> endobj 43 0 obj << /Type /Font /Subtype /Type1 /BaseFont /HSTHLL+CMBX10 /FontDescriptor 76 0 R /FirstChar 104 /LastChar 122 /Widths 52 0 R >> endobj 6 0 obj << /Type /Font /Subtype /Type1 /BaseFont /FQQHSA+CMBX12 /FontDescriptor 78 0 R /FirstChar 49 /LastChar 120 /Widths 72 0 R >> endobj 29 0 obj << /Type /Font /Subtype /Type1 /BaseFont /NABPZQ+CMEX10 /FontDescriptor 80 0 R /FirstChar 80 /LastChar 89 /Widths 56 0 R >> endobj 9 0 obj << /Type /Font /Subtype /Type1 /BaseFont /CMZAKG+CMMI10 /FontDescriptor 82 0 R /FirstChar 34 /LastChar 121 /Widths 69 0 R >> endobj 37 0 obj << /Type /Font /Subtype /Type1 /BaseFont /ALLWHA+CMMI5 /FontDescriptor 84 0 R /FirstChar 115 /LastChar 115 /Widths 54 0 R >> endobj 27 0 obj << /Type /Font /Subtype /Type1 /BaseFont /RYRTXK+CMMI7 /FontDescriptor 86 0 R /FirstChar 84 /LastChar 115 /Widths 58 0 R >> endobj 42 0 obj << /Type /Font /Subtype /Type1 /BaseFont /UFOYRL+CMMIB10 /FontDescriptor 88 0 R /FirstChar 13 /LastChar 13 /Widths 53 0 R >> endobj 7 0 obj << /Type /Font /Subtype /Type1 /BaseFont /XAOMHK+CMR10 /FontDescriptor 90 0 R /FirstChar 11 /LastChar 122 /Widths 71 0 R >> endobj 5 0 obj << /Type /Font /Subtype /Type1 /BaseFont /HCOSKL+CMR12 /FontDescriptor 92 0 R /FirstChar 44 /LastChar 121 /Widths 73 0 R >> endobj 4 0 obj << /Type /Font /Subtype /Type1 /BaseFont /KIPKVW+CMR17 /FontDescriptor 94 0 R /FirstChar 67 /LastChar 122 /Widths 74 0 R >> endobj 30 0 obj << /Type /Font /Subtype /Type1 /BaseFont /XAVFRM+CMR7 /FontDescriptor 96 0 R /FirstChar 22 /LastChar 61 /Widths 55 0 R >> endobj 11 0 obj << /Type /Font /Subtype /Type1 /BaseFont /PHHPUH+CMSLTT10 /FontDescriptor 98 0 R /FirstChar 34 /LastChar 126 /Widths 64 0 R >> endobj 28 0 obj << /Type /Font /Subtype /Type1 /BaseFont /XDIDIO+CMSY10 /FontDescriptor 100 0 R /FirstChar 0 /LastChar 106 /Widths 57 0 R >> endobj 26 0 obj << /Type /Font /Subtype /Type1 /BaseFont /ZWLUYF+CMSY7 /FontDescriptor 102 0 R /FirstChar 0 /LastChar 82 /Widths 59 0 R >> endobj 44 0 obj << /Type /Font /Subtype /Type1 /BaseFont /PLJCLY+CMTI10 /FontDescriptor 104 0 R /FirstChar 97 /LastChar 118 /Widths 51 0 R >> endobj 8 0 obj << /Type /Font /Subtype /Type1 /BaseFont /TBPIIU+CMTT10 /FontDescriptor 106 0 R /FirstChar 34 /LastChar 122 /Widths 70 0 R >> endobj 12 0 obj << /Type /Pages /Count 6 /Parent 107 0 R /Kids [2 0 R 14 0 R 17 0 R 20 0 R 24 0 R 32 0 R] >> endobj 38 0 obj << /Type /Pages /Count 4 /Parent 107 0 R /Kids [35 0 R 40 0 R 46 0 R 49 0 R] >> endobj 107 0 obj << /Type /Pages /Count 10 /Kids [12 0 R 38 0 R] >> endobj 108 0 obj << /Type /Catalog /Pages 107 0 R >> endobj 109 0 obj << /Producer (MiKTeX pdfTeX-1.40.17) /Creator (TeX) /CreationDate (D:20210112140123+01'00') /ModDate (D:20210112140123+01'00') /Trapped /False /PTEX.Fullbanner (This is MiKTeX-pdfTeX 2.9.6100 (1.40.17)) >> endobj xref 0 110 0000000000 65535 f 0000001706 00000 n 0000001594 00000 n 0000000015 00000 n 0000201302 00000 n 0000201163 00000 n 0000200182 00000 n 0000201024 00000 n 0000202144 00000 n 0000200462 00000 n 0000023133 00000 n 0000201579 00000 n 0000202285 00000 n 0000003428 00000 n 0000003313 00000 n 0000001852 00000 n 0000004961 00000 n 0000004846 00000 n 0000003530 00000 n 0000005968 00000 n 0000005853 00000 n 0000005052 00000 n 0000022150 00000 n 0000008820 00000 n 0000008705 00000 n 0000006082 00000 n 0000201863 00000 n 0000200743 00000 n 0000201722 00000 n 0000200322 00000 n 0000201441 00000 n 0000010097 00000 n 0000009982 00000 n 0000008992 00000 n 0000012373 00000 n 0000012258 00000 n 0000010188 00000 n 0000200602 00000 n 0000202394 00000 n 0000016792 00000 n 0000016677 00000 n 0000012555 00000 n 0000200883 00000 n 0000200040 00000 n 0000202002 00000 n 0000018848 00000 n 0000018733 00000 n 0000016988 00000 n 0000019865 00000 n 0000019750 00000 n 0000018962 00000 n 0000019956 00000 n 0000020092 00000 n 0000020222 00000 n 0000020244 00000 n 0000020268 00000 n 0000020518 00000 n 0000020599 00000 n 0000021216 00000 n 0000021428 00000 n 0000021951 00000 n 0000022395 00000 n 0000022420 00000 n 0000022480 00000 n 0000022514 00000 n 0000022904 00000 n 0000023378 00000 n 0000023403 00000 n 0000023465 00000 n 0000023500 00000 n 0000024002 00000 n 0000024376 00000 n 0000024998 00000 n 0000025422 00000 n 0000025851 00000 n 0000026201 00000 n 0000033694 00000 n 0000033917 00000 n 0000042629 00000 n 0000042874 00000 n 0000050234 00000 n 0000050494 00000 n 0000063867 00000 n 0000064171 00000 n 0000071239 00000 n 0000071457 00000 n 0000080024 00000 n 0000080254 00000 n 0000087240 00000 n 0000087466 00000 n 0000109220 00000 n 0000109662 00000 n 0000118214 00000 n 0000118459 00000 n 0000127616 00000 n 0000127858 00000 n 0000135177 00000 n 0000135413 00000 n 0000154497 00000 n 0000155064 00000 n 0000164078 00000 n 0000164404 00000 n 0000171846 00000 n 0000172087 00000 n 0000182175 00000 n 0000182419 00000 n 0000199619 00000 n 0000202490 00000 n 0000202558 00000 n 0000202611 00000 n trailer << /Size 110 /Root 108 0 R /Info 109 0 R /ID [<8BF9B8A6CA950E70DE512AE3FB76A665> <8BF9B8A6CA950E70DE512AE3FB76A665>] >> startxref 202834 %%EOF sampling/inst/doc/calibration.Snw0000644000176200001440000003676713762142022016610 0ustar liggesusers\documentclass[a4paper]{article} \usepackage{pdfpages} %\VignetteIndexEntry{calibration and adjustment for nonresponse} %\VignettePackage{sampling} \newcommand{\sampling}{{\tt sampling}} \newcommand{\R}{{\tt R}} \setlength{\parindent}{0in} \setlength{\parskip}{.1in} \setlength{\textwidth}{140mm} \setlength{\oddsidemargin}{10mm} \title{Calibration and generalized calibration} \author{} \usepackage{Sweave} \usepackage[latin1]{inputenc} \usepackage{amsmath} \begin{document} \maketitle <>= library(sampling) ps.options(pointsize=12) options(width=60) @ \section{Example 1} This is an example of using the \verb@calib@ function for calibration and nonresponse adjustment (with response homogeneity groups). @ \noindent We create the following population data frame (the population size is $N=250$): \begin{itemize} \item there are four variables: \verb@state@, \verb@region@, \verb@income@ and \verb@sex@; \item the \verb@state@ variable has 2 categories: 'A' and 'B'; the \verb@region@ variable has 3 categories: 1, 2, 3 (regions within states); \item the \verb@income@ and \verb@sex@ variables are randomly generated using the uniform distribution. \end{itemize} <>= data = rbind(matrix(rep("A", 150), 150, 1, byrow = TRUE), matrix(rep("B", 100), 100, 1, byrow = TRUE)) data = cbind.data.frame(data, c(rep(1, 60), rep(2,50), rep(3, 60), rep(1, 40), rep(2, 40)), 1000 * runif(250)) sex = runif(nrow(data)) for (i in 1:length(sex)) if (sex[i] < 0.3) sex[i] = 1 else sex[i] = 2 data = cbind.data.frame(data, sex) names(data) = c("state", "region", "income", "sex") summary(data) @ \noindent We compute the population stratum sizes: <>= table(data$state) @ We select a stratified sample. The \verb@state@ variable is used as a stratification variable. The sample stratum sizes are 25 and 20, respectively. The method is 'srswor' (equal probability, without replacement). <>= s=strata(data,c("state"),size=c(25,20), method="srswor") @ We obtain the observed data: <>= s=getdata(data,s) @ The \verb@status@ variable is used in the \verb@rhg_strata@ function. The \verb@status@ column is added to $s$ (1 - sample respondent, 0 otherwise); it is randomly generated using the uniform distribution U(0,1). The response probability for all units is 0.3. <>= status=runif(nrow(s)) for(i in 1:length(status)) if(status[i]<0.3) status[i]=0 else status[i]=1 s=cbind.data.frame(s,status) @ We compute the response homeogeneity groups using the \verb@region@ variable: <>= s=rhg_strata(s,selection="region") @ We select only the sample respondents: <>= sr=s[s$status==1,] @ We create the population data frame of sex and region indicators: <>= X=cbind(disjunctive(data$sex),disjunctive(data$region)) @ We compute the population totals for each sex and region: <>= total=c(t(rep(1,nrow(data)))%*%X) @ The first method consists in calibrating with all strata. The respondent data frame of \verb@sex@ and \verb@region@ indicators is created. The initial weights using the inclusion prob. and the response probabilities are computed. <>= Xs = X[sr$ID_unit,] d = 1/(sr$Prob * sr$prob_resp) summary(d) @ We compute the g-weights using the linear method: <>= g = calib(Xs, d, total, method = "linear") summary(g) @ The final weights are: <>= w=d*g summary(w) @ We check the calibration: <>= checkcalibration(Xs, d, total, g) @ The second method consists in calibrating in each stratum. The respondent data frame of \verb@sex@ and \verb@region@ indicators is created in each stratum. The initial weights using the inclusion prob. and response probabilities are computed in each stratum. <>= cat("stratum 1\n") data1=data[data$state=='A',] X1=X[data$state=='A',] total1=c(t(rep(1, nrow(data1))) %*% X1) sr1=sr[sr$Stratum==1,] Xs1=X[sr1$ID_unit,] d1 = 1/(sr1$Prob * sr1$prob_resp) g1=calib(Xs1, d1, total1, method = "linear") checkcalibration(Xs1, d1, total1, g1) cat("stratum 2\n") data2=data[data$state=='B',] X2=X[data$state=='B',] total2=c(t(rep(1, nrow(data2))) %*% X2) sr2=sr[sr$Stratum==2,] Xs2=X[sr2$ID_unit,] d2 = 1/(sr2$Prob * sr2$prob_resp) g2=calib(Xs2, d2, total2, method = "linear") checkcalibration(Xs2, d2, total2, g2) @ <>= <> <> <> <> <> <> <> <> <> <> <> <> <> <> sampling.newpage() @ \section{Example 2} This is an example of: \begin{itemize} \item variance estimation of the calibration estimator (using the \verb@calibev@ and \verb@varest@ functions), \item variance estimator of the Horvitz-Thompson estimator (using the \verb@varest@ and \verb@varHT@ functions). \end{itemize} We generate an artificial population and use Till\'e sampling. The population size is 100, and the sample size is 20. There are three auxiliary variables (two categorical and one continuous; the matrix $X$). The vector $Z=(150, 151, \dots, 249)'$ is used to compute the first-order inclusion probabilities. The variable of interest $Y$ is computed using the model $Y_j=5*Z_j*(\varepsilon_j+\sum_{i=1}^{100} X_{ij}), \varepsilon_j\sim N(0,1/3), iid, j=1,\dots, 100.$ The calibration estimator uses the linear method. Simulations are conducted to estimate the MSE of the two variance estimators of the calibration estimator. Since the linear method is used in calibration, the calibration estimator corresponds to the generalized regression estimator. For the latter an approximate variance can be computed on the population level and used in the bias estimation of the variance estimators. For the Horvitz-Thompson estimator, the variance can be computed on the population level and compared with the simulations' result. Use 10000 simulation runs to obtain accurate results (for time consuming reason, in the following program, the number of runs is only 10). <>= X=cbind(c(rep(1,50),rep(0,50)),c(rep(0,50),rep(1,50)),1:100) # vector of population totals total=apply(X,2,"sum") Z=150:249 # the variable of interest Y=5*Z*(rnorm(100,0,sqrt(1/3))+apply(X,1,"sum")) # inclusion probabilities pik=inclusionprobabilities(Z,20) # joint inclusion probabilities pikl=UPtillepi2(pik) # number of runs; let nsim=10000 for an accurate result nsim=10 c1=c2=c3=c4=c5=c6=numeric(nsim) for(i in 1:nsim) { # draws a sample s=UPtille(pik) # computes the inclusion prob. for the sample piks=pik[s==1] # the sample matrix of auxiliary information Xs=X[s==1,] # computes the g-weights g=calib(Xs,d=1/piks,total,method="linear") # computes the variable of interest in the sample Ys=Y[s==1] # computes the joint inclusion prob. for the sample pikls=pikl[s==1,s==1] # computes the calibration estimator and its variance estimation cc=calibev(Ys,Xs,total,pikls,d=1/piks,g,with=FALSE,EPS=1e-6) c1[i]=cc$calest c2[i]=cc$evar # computes the variance estimator of the calibration estimator (second method) c3[i]=varest(Ys,Xs,pik=piks,w=g/piks) # computes the variance estimator of the HT estimator using varest() c4[i]=varest(Ys,pik=piks) # computes the variance estimator of the HT estimator using varHT() c5[i]=varHT(Ys,pikls,2) # computes the Horvitz-Thompson estimator c6[i]=HTestimator(Ys,piks) } cat("the population total:",sum(Y),"\n") cat("the calibration estimator under simulations:", mean(c1),"\n") N=length(Y) delta=matrix(0,N,N) for(k in 1:(N-1)) for(l in (k+1):N) delta[k,l]=delta[l,k]=pikl[k,l]-pik[k]*pik[l] diag(delta)=pik*(1-pik) var_HT=0 var_asym=0 e=lm(Y~X)$resid for(k in 1:N) for(l in 1:N) {var_HT=var_HT+Y[k]*Y[l]*delta[k,l]/(pik[k]*pik[l]) var_asym=var_asym+e[k]*e[l]*delta[k,l]/(pik[k]*pik[l])} cat("the approximate variance of the calibration estimator:",var_asym,"\n") cat("first variance estimator of the calibration est. using calibev function:\n") cat("MSE of the first variance estimator:", var(c2)+(mean(c2)-var_asym)^2,"\n") cat("second variance estimator of the calibration est. using varest function:\n") cat("MSE of the second variance estimator:", var(c3)+(mean(c3)-var_asym)^2,"\n") cat("the Horvitz-Thompson estimator under simulations:", mean(c6),"\n") cat("the variance of the HT estimator:", var_HT, "\n") cat("the variance estimator of the HT estimator under simulations:", mean(c4),"\n") cat("MSE of the variance estimator 1 of HT estimator:", var(c4)+(mean(c4)-var_HT)^2,"\n") cat("MSE of the variance estimator 2 of HT estimator:", var(c5)+(mean(c5)-var_HT)^2,"\n") @ <>= <> sampling.newpage() @ \section{Example 3} This is an example of generalized calibration used to handle unit nonresponse with different forms of response probabilities. Consider the population $U$, the sample $s$ and the set of respondents $r$ with $r\subseteq s \subseteq U.$ The response mechanism is given by the distribution $q(r|s)$ such that for every fixed $s$ we have $$q(r|s)\geq 0, \mbox{ for all } r\in \mathcal{R}_s \mbox{ and } \sum_{s\in {\mathcal R}_s} q(r|s)=1,$$ where ${\mathcal R}_s=\{r | r \subseteq s\}.$ The variable of interest $y_k$ is known only for $k\in r.$ Under unit nonresponse we define the response indicator $R_k=1$ if unit $k\in r$ and 0 otherwise and the response probabilities $p_k=Pr(R_k=1| k\in s).$ It is assumed that $R_k$ are independent Bernoulli variables with expected value equal to $p_k.$ We assume that the units respond independently of each other and of $s$ and so $$q(r|s)=\prod_{k\in r} p_k \prod_{k \in \bar{r}} (1-p_k).$$ The nonresponse model can be rewritten as $$q(r|s, \boldsymbol{\gamma})=\prod_{k\in r} F_k^{-1}(\boldsymbol{\gamma}) \prod_{k \in \bar{r}} (1-F^{-1}_k(\boldsymbol{\gamma})).$$ In calibration method it is assumed that $$\sum_{k\in r} \mathbf{x}_kd_kF_k(\boldsymbol{\gamma})=\sum_{k\in r} \mathbf{x}_kd_kF(\boldsymbol{\gamma}^T\mathbf{x}_k)=\sum_{k\in U} \mathbf{x}_k,$$ where $F_k(\boldsymbol{\gamma})=F(\boldsymbol{\gamma}^T\mathbf{x}_k), p_k=F_k(\boldsymbol{\gamma})^{-1},$ and $d_k$ are the initial weigths. In generalized calibration a different equation is used $$\sum_{k\in r} \mathbf{x}_kd_kF(\boldsymbol{\gamma}^T\mathbf{z}_k)=\sum_{k\in U} \mathbf{x}_k,$$ where $\mathbf{z}_k$ is not necessary equal to $\mathbf{x}_k,$ but $\mathbf{z}_k$ and $\mathbf{x}_k$ have to be highly correlated. $\mathbf{z}_k$ should be known only for $k\in r.$ The components of $\mathbf{z}_k$ that are not also components of $\mathbf{x}_k$ are often known as \emph{instrumental variables}. Let $w_k$ be the final weights (obtained after applying generalized calibration). It is possible to assume different forms of response probabilities: \begin{itemize} \item Linear weight adjustment (it can be implemented by using the argument \texttt{method="linear"} in gencalib() function or \texttt{method="truncated"} if bounds are allowed): $p_k=1/(1+ {\boldsymbol\gamma}^T\mathbf{z}_k)$ and $w_k=d_k(1+\mathbf{h}^T\mathbf{z}_k),$ where $\mathbf{h}$ is a consistent estimate of ${\boldsymbol\gamma}.$ \item Raking weight adjustment (it can be implemented by using the argument \texttt{method="raking"} in gencalib()): $p_k=1/\exp(\boldsymbol{\gamma}^T\mathbf{z}_k)$ and $w_k=d_k \exp(\mathbf{h}^T\mathbf{z}_k).$ \item Logistic weight adjustment (it can be implemented by using the argument \texttt{method="raking"} in gencalib()): $p_k=1/(1+\exp(\boldsymbol{\gamma}^T\mathbf{z}_k)), w_k=d_k (1+\exp(\mathbf{h}^T\mathbf{z}_k)),$ but we calibrate on $\sum_{k\in U} \mathbf{x}_k-\sum_{k\in r} \mathbf{x}_k d_k$ instead of $\sum_{k\in U} \mathbf{x}_k.$\item Generalized exponential weight adjustment (Folsom and Singh, 2000; it can be implemented by using the argument \texttt{method="logit"} in gencalib()): $$p_k=1/F(\boldsymbol{\gamma}^T\mathbf{z}_k), w_k=d_kF(\mathbf{h}^T\mathbf{z}_k),$$ $$F(\mathbf{h}^T\mathbf{z}_k)=\frac{L(U-C)+U(C-L)\exp(A\mathbf{h}^T\mathbf{z}_k)}{(U-C)+(C-L)\exp(A\mathbf{h}^T\mathbf{z}_k)}\in (L, U),$$ where $A=(U-L)/((C-L)(U-C))$ and $L\geq 0,1C>L,$ ($C=1$ in the paper of Deville and Sarndal, 1992). The g-weights are centered around of $C.$ For $L=1, C=2$ and $U=\infty, F(\mathbf{h}^T\mathbf{z}_k)$ approaches $1+\exp(\mathbf{h}^T\mathbf{z}_k)$ and for $C=1, L=0, U=\infty,$ $\exp(\mathbf{h}^T\mathbf{z}_k).$ \end{itemize} We exemplify the last form of response probabilities (generalized exponential weight adjustment) using artificial data. We generate a population of size $N=400$ and consider the auxiliary information $X$ following a Gamma distribution with parameters 3 and 4. The instrumental variable $Z$ is generated using the model $Z=2X+\varepsilon,$ where $\varepsilon\sim U(0,1).$ The variable of interest is $Y$ generated using the model $Y=3X+\varepsilon_1,$ where $\varepsilon_1\sim N(0,1).$ We consider here that the nonresponse is not missing at random and the response probabilities $p$ depend on the variable of interest $y$ which may be missing. We draw a simple random sampling without replecement of size $n=100$ and generate the set of respondents $r$ using Poisson sampling with the probabilties $p.$ The bounds are fixed to 1 and 5, and the constant $C=1.5.$ Three estimators are computed: \begin{itemize} \item the generalized calibration estimator using $Z$ as instrumental variable, \item the generalized calibration estimator using $Y$ as instrumental variable, \item the generalized calibration estimator using $X$ as instrumental variable, which is the same with the calibration estimator, but the g-weights are centered around $C$. \end{itemize} The convergence of the method is not guaranteed due to the bounds. Thus $g1, g2, g3$ can be null. If it the case, repeat the code (considering another $s$ and $r$). <>= N=400 n=100 X=rgamma(N,3,4) total=sum(X) Z=2*X+runif(N) Y=3*X+rnorm(N) print(cor(X,Y)) print(cor(X,Z)) L=1 U=5 C=1.5 A=(U-L)/((C-L)*(U-C)) p=((U-C)+(C-L)*exp(A*Y*0.3))/(L*(U-C)+U*(C-L)*exp(A*Y*0.3)) summary(p) bounds=c(L,U) s=srswor(n,N) r=numeric(n) for(j in 1:n) if(runif(1)>= <> sampling.newpage() @ \end{document} sampling/inst/doc/calibration.R0000644000176200001440000003420713777316644016250 0ustar liggesusers### R code from vignette source 'calibration.Snw' ################################################### ### code chunk number 1: calibration.Snw:21-24 ################################################### library(sampling) ps.options(pointsize=12) options(width=60) ################################################### ### code chunk number 2: calib1 ################################################### data = rbind(matrix(rep("A", 150), 150, 1, byrow = TRUE), matrix(rep("B", 100), 100, 1, byrow = TRUE)) data = cbind.data.frame(data, c(rep(1, 60), rep(2,50), rep(3, 60), rep(1, 40), rep(2, 40)), 1000 * runif(250)) sex = runif(nrow(data)) for (i in 1:length(sex)) if (sex[i] < 0.3) sex[i] = 1 else sex[i] = 2 data = cbind.data.frame(data, sex) names(data) = c("state", "region", "income", "sex") summary(data) ################################################### ### code chunk number 3: calib2 ################################################### table(data$state) ################################################### ### code chunk number 4: calib3 ################################################### s=strata(data,c("state"),size=c(25,20), method="srswor") ################################################### ### code chunk number 5: calib31 ################################################### s=getdata(data,s) ################################################### ### code chunk number 6: calib32 ################################################### status=runif(nrow(s)) for(i in 1:length(status)) if(status[i]<0.3) status[i]=0 else status[i]=1 s=cbind.data.frame(s,status) ################################################### ### code chunk number 7: calib4 ################################################### s=rhg_strata(s,selection="region") ################################################### ### code chunk number 8: calib5 ################################################### sr=s[s$status==1,] ################################################### ### code chunk number 9: calib6 ################################################### X=cbind(disjunctive(data$sex),disjunctive(data$region)) ################################################### ### code chunk number 10: calib7 ################################################### total=c(t(rep(1,nrow(data)))%*%X) ################################################### ### code chunk number 11: calib8 ################################################### Xs = X[sr$ID_unit,] d = 1/(sr$Prob * sr$prob_resp) summary(d) ################################################### ### code chunk number 12: calib9 ################################################### g = calib(Xs, d, total, method = "linear") summary(g) ################################################### ### code chunk number 13: calib10 ################################################### w=d*g summary(w) ################################################### ### code chunk number 14: calib11 ################################################### checkcalibration(Xs, d, total, g) ################################################### ### code chunk number 15: calib12 ################################################### cat("stratum 1\n") data1=data[data$state=='A',] X1=X[data$state=='A',] total1=c(t(rep(1, nrow(data1))) %*% X1) sr1=sr[sr$Stratum==1,] Xs1=X[sr1$ID_unit,] d1 = 1/(sr1$Prob * sr1$prob_resp) g1=calib(Xs1, d1, total1, method = "linear") checkcalibration(Xs1, d1, total1, g1) cat("stratum 2\n") data2=data[data$state=='B',] X2=X[data$state=='B',] total2=c(t(rep(1, nrow(data2))) %*% X2) sr2=sr[sr$Stratum==2,] Xs2=X[sr2$ID_unit,] d2 = 1/(sr2$Prob * sr2$prob_resp) g2=calib(Xs2, d2, total2, method = "linear") checkcalibration(Xs2, d2, total2, g2) ################################################### ### code chunk number 16: calibration.Snw:157-176 (eval = FALSE) ################################################### ## data = rbind(matrix(rep("A", 150), 150, 1, byrow = TRUE), ## matrix(rep("B", 100), 100, 1, byrow = TRUE)) ## data = cbind.data.frame(data, c(rep(1, 60), rep(2,50), rep(3, 60), rep(1, 40), rep(2, 40)), ## 1000 * runif(250)) ## sex = runif(nrow(data)) ## for (i in 1:length(sex)) if (sex[i] < 0.3) sex[i] = 1 else sex[i] = 2 ## data = cbind.data.frame(data, sex) ## names(data) = c("state", "region", "income", "sex") ## summary(data) ## table(data$state) ## s=strata(data,c("state"),size=c(25,20), method="srswor") ## s=getdata(data,s) ## status=runif(nrow(s)) ## for(i in 1:length(status)) ## if(status[i]<0.3) status[i]=0 else status[i]=1 ## s=cbind.data.frame(s,status) ## s=rhg_strata(s,selection="region") ## sr=s[s$status==1,] ## X=cbind(disjunctive(data$sex),disjunctive(data$region)) ## total=c(t(rep(1,nrow(data)))%*%X) ## Xs = X[sr$ID_unit,] ## d = 1/(sr$Prob * sr$prob_resp) ## summary(d) ## g = calib(Xs, d, total, method = "linear") ## summary(g) ## w=d*g ## summary(w) ## checkcalibration(Xs, d, total, g) ## cat("stratum 1\n") ## data1=data[data$state=='A',] ## X1=X[data$state=='A',] ## total1=c(t(rep(1, nrow(data1))) %*% X1) ## sr1=sr[sr$Stratum==1,] ## Xs1=X[sr1$ID_unit,] ## d1 = 1/(sr1$Prob * sr1$prob_resp) ## g1=calib(Xs1, d1, total1, method = "linear") ## checkcalibration(Xs1, d1, total1, g1) ## cat("stratum 2\n") ## data2=data[data$state=='B',] ## X2=X[data$state=='B',] ## total2=c(t(rep(1, nrow(data2))) %*% X2) ## sr2=sr[sr$Stratum==2,] ## Xs2=X[sr2$ID_unit,] ## d2 = 1/(sr2$Prob * sr2$prob_resp) ## g2=calib(Xs2, d2, total2, method = "linear") ## checkcalibration(Xs2, d2, total2, g2) ## ## ## ## sampling.newpage() ## ################################################### ### code chunk number 17: ex1 ################################################### X=cbind(c(rep(1,50),rep(0,50)),c(rep(0,50),rep(1,50)),1:100) # vector of population totals total=apply(X,2,"sum") Z=150:249 # the variable of interest Y=5*Z*(rnorm(100,0,sqrt(1/3))+apply(X,1,"sum")) # inclusion probabilities pik=inclusionprobabilities(Z,20) # joint inclusion probabilities pikl=UPtillepi2(pik) # number of runs; let nsim=10000 for an accurate result nsim=10 c1=c2=c3=c4=c5=c6=numeric(nsim) for(i in 1:nsim) { # draws a sample s=UPtille(pik) # computes the inclusion prob. for the sample piks=pik[s==1] # the sample matrix of auxiliary information Xs=X[s==1,] # computes the g-weights g=calib(Xs,d=1/piks,total,method="linear") # computes the variable of interest in the sample Ys=Y[s==1] # computes the joint inclusion prob. for the sample pikls=pikl[s==1,s==1] # computes the calibration estimator and its variance estimation cc=calibev(Ys,Xs,total,pikls,d=1/piks,g,with=FALSE,EPS=1e-6) c1[i]=cc$calest c2[i]=cc$evar # computes the variance estimator of the calibration estimator (second method) c3[i]=varest(Ys,Xs,pik=piks,w=g/piks) # computes the variance estimator of the HT estimator using varest() c4[i]=varest(Ys,pik=piks) # computes the variance estimator of the HT estimator using varHT() c5[i]=varHT(Ys,pikls,2) # computes the Horvitz-Thompson estimator c6[i]=HTestimator(Ys,piks) } cat("the population total:",sum(Y),"\n") cat("the calibration estimator under simulations:", mean(c1),"\n") N=length(Y) delta=matrix(0,N,N) for(k in 1:(N-1)) for(l in (k+1):N) delta[k,l]=delta[l,k]=pikl[k,l]-pik[k]*pik[l] diag(delta)=pik*(1-pik) var_HT=0 var_asym=0 e=lm(Y~X)$resid for(k in 1:N) for(l in 1:N) {var_HT=var_HT+Y[k]*Y[l]*delta[k,l]/(pik[k]*pik[l]) var_asym=var_asym+e[k]*e[l]*delta[k,l]/(pik[k]*pik[l])} cat("the approximate variance of the calibration estimator:",var_asym,"\n") cat("first variance estimator of the calibration est. using calibev function:\n") cat("MSE of the first variance estimator:", var(c2)+(mean(c2)-var_asym)^2,"\n") cat("second variance estimator of the calibration est. using varest function:\n") cat("MSE of the second variance estimator:", var(c3)+(mean(c3)-var_asym)^2,"\n") cat("the Horvitz-Thompson estimator under simulations:", mean(c6),"\n") cat("the variance of the HT estimator:", var_HT, "\n") cat("the variance estimator of the HT estimator under simulations:", mean(c4),"\n") cat("MSE of the variance estimator 1 of HT estimator:", var(c4)+(mean(c4)-var_HT)^2,"\n") cat("MSE of the variance estimator 2 of HT estimator:", var(c5)+(mean(c5)-var_HT)^2,"\n") ################################################### ### code chunk number 18: calibration.Snw:263-267 (eval = FALSE) ################################################### ## X=cbind(c(rep(1,50),rep(0,50)),c(rep(0,50),rep(1,50)),1:100) ## # vector of population totals ## total=apply(X,2,"sum") ## Z=150:249 ## # the variable of interest ## Y=5*Z*(rnorm(100,0,sqrt(1/3))+apply(X,1,"sum")) ## # inclusion probabilities ## pik=inclusionprobabilities(Z,20) ## # joint inclusion probabilities ## pikl=UPtillepi2(pik) ## # number of runs; let nsim=10000 for an accurate result ## nsim=10 ## c1=c2=c3=c4=c5=c6=numeric(nsim) ## for(i in 1:nsim) ## { ## # draws a sample ## s=UPtille(pik) ## # computes the inclusion prob. for the sample ## piks=pik[s==1] ## # the sample matrix of auxiliary information ## Xs=X[s==1,] ## # computes the g-weights ## g=calib(Xs,d=1/piks,total,method="linear") ## # computes the variable of interest in the sample ## Ys=Y[s==1] ## # computes the joint inclusion prob. for the sample ## pikls=pikl[s==1,s==1] ## # computes the calibration estimator and its variance estimation ## cc=calibev(Ys,Xs,total,pikls,d=1/piks,g,with=FALSE,EPS=1e-6) ## c1[i]=cc$calest ## c2[i]=cc$evar ## # computes the variance estimator of the calibration estimator (second method) ## c3[i]=varest(Ys,Xs,pik=piks,w=g/piks) ## # computes the variance estimator of the HT estimator using varest() ## c4[i]=varest(Ys,pik=piks) ## # computes the variance estimator of the HT estimator using varHT() ## c5[i]=varHT(Ys,pikls,2) ## # computes the Horvitz-Thompson estimator ## c6[i]=HTestimator(Ys,piks) ## } ## cat("the population total:",sum(Y),"\n") ## cat("the calibration estimator under simulations:", mean(c1),"\n") ## N=length(Y) ## delta=matrix(0,N,N) ## for(k in 1:(N-1)) ## for(l in (k+1):N) ## delta[k,l]=delta[l,k]=pikl[k,l]-pik[k]*pik[l] ## diag(delta)=pik*(1-pik) ## var_HT=0 ## var_asym=0 ## e=lm(Y~X)$resid ## for(k in 1:N) ## for(l in 1:N) {var_HT=var_HT+Y[k]*Y[l]*delta[k,l]/(pik[k]*pik[l]) ## var_asym=var_asym+e[k]*e[l]*delta[k,l]/(pik[k]*pik[l])} ## cat("the approximate variance of the calibration estimator:",var_asym,"\n") ## cat("first variance estimator of the calibration est. using calibev function:\n") ## cat("MSE of the first variance estimator:", var(c2)+(mean(c2)-var_asym)^2,"\n") ## cat("second variance estimator of the calibration est. using varest function:\n") ## cat("MSE of the second variance estimator:", var(c3)+(mean(c3)-var_asym)^2,"\n") ## cat("the Horvitz-Thompson estimator under simulations:", mean(c6),"\n") ## cat("the variance of the HT estimator:", var_HT, "\n") ## cat("the variance estimator of the HT estimator under simulations:", mean(c4),"\n") ## cat("MSE of the variance estimator 1 of HT estimator:", var(c4)+(mean(c4)-var_HT)^2,"\n") ## cat("MSE of the variance estimator 2 of HT estimator:", var(c5)+(mean(c5)-var_HT)^2,"\n") ## ## sampling.newpage() ## ################################################### ### code chunk number 19: gen1 ################################################### N=400 n=100 X=rgamma(N,3,4) total=sum(X) Z=2*X+runif(N) Y=3*X+rnorm(N) print(cor(X,Y)) print(cor(X,Z)) L=1 U=5 C=1.5 A=(U-L)/((C-L)*(U-C)) p=((U-C)+(C-L)*exp(A*Y*0.3))/(L*(U-C)+U*(C-L)*exp(A*Y*0.3)) summary(p) bounds=c(L,U) s=srswor(n,N) r=numeric(n) for(j in 1:n) if(runif(1)>= library(sampling) ps.options(pointsize=12) options(width=60) @ 1) Some examples of using maximum entropy sampling design and related functions: a) First example @ Sample of Belgian municipalities, sample size 50 <>= data(belgianmunicipalities) attach(belgianmunicipalities) n=50 @ Inclusion probabilties proportional to the 'averageincome' variable <>= pik=inclusionprobabilities(averageincome,n) @ Draw a sample <>= s=UPmaxentropy(pik) @ The sample is <>= as.character(Commune[s==1]) @ Joint inclusion probabilities <>= pi2=UPmaxentropypi2(pik) @ Check the result <>= rowSums(pi2)/pik/n detach(belgianmunicipalities) @ b) Second example @ Selection of samples from Belgian municipalities data set, sample size 50. Once matrix q is computed, a sample is quickly selected. Simulations can be run to compare the results. <>= data(belgianmunicipalities) attach(belgianmunicipalities) pik=inclusionprobabilities(averageincome,50) pik=pik[pik!=1] n=sum(pik) pikt=UPMEpiktildefrompik(pik) w=pikt/(1-pikt) q=UPMEqfromw(w,n) @ Draw a sample using the q matrix <>= UPMEsfromq(q) @ Simulations to check the sample selection; the difference between pik and the computed inclusion prob. tt is almost 0. <>= sim=10000 N=length(pik) tt=rep(0,N) for(i in 1:sim) tt = tt+UPMEsfromq(q) tt=tt/sim max(abs(tt-pik)) detach(belgianmunicipalities) @ 2) This is an example of unequal probability (UP) sampling functions: selection of samples using the Belgian municipalities data set, with equal or unequal probabilities, and study of the Horvitz-Thompson estimator accuracy using boxplots. The following sampling schemes are used: Poisson, random systematic, random pivotal, Till\'e, Midzuno, systematic, pivotal, and simple random sampling without replacement. Monte Carlo simulations are used to study the accuracy of the Horvitz-Thompson estimator of a population total. The aim of this example is to demonstrate the effect of the auxiliary information incorporation in the sampling design. We use: \begin{itemize} \item some $\pi$ ps sampling designs with Horvitz-Thompson estimation, using in the sampling design the information on size measures of population units; \item simple random sampling without replacement with Horvitz-Thompson estimation, where no auxiliary information is used. \end{itemize} <>= b=data(belgianmunicipalities) pik=inclusionprobabilities(belgianmunicipalities$Tot04,200) N=length(pik) n=sum(pik) @ Number of simulations (for an accurate result, increase this value to 10000): <>= sim=10 ss=array(0,c(sim,8)) @ Defines the variable of interest: <>= y=belgianmunicipalities$TaxableIncome @ Simulation and computation of the Horvitz-Thompson estimator: <>= ht=numeric(8) for(i in 1:sim) { cat("Step ",i,"\n") s=UPpoisson(pik) ht[1]=HTestimator(y[s==1],pik[s==1]) s=UPrandomsystematic(pik) ht[2]=HTestimator(y[s==1],pik[s==1]) s=UPrandompivotal(pik) ht[3]=HTestimator(y[s==1],pik[s==1]) s=UPtille(pik) ht[4]=HTestimator(y[s==1],pik[s==1]) s=UPmidzuno(pik) ht[5]=HTestimator(y[s==1],pik[s==1]) s=UPsystematic(pik) ht[6]=HTestimator(y[s==1],pik[s==1]) s=UPpivotal(pik) ht[7]=HTestimator(y[s==1],pik[s==1]) s=srswor(n,N) ht[8]=HTestimator(y[s==1],rep(n/N,n)) ss[i,]=ht } @ Boxplots of the estimators: <>= colnames(ss) <- c("poisson","rsyst","rpivotal","tille","midzuno","syst","pivotal","srswor") boxplot(data.frame(ss), las=3) <>= <> <> <> <> <> sampling.newpage() @ \end{document} sampling/inst/doc/HT_Hajek_estimators.pdf0000644000176200001440000044313513777316616020223 0ustar liggesusers%PDF-1.5 % 3 0 obj << /Length 2659 /Filter /FlateDecode >> stream xZIoGWm@X骮m0 0L 2@)JE&)eY$%^mŷ/kSH'4.derV mqyU^~?fu-m𳾙L*0{YBESۮr{\{jɽkbWdjdMRTIHScױ e})B1 W7{٘bj [*_ V {GrhDc^Z4.*m-h)#\V<^GMTr_tA-?he4˖TuQ~=\: }衄uaZ4^23\Z]`*+s~cfS͑ATxv8K+k_pp¶h#;!> :k\yXRFԻ*Y$BA r7>a= )F@釉1epCӣBEVS edy-`J0}]&l:2xJ=e<muij÷a8n5n}pBUpB;Ŋ)`\FZ 4mb^ԉHntmJB9N[W|1MT 2ޗvƲ(ޒO\yNvv6l'Y oz ߶0nDy+ ǸE׺+C2YXإ(F۪U1veǻO=q~̯yS*٤\L m9{ GfečMyGL1t Qwwq|`7R6:jW1Bp j HtU@䴖/?_|`Z+ӈJ/Fh[6O FΘ 6 T8[IT)0S/TWCFH_RW-} (|R3~ ooK(LYDGԖ=i$g'Dǜ3 im˻KCM_Tn1DI=7i8uꉁ|}o߱T& 22uq^'uzsr iK3@.\0Hd_K~5:Gu]QWÄ#aNq\ubSK?T֔k;q36TyDvbrAv:X˰ݍA{-9ɼFBhO1/d „ڜѺ{jݏޤJ?[y*O- oQTiT6VWR͂tosS}a)t}&ZT:#uw%vE1[ݑ-MޝJ9v5FSI fƣI mv'Toj27(iGŧ۰ew[.0Gf 8-o> vTd)~b\OfW %c_ l+:;8]AbϷ]}OPsg)gn?37A[ 35*Fc~;`~cwcF;ϵ? K=vB0 ims20rTu]pesYDg'pyf9Tȑ.$)IU)!جcV򮻀`\<n~ng#bȌu~@>OX[˜0@|2["]> endobj 1 0 obj << /Font << /F35 4 0 R /F19 5 0 R /F8 6 0 R /F11 7 0 R /F14 8 0 R /F10 9 0 R /F1 10 0 R /F7 11 0 R /F13 12 0 R >> /ProcSet [ /PDF /Text ] >> endobj 16 0 obj << /Length 1567 /Filter /FlateDecode >> stream xXKs6Wh X 43t=)DU.H, }|ŋQLF|ea( Gl[l"TO lRI'j#KD$S,MDHg;92 'qZΔ;h~f p#%/>2 Wfa+ .=L ` Jw$(N;pQߍ'+Y0}ːM7Q:4#W>[Q(ۛHIs:̣9N5Rm lcvPgWཉTt,|}AF蠈#,s]8e+/Y| +#(TP$9VꦉZBMkgBi\sE͸]5묚L[GEƞƴ1vvNRT;gdK77TcCP~Y}@հRː X)0U K~,X*3&I\+{gE ~TXO ˆ=^XO 7jXˊ5rۥ%gzB:v'U mXpfgZ6˧GL ޶3n@sjO`s޳5eϚq&mWuo涻tQޅ~ںvAN_T%;E-ebie;obuj÷\ St>]M+"a kӿc%ΖǏ]".i7ZjaLY>l]u[l6D̆ltr/yM&l4- tvz}Z^3Le Z zW#¥H꿡هi y=P,믮 [E\ 5Go^S}WmV9Ȥf?m?[~pAW8n@ ;%_5{jz]Y7TY+uf<`W e*eѧae=SۼkI+|7G<m38i ae$.QߍaIv endstream endobj 15 0 obj << /Type /Page /Contents 16 0 R /Resources 14 0 R /MediaBox [0 0 595.276 841.89] /Parent 13 0 R >> endobj 14 0 obj << /Font << /F8 6 0 R /F11 7 0 R /F10 9 0 R /F14 8 0 R /F45 17 0 R /F47 18 0 R >> /ProcSet [ /PDF /Text ] >> endobj 21 0 obj << /Length 1061 /Filter /FlateDecode >> stream xXKO@W%x٧׋DT T-)P)" ^J:'q 0kvoct[{Km(B=#1*UH )t^ZI  GL38\ AA=5w&7.?Rx4w?FΩպx{rhm @>{\{ᣫ2a9Z8LǸ>H݆.tDlf7ƐUM9"DtWu^ hlcuLs1a^QV:X+Y'grgþDkң`>G3Գl;fє7+ 7P3DSzC5ˍY"77Hϛ$c}1ն˞y(hC#IuK)eEͧyf02XM猄ӰaTqCe8 t ̼(^bṍWXBQxdEnGcp"B JKMHN1#xѡFg:$Qn"8&/7fkcڿ%}z5hh$QV$KWD \02SG=yj(3tiWl̗gt;6Lv7*F鄂0D7~4e{C!:Qd/K GŪRӂD¢!jeЈGu3ڇ?bxn8qN/PxL9UqUM1{mGJLjڏy&e6X XR /WWjZa4LCVC endstream endobj 20 0 obj << /Type /Page /Contents 21 0 R /Resources 19 0 R /MediaBox [0 0 595.276 841.89] /Parent 13 0 R >> endobj 19 0 obj << /Font << /F47 18 0 R /F8 6 0 R /F10 9 0 R /F9 22 0 R /F45 17 0 R >> /ProcSet [ /PDF /Text ] >> endobj 25 0 obj << /Length 423 /Filter /FlateDecode >> stream xVMK1WE6&xTD{B[Z+V;ټZzxlv2y!GuoD渳eI!ҖrY8VUvܗ 0R2S Kɝ1A&۠d Me8D3ZòYU>}& Wy'hxO 4[AĴ?꒖PA+Zy3PٰsK>? ۚÿJ9m\*`C {fw8tk &0OItR`EMRqJKRQP&9Z7FKqI:b5@ݍKFjDf5F%WY jCc$%[zՔɫKYAJ=p ˵1\X܎vu endstream endobj 24 0 obj << /Type /Page /Contents 25 0 R /Resources 23 0 R /MediaBox [0 0 595.276 841.89] /Parent 13 0 R >> endobj 23 0 obj << /Font << /F45 17 0 R /F47 18 0 R /F8 6 0 R >> /ProcSet [ /PDF /Text ] >> endobj 26 0 obj [1110.4 626.7 772.9 1138.9 955.6 1284 1075.7 1047.5 875.4 1082.2 1030 856.3 832.3 943.9 827.8 1279.2 1112.9 824.3 943.1 597.2 597.2 597.2 1361.1 1361.1 597.2 774.4 633.3 649.4 739.7 677 684 700.6 827.6 533.6 588.2 758.1] endobj 27 0 obj [525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525] endobj 28 0 obj [525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525] endobj 29 0 obj [769.8] endobj 30 0 obj [569.5 569.5 569.5 569.5 569.5 569.5 569.5 569.5 569.5 323.4 323.4 323.4 877] endobj 31 0 obj [1055.6 944.5 472.2 833.3 833.3 833.3 833.3 833.3 1444.5] endobj 32 0 obj [838.7 724.5 889.4 935.6 506.3 632 959.9 783.7 1089.4 904.9 868.9 727.3 899.7 860.6 701.5 674.8 778.2 674.6 1074.4 936.9 671.5 778.4 462.3 462.3 462.3 1138.9 1138.9 478.2 619.7 502.4 510.5 594.7 542 557.1 557.3 668.8 404.2 472.7 607.3 361.3 1013.7 706.2 563.9 588.9 523.6 530.4 539.2] endobj 33 0 obj [777.8 277.8 777.8 500 777.8 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1000 1000 777.8 777.8 1000 1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 275 1000 666.7 666.7 888.9 888.9 0 0 555.6 555.6 666.7 500 722.2 722.2 777.8 777.8 611.1 798.5 656.8 526.5 771.4 527.8 718.7 594.9 844.5 544.5 677.8 762 689.7 1200.9 820.5 796.1 695.6 816.7 847.5 605.6 544.6 625.8 612.8 987.8 713.3 668.3 724.7 666.7 666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 500] endobj 34 0 obj [405.9 437.5 496.5 469.4 353.9 576.2 583.3 602.6 494 437.5 570 517 571.4 437.2 540.3 595.8 625.7 651.4 622.5 466.3 591.4 828.1 517 362.8 654.2 1000 1000 1000 1000 277.8 277.8 500 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 777.8 500 777.8 500 530.9 750 758.5 714.7 827.9 738.2 643.1 786.3 831.3 439.6 554.5 849.3 680.6 970.1 803.5 762.8 642 790.6 759.3 613.2 584.4 682.8 583.3 944.4 828.5 580.6 682.6 388.9 388.9 388.9 1000 1000 416.7 528.6 429.2 432.8 520.5 465.6 489.6 477 576.2 344.5 411.8 520.6 298.4 878 600.2 484.7 503.1 446.4 451.2 468.8 361.1 572.5 484.7 715.9 571.5 490.3] endobj 35 0 obj [555.6 555.6 833.3 833.3 277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 277.8 277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 500 500] endobj 36 0 obj [272 326.4 272 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 272 761.6 462.4 462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 611.8 897.2 734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 489.6 272 489.6 272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 272 816 544 489.6 544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8] endobj 37 0 obj [301.9 249.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 458.6 249.6 249.6 249.6 719.8 432.5 432.5 719.8 693.3 654.3 667.6 706.6 628.2 602.1 726.3 693.3 327.6 471.5 719.4 576 850 693.3 719.8 628.2 719.8 680.5 510.9 667.6 693.3 693.3 954.5 693.3 693.3 563.1 249.6 458.6 249.6 458.6 249.6 249.6 458.6 510.9 406.4 510.9 406.4 275.8 458.6 510.9 249.6 275.8 484.7 249.6 772.1 510.9 458.6 510.9 484.7 354.1 359.4 354.1 510.9 484.7 667.6 484.7 484.7 406.4] endobj 38 0 obj << /Length1 1413 /Length2 6118 /Length3 0 /Length 7081 /Filter /FlateDecode >> stream xڍtT]6 RH!Jw0 0 C CH#%"t)J"- H*)!J>>>}kֺ>>{s]7' !B"5] @DDLHDD'4 |p0&Bu0=_P JɊDEDd&u +A|8^(y߯0/(##%; A@ @txy`(G yW$KVX_#G( HW8~ yB&D 0qÝ p!0_`"E9Pr~'`\P@_SG`N M>9~h@7z!}|fU5`NjpOO C?u(9wuaWP1|MaPo_M1 !"#*%) x `W_ A h/f H0rGAH/$?WD@ F!.Pѿ߄!o Xכœ0Կ鿯XXB@UU8@PTFRHIY$kÜ9{#?FϿn#"!yz*#M_8_yB=P7E@~cS!yWoT _ ф@ H_+nkPuED 1 s#?R;2$@PD7|7t2@XGޤn 8DTZ ~1EDBE n[#7z$&"j#[NUW>sg gdiU#g4x^7c>1l>l4L45LxSIDy5;, g4A!ՉV@]ϫ'V W$_L4M {1Y3Nώd& 5vx25D[b%hѤrQ; V؇GЪk&ѥ%sEclI^ZJG&aHwln Z}ǠPմ-UH G38\XMr5]L\6&hrR< Z!$b=%QϤzrhe| lU A(P~ŒM/nū=I`S> _?gݤ /O\&M/v+UJzX r8m9 IyZi WBGnJOR5u OBOf )̯[X a{SmBw$ znb}9cɎg{Wf?|QRb3@$WZE'4#۩g픅a5=sE*i#.-NCX# z^JQ7/m3`fcgTLnc4wk̢tSKCBV+xN֠%ق-a ZżNpvFVYTl4&FF(%g p"?x{̱H~E &&E|:yLJ:L*1&Wrm*x؎l=˾~]Q$Ŷ#OG}·V4'ʥJϨ6(6Nj%dW[݋b5aΝ&d-.:E*m([Q~zدǡSɍi#3+ʠ+ܷЊ-e=\@U *-_g~#<-+汛Iѵ5m}i\jݶ88Ο!FMV[S)-)g:u^;U츘L9ԧ.6/'"o?껷6xtnK+۷Y>-;ڳF'\})PX2'RC?KΪ$Yf4(9~ړ%> /4]Ǭ,]%c]hO{6uo%y|65DYm*ԿWBkdՋa[&V2Tr G<""J՘*gf;CxI !!{GIsYsXT_l26 5v/ZggJz5p.KT9͹eM . #z.h۪Oe.|xhH]+/LWOC]s 1a~韕a39X-+? oTWF=lu+"+| H^;r ~G͞?Ͷ겔AN/6Do0 WݗpTR$'СQ9ߦ&ҫ:ȭ*joԭ4eCצ2}.tqp|T:l (SwC2Ŭ~S㮬.܈Tkm#JPob]؄w1'-/l˒٠}EmUd5VOH3c*əoB} ;AKӊ#߶yMBڿ=c^*N $MH.3r'pHPƄjL u#%9dc2+=RSyf[p~~_<yGCKfHv@W ;ofz鹣,'h)>ePR&*ڶ%6"ʁ5m\`csrÒh4.@Qy+CxұO=ƅw՜FA6$|z{!dehQ.\g<2+#(I_Y8v1kқİږ" rs&ѽF/mb2jgpx@wPuO \# YqP LPW'j<<˺Hg>^!}0IbS[l݂ KRơ;4Pou0ȦiQ[.\FUmna ^n$`/4Op& Ҥ>]_姃cB2݆bA2Jc}熙< -D"m ۦ:BWIf^O7<..$2.iԏ%T$,%P ֘ {8Q:1HK3%(јșwdl§\ x;FN[AyP T;V${NaMoEطWI|r|)uuQ ҿxF`yиn/p4Eh9yJMVuiƀʮ)&w S~P oRL@L=/ JREժAc[T|}+Mzm^o~sZB?9 eX2G·~ *8#~UT׸5ufwl-(&W6sÙϑWG. N2,a jmLIX qbeopnAIFn'QQ6Ǚ(?Yf mYoIuz44jL֖i?\O7-Ux{jiӎJR%hŠQIdG]4'PP]g_ڀf}?37)BS&gSdERptR{P52V&+ڴ0l[@Si99nmwn$fGDD<҃Zg5B=c2ZRjGe*BƱG:E³SzVBTcp8evVꥈK:$n1Y.w 1#וpN&FG r TևƯCWOr"S;XE,h9m_̙7"ux5laq-hIj|Wϛa2=a<"){w,=}{_b, jPT~5s[di܆Luc8 tx8th9nY.v+VD*༉bh6Sޜф!'ϧ԰v(Yh gkD71\6kwaIS[ToM8rrs&—[eB?p_;`BEi7͊<} BBsMzmtRa{>&ꝛ]5ѷ*_S2MJ}"M,PNZ|E"8Y؞4KpaX=^Ƥl_3tIrJ4`G-Pj)\28YC󀆪xEV!H.۲ɇr8${t+L#TtW/]ڎNadlˆ ӄXwy{\_:u7^Ml-UӋਔm7BOSh/F=IdV42`nKSASYEyeefF~qXˀ8|U.fމػnq9FϚRԗqEi^{|6_hB3s1]wsP!-;/*>uMz%5^c}~.Sj/TWԈ j>Ny-rh㈐v^*Yr"Qh:T=nihONCCiCkY;{91ͨ~dM8-H$U _k]{-=z'B(m+nKL6ĭ];c"w涄a4.}JCxCy$d6N}~ \I4>>/ : ư_ (u) $J;^bpsZ05c$dlCQZ ~&qo[=Ȩy伏1-ɢ9G+ZIOXEZc[ttw3||aZ [ryLo$ ƲOE"t䌻wlNHb =kD5diŇŧJwE 1F_*_-jRy+* PkϥUM/R "XRL~2sdHϵK8>yq0i}ҌWp5);ݱ'~)Kjv b_I- |c$vjv1EjH]*:n [*%6cġe.Tw$ggKn\ZSH[7 ,ZWkwfx@8XO W*u 9KagP5> w7Ƙi7Fo,sYȱ~A n>#=1.]ydMI)u7XF=ԬU]1Q[\Se`HdhLcO/J5,5j4R CRU;=v5-Js@WQG|6=U7oI{E@w{"e!vh/+Kc\bav=xWob~`t{  Al199) Ebg5}uI\.be$c;&1{YdO&=-Jڣ 5/ZP6zLQΜkS8{bn} )mE328QY}b,"ΠЁTn <^1j8wڴrTeV> endobj 40 0 obj << /Length1 1675 /Length2 9486 /Length3 0 /Length 10586 /Filter /FlateDecode >> stream xڍP.L a @pww03!; D/` rءP(AFMg@ x/ y"@·juo`),@,j/%]Y7ƄS/8Y L02+YsJe8dMT%/gO<ݹYdm,bgM%x^P5#M|!X GzMߍ)feӯIk+=q,bPjgwuI2 ΏU DŐ)髜UǘHt%+x*y>ʞ?E#`4*<ܛbtBO 9"=%Z՟?l#9~x\Q@%SaV߳CPE.:i`W)CzǗo((~d`QX@b:`]$q: o!k!hJӐ?ն]Kh^ W Zް5PӃ.盧S~ι*)0cn+!z˴H)WǕs*cAGH{vGYH *t+<05гȱVH%ק~$ H\X.%~{{U,hZB:]6yȢXE[S|%\3-LCy$+A7UlY3DDK,D0N֐O?i/`(;!~)KeiJuoq1}z$ISt=?. >zcVƇe;YZc`bݡHնggG߳pk8 *lJpѻ8,:[2̽:m-2Zj/mRm4zBX'vgLfL=tvN4N(M@UuL^qI`&Q `%8\H# s nSI]"4_cs~6rC!ҿ2P:Dg d{5}ؙaS=㡵9Y:~VԍBVyZxxY֮]_Z*01{|~X/@}rɵ_yw#JeL >H e"N$t׺QN&z־|ԑ?M`/ w㙽WZ_sx~#zN=-;i1n3Lyb>kX/K`mhaIT̏hn^+@5}rE+E'fX6%E)f\^^@+ OgDw7x"cu0?Ƥ^3BLx=]IJ@+>]֠eOѩ(܊R)Gp3-O[np&EG S+>]sɲxW KOE׋ӳ'(4,w6MNEo>hAE (?\~{ %BM0/Q4$j"֗丼Q Fe0\!|}T9-+'"`im.߫lMz䕾x~s%jxVV(P:׼[<0թ&k|}g$ ^2>t@5~QoWxU^?zͅw]6&Â^Z]!T7cWܗeJv~*tnN)f"DhKhįZG*P jI\W IC/kwt{U$6FC Omo5= zL0ay$p".ʞ=lj鯘~5K:e? GoFHDek}kc;/ iTgTB)&3@7 pH՘18m}ܣoA>yܴ6xC0£ϲE_ٕQfyݜs)1ݱj]k访[$'T׸Cܾ4Ujv70:=kWl${qL5DnokH1?jZK2k`hM&BH5H~\Z\V٨ƀej@I"{OK~@sVBٛ]tǞ酈k MKrY3(,uL9'}\m{,hb1b'3SK kʏZ>#rPc ~lcv;O0".ӂ\f:<W-$5GAaQp}bEgG hVMZʑ\#qNH7nEMΆi.[;,@nY9>+b;-u}-Gq\`!R&/o"}3)IadҔ1 d/)ԶIjE<σ?,K"5mj r~&4CSnLw|TH8Nk6"F5ʋRVۦg%~1J4 B2led-fI3,y^1+4+5;gaH%{ پpWҋJLjEW݄, L)iCQQPʣ0lt[~G og[VB4i>%ХdRrE _rJx%.;ٱ!i1]}=i\IxI E{=ڋb,+ ˦nڅ#Gm, <,yLJW/رW6mØ`Pړ4 wU䝻o>yXV8\CIJa2|hf|ʔG9"1.=[,B@,il3htnԷRi;[cm>[pFDLm2We1-&.&.1H. "dۿК<^} N/jkia|2#bq"U|K|G10 0/ %~f *TeUSҙ]shԉ=z^ؐD.>7cuY*q{+U'gݒz\JRD)mSo- : T!=;Vbs!wI]D*XXo,rW9?m*O|?ݲ)P}n4c9tv<fZx}.yvܝ!X5p ~oj٭GVFd088Њi=P@V05n:k:ͭ{2J/0O~]^zru:v<w=]:{UL9Hi5MSYܔtōh%WidO.k?BPa c.OI V:X;y#s'-,TgW7tMaNL׸K&X.ᓪ`M,-xaoZ*DJ2w%bXd;n8=BW*A`?‘)҈tʎt\EE۶W%W"2Y$2 9" g;aŊfG5wbQ0ylK^bJ˓|![6(>Y n>+tF%uWZֿti sTu[DUu(g>_kݡnJ~-ʭdԸsSL屆E˅xqk/ElSy#Trtbo m1iaFߑCれۂ/= hHMZ *+H$*^M]/sDx!!p_х-2sZa吆2@?>& J\KfI| (5\7C3õ _U/Ұ Ck)á^'w;^0.9MB`& 狸E|-2OeNP%}gn"fSӽW #Nrn_,H,pkC- )0]:[cG"ӗ^ fx{^V6,-( א8x>?;:zrw2<1 ;yP饺)) \ͷ%@Qwi+=u|tM.o]cBxŊ)kK(gbj˴ӪϬ`cG% 5]Gw1.zY-ovwKŚt*QRWkEQ̘O.:21ex)ta!w*æύB|^TQSwDz[];ՋR5^ g9\y0T{9fȚ]f &Q?-r~!/S'>S=mhUTԓK`uoD"ⅈ$gH?uZ]*9&/Q1QȒLa-^wE0T8_^gU/60}/W˷-lb9M3'H| baBl(Q۴8QU3 8fSsuw"8k&˭W#6=Q@N=tFG?QSڻnfP]J!Zݟ }iq5e+Ȱd8⿸4U哼A)Z[d\Ұ5lM YaLT*/sN3eV"e']T,n^Nx1x֓MT9kxĪ Z4v9Qc'Զ}KMFu 7PLl.< :ce`!e~,s(uR6}'EVInap`ȇL)K/$Y0m&x j7wۜ^;HbytԞ9PGieKAq|'`rn!e)I/UM ͓k1w'=uoH# <>+ /z9Y؈J 6y /y6=%=6:gSdeeYn 6G_]J `qZcc t >v =CO4)E{H#mHaJaui&?璕(X\TLG %(78 ʓ 7E ;v{*Iiná) 姁ϰ-tڃhⵦ?snij{ET֊J!y樯yF) #rn2q wf?k oOg6nCoгz$Grwz8|S¼ض*p?jZ=W j~&vIG3?=}'[|Cbs^c wɝF&xNCX _ .~CQSݘk8r"לn|q>;ٷ±MJk鶜HYWJ[ OSL|) 'L;q}uUMeN A݈0~6B3*rda=|"ل=2-r,HԬV_R.'_4T9 qͯhuxDo/?R_OO12/"af۹)@{#{"FⴚCTuMS RnDox?|Uۀڪ/f> HW*+ġ[_=%+4q7)8{Wt| @!| ]T* ?cBƞ2J(CkfڦO !$eNj:H=)[iEt?EЮ.=bTXOAdzԼ?b=V8J?[zj!-D\%J(}AZCyKsU>`6?ђee rQs/+!m.οv^9>mUҦ!C'DyJ+Scdz+O ,R~tBۥ3,K2sl$l`{CEgwo(S Sg&_# hyĄm~?I{UEg# MILDkxӸVd'k]HqQ^v.#U[u.Dk~ Ţkr׊3u =Rk}s%NH4,@X xRIkK҅n+ sxIdARŇՆZ콥v |6cܧm/L20JƧ?>-կ֡=?R+wЖO;ڸbI<Еϻwolm QoFs% dExgV~ e)׍xRv^/]*a%7>)U"\+ƜNNzc菝dyR.h#oJ'[bl0C;»Qe4dCw\;b*cRcxI)Ⓥ?6T >iݛ:1E97v&zѯ:<M= m?"HT~j'-90_Kh3w*ؼĊHa|SS#&ڭ.\+8&,Uu$DIYZ~]W;TNvZ H;p>*˃z瓌 B]SefD9f_Z]O2 4ֹ h3H| D.qU|ƽяo? !aMF<ӛ}^_+* _;*vwz,U Y¹qZw \*15CД6u檌Unc~L蟦D.k!ˎu`f~kK$j-19-eqĄDY endstream endobj 41 0 obj << /Type /FontDescriptor /FontName /RDUKTV+CMMI10 /Flags 4 /FontBBox [-32 -250 1048 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 72 /XHeight 431 /CharSet (/N/P/T/U/a/comma/epsilon1/k/n/o/p/period/pi/r/s/slash/t/x/y) /FontFile 40 0 R >> endobj 42 0 obj << /Length1 1457 /Length2 7538 /Length3 0 /Length 8532 /Filter /FlateDecode >> stream xڍv4]6щQw{`0hh!z]^BDDD/{o $y}5k͜9uVbt0:@al@! ^7 NƤ;@Bx >i Sq]N>!N~!࿀Bi(:@.t/=!60c0Z08Y$ ـO, `?J0`B@ Z4.`g7%U=d@L: _ r;pZj`+௽p9.WBd#Z v`2 A-Av.|b2~wJj@s@~ |e/P !` {9Y[;/ 5# V wag x98`' A_n>^+`r`ή` XB,`s5p7 ?|gk{_W&pzY:@< } j,&;&%`ӕG_:WNUZ989t ߦuTMrc^ S U#7$jg;;A;pҺPqP=Ѫ-!UBZㇸB^-!0 ?%5;u88+ח-pO1p9/q@ L-^'\׿ `B`|f3crx[v'0Äm>oZ_-0g,_U~$sgA9Jb7EuɌ\HS ;)kUU*sqz U5 ĉxKr)O9zIRBE]x_1-p;f e>~ZYLD. k4=#aZ X4KVMQr^;-⭢`^ri \"ԧ^r{]KLIWժ6{&N $rqoRs$b+O@ ^sCGnyl;ϕN뉮9_<ݍ2*J(^Q'LԷ{=h'[m#{Z5”fcq8|ZDh(\/?| {S?@򃠂!oRw$/Qh/bFJ;*$)] @ ?Jl|^#=j\b'izyu=h0sGޮRzaX۬-kd#zGN{_ d+EM TKp ˾'x1U_Z̭A6*3ṙڑ6K6x~.u-*?l<8fB{TZt,7;ґޚ eLL; E\ONkW$ebO">}&TC;K[")Q<15TYrG&_΍5b`_fRpQZ*ʢ]# wG9l1+M#{⫵\dDDeޤ;zOxL?0<"PM/R`Xc8Oe u5K_uʔ+ S(1X>Eu,L H%%P,؆U10:;T xiYN ƙJn }Zb~[1"vՂ5>\tIz_YNi ثsC#>[$ TȬl' M?ɞ{1q~7gTC.5ZAE쭢 6@a2aqBы>OIU|e'{{\6+{E䆖=+x&"<(ӧ@Ѫꦔ Ap$SB}6Z=̷jqC] Ft/ Îw O>fأ~drENIEpJF'>(Vv6!4ˊ["3M_vk@T`0nDˑUk9ػR%kMd^a:kϤtU$d?;2˜FmC]Ȍ$oTI {m 8(6*gIb(δSvGm6wt/3J(rEQkpuC˜R%Œ 8dh0Vs/|W-8˗2>w`8R<*љwIʲ{1I?9TG)__L\MsMYu9-U*|$‹Q v(:ڦY[E۳1݇NCeb53bZy3Q;%{CV)8Z'Fq2ѥvckct,aAZ )rxiD=}4_@eu~`XVGq"YײV\z?)}C] $p3U d2oY=f1,lk-d['k:6q+!>6FktE|5FU\z$s7?soC SW7,g;v(e h,KuQ&FF b$Y{xպכi>ꤺ4nk[%>@ } !ZH=UEnHRzGY>jUdqΨH:/[ZlH~w}9yQ>RW6fЬ;PIUߩg!R9m \xn#Psrugp=遶v]]LΧqv5:SLj>J$?Wἃ!XZhW𽏠6e.-~e5(S"]1>ؼ":'?q}AS B<va ZEڱcWÛHL^()ى)I>%@U Nk JPLA{!և w+E mV|1b,a(N# "))݆LMOL3N=pelx:}BrZ.j(}yV7z9x*hV8Kad^tp삋Iب5i~h z9Z尿!P(QLr{QJDOȝ'˫Wg2  y;ƚr+ent\ )>hP5G+M*c T#=JRo2'fnԥ ':5\U41KSr}/21w Qb=q/5~c r_(|+tAL<|يR ?lD=0rXüh);H, |=D&iz#Xmee5<;+!g{c`A>Ma$-zfñeLd0UO%^^!JoNvFKY+O0ʆ%}/@A!,+yfiM"ј:Ր[[v.+U$zV+sϣjmD0JQE[hеQKL7InK5bxQuxj(bl ݬp`Zb1wR U3%ӟ;*zwN)f[6?:k|mNFB e?>=-|GkrM;zȼИwz ;+L񈯎'$ (8Q#kI;pZUiiMqe\GbmL_jVr: 넑VQqVb~蛐w6%/szʊc[pty#Ή-~xsxX:G]ƕ#rw[l6}NSQ)("l0 Ek8AZ" k=[VoAk:SUrz3Esz*GqVV/EqTlk"Q=qLEEeiU8&СU {r΋Kjf\Ĵ _D-S (N>%d%/|.|DC5c N:mR ~X)O2ӊ%#v%m]&əf?S܀[kO&{ꝧ(L( N9vFweJP&#Rޓ/K nrxHz .U.6!pOYW4y>fW͸ܿIX=w6?PsEBԭCgn4Mt{Z;8CbIcb)Iy;LF̦B|n`zߌX1C=Q\waDY :SIi:'U['{&H<|a2+p#K!/#룧9Ε^n؎ܲ6tjH[Vd՞о@dR?) >E4=7YsIv9wPq W3hRM]pm#;V=V<Ɏ:e CjTyB5~BsyL4v-:_ƙ4ױiĘZS檘4V!R6 Nn/0m'AHl%Qu?I lgω'zcy+t\wK8/iC|QW/a}DЂ01}X4~Dt.O-> QYѭ1`['"I}yY;X4)K/*q%1j| *ŝ#j LhS6g8wj<#:e ld!'E*6kiZ65d&Z dηZ-'bD#P[p%$f!E36 G~\y 'o)ʙ‹*RP*&A;!:H-}OPb?}ry%7{6r)Ca"k<̜1lrl5)!ꈴB.bQdlRǭ]dr9vvcFLTXt`FҼŰ1&xM,JmR<^LQ|ūЌbY7$[Y4 hw;Ä Vh`ȁ~i3 N@$| &#S52S%8eG]/(/\MoSXK6^ݟs:d/$gu8FPL~1\>32U9Tly-#)EԁnY[y82QF"?3g3WRۇ $Si?7(>_H`u?A'yyS:H}|~Duv-r #> ; LI`$nHӦ&ybETg=r13 t. ԟ3!^wuD'Y&]PmZf num<\Άy>8m-f#bԲmݹ~RP'%E*t~!&OF}ccǃ]Jm3DO4 drZJ$1 2e z"$q@䲀{먢ޥ%*{Tv-eьiIɻHK ^Ɯص;nMLدS$2)I38~s>„HR=I !#R5oT 5틠.م{pFkYXڮYFřwt=Aw:g:u|]fD6"֤ʞH^:ޔg8P?.Lvᐗ\?; {+>LVYT eCSi,^ EW&Ʌ^ ~O9U9JūGΓH7F8&©FHŇ}v{5#C ·7]9B|~"y im\pK>HMYOd6Y9hKV}X(bYfF0m$TS-2fA.Vqe^gԙA@TtŽ9c#v}t?V">_TqVKsa{5-`S1T}_:?~$:myGzy(-LF"r9C=@* iq 2C#-Xkth0M"611M!?۰ca׆}1ɪu O)u_`w4}ܭ˒g7j"wqVzSNԂ߯˸415>Q[Ȥ,XQ${1|k@ + /ݻ۬ՍeFU;N gNtH' \uor2:c^pPh#3D l'AXxXEY z\2uV%ETUK+T  _ڬd!_ (hn̕& P4{|::մnèD:Ɨ]"sҹ'wXE^ y\<%@TۛE|{L!P8ኼ _&}/q |lp z{V:o0 4}m MKo[տǑH|j ^NS0^;^Z R R8f;9q(.c[2ԓҝ#"nθj/Co>`Α%^eFˏ+#Hft=m _h' ^|{D40A-o݅tBYaFLHRD:VeN]IAi^JE= h|VC*xm`~J}qka endstream endobj 43 0 obj << /Type /FontDescriptor /FontName /ADIOYN+CMMI5 /Flags 4 /FontBBox [37 -250 1349 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 90 /XHeight 431 /CharSet (/H/T/a/e/j/k) /FontFile 42 0 R >> endobj 44 0 obj << /Length1 1557 /Length2 9051 /Length3 0 /Length 10092 /Filter /FlateDecode >> stream xڍP-00 ]Bpwww ,@ 8AKpy${_^M^ݫP`p48:@XYI%%9^ rh!v(4 W$]@)䅧wsyy@/@lPb;:\Qh$\V֐7g2 ۃ\%S5v Gs0_)腬!'66VS{WVG+fb P\A MAuƊBдepx/;9%xy8@CNrlNwD`?N^`+%PQdxBv/`;SŸM2jӗnqeunw)K;XH:ۃ (_:8z8 ,psbr;PY n /' y[Ndm~ `l zAq5u .n ?t7BagX!3/f_]ߟ޾eӒUҗ`$$=>,n r,࿫*``U˘U{9LE ?"7r_'OῳDɸqܦ`; /u,8/U*,n땃,ՋYعX\2`O*bndk^5;Hem_/el?^v0ww<SS/AyQ6x`ylҿM/M `Sؔ8l .?EF/YL_|]ːHe@^D 'ei\0Ħ!Năe{R$Fe 2$=cP!4.cdӫ,|pHuB.gEn?|=sMJ9"ZeJ,GdQ ! L_DZ2^.垏ueYڇvmKBM?b #S3(znQ`I Jq!j`<䖺d`e0aH,9߉q+9xDƃeqcE%!l BSׇE]@ZJ &ƝeGEX-vaC,#] $wVfnR4-D #%lЈLK~f/PRZ(C0mgWVo%G;,gx\^-5D8h.7]O%ŠN7GUco:h!*@Z>ӱ;dT(4j ƌz]6q򒫪 }9ZLNŐ1;بET2hqȭF3%iB-* Ӄ}\Ѕkh- λ苂 v`t)]/kGxi[iavIo،9`|I9ʏƿFa $8O>2m`GVpK pmj xP8g溚gHUZ{s|#S*1`~g6#L$;z.??;h|,E.(-6 >#% Bs3j5i̲d8\wԒgdζ t}LiíCpM$hJF^گXS.e8® ^g/+ql*D:u,4_iɣ$"t7[R &58rװ"9ӵp`nD߬Z.$5u hk2ʼni)2DP=}_ݿ5{uGb'E=Jڞ"n a|5Dt]S<'p_nJh&tVgܸu챮|9n UhО\yIQM^h`V S./j^)-L'񋳛ҙ{-pL~fIq-3_6&cVx"3;z"i,PtWW–pyN.jn?}:swvCo]hVޑ#1-ky %DhlR6E $PLvٽݛS4QU=wAsT3qTF5t2{Q~"*lypڏ A0tؚy$ke]Ha"U$o29iPp,=ΩޅȊ3rk@\^Diȣ ELh2(x'?&UT_+2;?nZj.4zchrƄh7D8TiG37AhfTckD)ƨJϻ#{VJ[Pnj NځN+XjrǏ)p8ޚCW?l<[.mʼwEJTv`tywZ }w%i l%fl6(nU"]CYbOmFvI=P#CVEK Xy3_%_ys#؟SÏ|U㺄}n6!PNKf"@4~KΛ!h@\?Jq9DnIF]Z,|[^!-{ڎ`"|{Sh$< k]c\,{ }YuqS>*Xs 4FiP+`*Y_T ~}n$"a?2e$'zEls}''5-s /Yt.(궖C75f~pUȢ[gw59I:~t~ /Kzg зOj[PxOr(2)ݜڠz`3!M^;eD2yB%1?nm{).}v%OH WH4,lvX'{ M4cg]ZG%MptC'uzcW5|.oyv `R` umC> [ h`g8MibSin:ݲOmr)tp6R-;ٴ3Sj+-7Ap!omeL)Mԗgs!Co.IJ|ȥԙohX*j T>n9#*1hC=F? TAxnT`{*'kK@՚ci.͚FdL"WHJϷnǽpWd'EN׶3& UxI@V'g% =2rt{E :kh$}> R,N*Bqҿ(>jm# z%>NeӼh.wcOnj;  J~T^ D`1gӧ*of)D\c8OMcXHqDC3jS_HK='$5 f<3L)Kk~b~v}N~ˈ$ݖ * yO0LB?s `jڋl8w)>k+pquzRL/| aS L\u%e#!Wˌgj8BtxҦJ0KAQE τhɳD="m~4젳->{yI@ũT jGnw;]m{Ss2fkLH wEͻ-+=箐q})M:Bs`G"ź q'C"ԑdN#LmQeI %l2|*ܚzIN)X9 ;;X\d$Iz'D Zxw_ޞc墚;l&Gl^a=/7*شA.ip7vk wgXw u:y`2יL.0I? l~H"G9Y)[(lz*diL/3V5RQzaּoy _.|%~03Bu3%BtKpSvك#Tԛ.b[%X_I10z&E6ڜ?[ϨܨڣMV[UK+D.A(dc\G-*71QA|$ r?bQ [_mU>,.S%t 4j'wrR")x,iW$44ܕ̬ۻe W欂E}_ۢPIMo٢khFvW( >[1o=D X^c";V=*]h™Ar )yE߷S^HA b%`pE:ui(AIpgF N!6+ZbNEdB vkLBO;b 1/a%z<\=i͛X?bIuyvzTm"hy>qLix";7J0 nMқA6tCv !oVO %xW8O!6M;>r98'*DLs b S aWsI̋kKUb3;f$`kjQSƠ:[7G}w*Py*X蘱YJ <P%l bk+Q *kɤ-&ME F$ڱV;.4dz\NOx >VI%x'>IQ+/Cz[JFBf'ls*TKf)+YW"]@hxCD=mBFSԈDmDCqiiɾHwPmq4z{K^h*80Af3GKo Q8g+5q &n^9x* G|P5="MT}ul*1);\J6ݺrT/׍\8Huh4L,~!EjP]KlJcrL^ژkYP5:=;=Kh/pzxD?;N;8Bx*z{/0m )v@i&!OMep|m7PȠn#ݟUj;B4owVMvFGP7Tšz[ZωUi1x_cWN>J|݉T|b}l"\,ǗT~k>hn4IoG %qxO}̵4?i)Ă'u}n2kDqOt}6B}xrdޑ-q|8D)ޮ[n p4ZN̮G&c-_~qSsvC:81sboC{)"Զľ)ދ9ZDjBrr{~f=VX7ބ$&@sp>6pͽҒ+bN H4K]FӸ<|+_Bd{93P"& @5Q̓wd.Lfa-J+O:<͙OvgAC~k]CEI/V֛-C_p*#5j˚GZϛ'=3s.{%C+En9hˑ}]7w*l#6 6uCߘ7cJBZ-zG쟄pBIOJS-><ҟS^M!f]l(eָNR9!4. E5eVxFbF^]b1/g%}XbIQgsTjl>b@# e+JP8aGYfՅ}YTP-/eP}v[|Y[jCs`*!9{m==r u|nWt\{#=Ļ3mWٳ1W?>oЬ+-w~p?*tEE\QĬrS*v8?K+: atcN;g-:i7yfT#Yա"KCyg Q16-wEyGWwYF\v*fUtgn ` w )fق#Qо2=Q阣)):Lcp F'y6hf Z Nk~ mz_TQG?欏@50V#hw}ԕ.-}IC7X[LG6k2]/6l"~봡R=|dAݩޘ esvN}6uPxUtI%+k뺡S!B:u A1E2qqum0x{0J5 TުɏON4;zH #KƜ'=iخWqߞ ÎX@zer6f~2r 7XjrDHٍ]Vc斌Z&8N*IM{ewn959zFtbn2)oG`zϿ1YĞE,L,螈t?wkkt &S=^6/IFz jVTQ70k@;rq2ͥtJ( /~F #8騾LnϦ 6$'"GTM$u`S~yrpUg5Kp[EgUo 3LR逻Qic'0ʯƒV4,#7xםm%0sX܃US[Nx 6[n0jPڊamMP}:@9io42lLA=H1pPܔNgM0QeoOmHVkd+tR||m4IvYTě$fR@x(iYGY:[9. 99۠_/]8ZyRcF. c9a蒹o DF,U_$Z1`yƓ鍴 \:Ou,I3B~P 6x,LW9bB CVVXSt{ 1SB^^c]Iig40nx+XQtVPFtK-A=dK zgvcT f9ek{t +s\`ooBӄ0KNnu[!KV4. {w[&$'h1 XKeƏo"Y4H_EBcvI'.F4)7GnΧ^H~ZүjXå Lnc"W0HR+gzc8,*F=?JW_*iW`RBn.]հUĥ3;55mrRXѠ0N/Cc'߾UD u xG>rq{cO&k*Ҝ{p!}E;R޻le(0>`㽮ak~n(^I;~#VjyPpq+p6kGY׀}Hx߀[e!r9?'G^~$20X4ɜk:%]QpR%b#->LF?rHƸM bjn^ ͏)Vb#c{ hg]lݓ& ߖ55焥#| TɆGLu$imtrM ]ɚ+BHܒt ߩ&i;,˄: {&"; a~tY*ȓaMzŚ)Jz)VaݏW8ZܟPgtD?K`$&oWI3yjF.ƨ}A,]Cm-pwp7J9>dx3;ܴ( EFiYpA13pJ]ƈ uJOolnFh1)eo#ʾ Ǫѕcth%xҮIVqqr]}abg>.4=)Z&6kgfNHTޱ [/J'qYY'34̚ǁ΋vp\"ѻ70\qrftLsi"H:!;[i 4R%T !秉d-:oQsS Ŏ=>p2`> T$^:w,Y15uI ӝ7drs";TD,<]W endstream endobj 45 0 obj << /Type /FontDescriptor /FontName /UHPUZB+CMMI7 /Flags 4 /FontBBox [-1 -250 1171 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 81 /XHeight 431 /CharSet (/E/H/M/N/S/T/U/a/e/i/j/k/s) /FontFile 44 0 R >> endobj 46 0 obj << /Length1 2386 /Length2 19283 /Length3 0 /Length 20695 /Filter /FlateDecode >> stream xڌPZ k8'\  ww;wfr*e4Lb@ig'03+?@BIʎLMi vیL :;#@4Clf`H@`gge'4(1䝝n. [k0|0+ Z96@Gȉf g [ ( ڀ.,,fn ka:F-t<(9ic] i [ $@h)T\N+66f;/"[%YX8;9y:YliEf`dW3$bj3HndvcvuEh *K9YJ8;:n'i Z@df{NΞNVNV5a¢dwĄf XYYy8@W†/zMo࿜l!8 Mm?Ⱦnf@2 0Z:!aVcA^VX'#zY:;9x |Yd$ĥ>qqg//'+ג@>/G3j!2b/_:r);Cxg YX- ?Rm_,oK vwp?n3G[@ JΐkCu_Z%ʁ A2ںIz-Um6ovnPgA=p\@#,-b\32dA%_K `avrCRV &`7HA?"_ `,Ep*AN"^8,N?©_AfEl:, #㇜iA [D )W AqX2,m m`S dF,oeY?)5 A8G>$R͟> BxBeBt/dhfplLj䂰9AV~9B !s|c99o+4ycL?gqWwg09m_~66 f.H r ȋ1OH`O$@s9{ByU,A1z!OŁ@/¬@]mh]'ΨNM2]UfF,ykEg7[~<=|VѮUF}4W4 wcyS^.n}V!>]=0M勌Xۭn$scMqr8 MOerԴE J % Eq?]7׶ܽB|K{ ҤmQPHC.g{nrdCa1gO@+ g5ё/VMZbu5}a8q7mGdE ^g6}D⚄* kW] vASIDh ~NΙSs/'J$ضM&@Vd«1NǼ* # FÌB}7Pr!G_I2..Q S+!? %.AA 8!Jb)BJ<׈z rVMEA0 EZUǾi]|jnZ~ b}}uu %O!.p.Ar% ' ɥxNjMKs?Hm1]K 6N\Q;1O:p4а7 Aɭ\K~'Qk$JJ9z߆<|f 0t [ؤ,I=eANFo 0;Pރ%47}h]h|?GKDz p-nY+hDJbz4=RZ*J4e.̎{+ZNVn9~ffz8&gMs:91㹱n\ֽ4yᾗ'x"_φ8bX:}ܱ F+ WtҸ)e:ʖ+;M~?*dP7뻭@OcUqāA3@tt#ڨ3^_XlNͺO`~'/q-;ˡZU=T[NC\` vDXm@-N QPiP =xMt`^PLgRu0^?yo+rݚEUXɒ8I)lY`()͍?:~{m@@r(/kj-k ,0c6-kSbkSob0y[z{ bLpyY$ $>4%LJF28"ngMD9eT<&|FpLsF闳җm`U)1 #Uqik 絎DLaU0d2ϒuY RH?(Hi?}nux`]ٙh>YB޴W62pތS zoUxflfMEn!,bQ,Y%(,CY=JIJN&QlޚhɁn\(NMG>k'vaׂ 9C#:XF+,_Mˢj" Ւ˖m5qc7&J!Ԛߕ[xԿ2{\5ĨEQzUG._ϦB:f0dik녡DG1ۯ)%t<=4O6NY5zKf] 紺/,N&Nɰy(SDkws#W+*Hׯ-gv9|=6U*0B\2+ʃn}Lu7d] E5n؉*"UfH`gI&?^,@`+{AQ-Q5Byu(Hd;j܇MB@)pF}\>Eiq(4T="i pPmEKZG׽4j)RZc]?bڞfwXvC߉};"Ù]ثK3^&:ax45;:iP5t}X*˓Ȍ5텢Y(PcAoS7_v>Ŧ:ѣW9\F%aE 70)N <ž* LJLSOV~xgl>gYmhD*a}54ۙ)fX gzl;6޽N:w`7JSٷqVWN]vxtqWEsmfۢq#/N0-%b<,g{|rW VcϏ _uS0lwwS/iw,V!-L.ɣ2kK:E9oۣVPS~b+hɮHm}4,#.7ucR׺nh^o|B%K@=yQa;:Am׹cmIԖ] b P^3LZAB|$TgFt][DXBX/H~IÞ`4YiW4,5s/ʦX2K2a2;s%&7,Cy*'$ ՠ./fVaӜz@{X.yoiJhmK# k:.dG:D4EOv_Qhv~a3i,-h<]X~4%B_I g\E%FX5}s:i0>~y2Ó`EP1TFCk-!ٗ'AmGAᙯ|rS8Z>}ҙV aתk%CtROZEtgؑp\-(q"l޸e915& +mQT]пq /Q,*ql-8=@a"I>p;.i"~=/pD_.%c`XޣQ.l,Y{5>>9)C-`yUPS.xqIĂzXDz_]Hw蘲lٞ{+:Kkўp"Œ)*|i@brD,ALvhn_ϑ #A Ls+:E;Q#be2!==x'NeUy:Huj>̡‚2:gTk7Qu@A?bWωP(2gD>P∖/n K!UcܠOV5M"eu[g2f˾ BQݹ=1cJ]eFjl M:hMyCTQYqJ)Vd2(Re_S'[q:-mz%罡%e9Ԝ6wm p%hАzsls^^.unB\2=,H>\a |%6hpI :Ђ@#֗hұIn0T CDצ]a&2M?\&MȂ URVHƒJ,i ʸdOCRz;{TV'ޘ\wVC􅆪MNZfCPM*U^&zM $%ς]8AM}ܼMS kMBZ[Tas"uT0FK;ԓ' ?đce/5'N)M=%[9 8O'>&_/Sh.l}\a^8.QafeCBGQ{E[ܰdIEˆz(Иx\3Q2ZCYFri0)(%49o :r{sPO8fbR 'l#tA.){6]~ ͍^({y:Oi4eY.92*õȶ1S8#6W[.c7f ΢q^>_~~/PP Mq-q[E)U* x n:5W>]bP; DB{·5Z1!}훮QϜ3tsۧHKi }{yC8. 1{ ˞qi/#[\z ] P#"LY#dE VmB\d۬Y j, /Z|en~Ҏ Io<9T\f?OML+ T/$}TZ(L:fj.. L),82ެPa"+54K> ;^(-jiS~#q~`4Zt v~=H#Ua6+0H4rj*_tPv(}1''pBrbxhK@/7 Ƽ|~u QM^~rq xY>M+gǞY ַlyK^:5e+g)±d\~<B1ضkGFަn{Fy͜29pߏV3{T"RYl|Q1^JmEGҸƐ"Z,}CGqsLm}ŏKK]x8fw=5UaslSM;enӀiδ,>83|qaώ:ьN>P*[#/ē_2Ziv8bX{ŌIK ꭍ5r 1OG9öiQxƏs #96b ']W)ܕ/ml |s5nRoeN=z|1mi͊*@d,5iVXcMS+=9Cєܲ%yWrM<7^eRd^eXsՌ^5zs$o^D#?)W7 S{{ΑbE84h)KaI5wkAN) QבJIg^j K_lbSpKaM{PG>UN9U&롘"rpgque F@SZQ=%̿sNÐOIv#'t)0h FtFF9ۻDQX}bkK<~'8׻eGF:e|*ۈj]M/;DdG{l?(ũS{|<|<6/}nzFiU㞅!:FqnnILVioMl } r>pF/+sA6lx.@' }bڷgBА"?mtېww#D"T,}(x'G805GBuD`i[;/s_O%_Ə| bɼ^ehKH`ZuCuYW]蹅(a %gDqͳho%7Z %ROtCl{ȐӅG@U0QـZgI[.|\jqQ:|ZjLŴJk] '!sE[1|ML4c(Fc 2ѕt+oڈjZ{'^Ĝأ%6#ǯ,ԥݧXM>*c?-ϫ?{Tr(ZXl/1"+]L$g>xFvD%-ueA)ұήn& V"L`Nj$ZPzyXApA+rZa(]'ޥJF&܍_Rm a^u4!xŁ?\_ 1Z nIB-mI\`OAa׉JkSO9;ϼn39eg\LL=cL ><_JQ_^>®? ~3R'%R)+D֯m]H Ïj8m*G6B5(3 t 8[;E By|'5){>Fg }q#ڼ؛~ uq(erRܗ:٩Q R(Eg NIkS959IIzQƷ7h'J "M@ wEV%PYQ)ئ}uI4=\,&vz!};A<g5RC8ITelJ9͈qbQkdn$֔t .{woVmV 5à,X3D/ 0{M^""E-oOEK|?ʼbPpz-BclzKnzUQ ܈ɵ%*t/H(34E癡xE~gyxsRF&(; BK>qvzˣ&;H䟲N= dU<] wWT!+( (. $9ngROuMM J"uOfܥ(q0~LN߱$?@@HkWi}!{uc@w";%ir+A>`kOUIc6+d : &J6|zp[&LM3(SS,^2 QI ދKn1JX֧l~c e?tr1JT~QwQy5E'!ӽQɥ=#QTyA)F ֍$mbbwFj?j/m]n( $~;W`Pъ 9nxOǸ#]-<kk0Sό2E$ggle]9|پ k>|vp?w[(y#$#l Mޔ%dᲉ-ˣ>T$++myкUg36Ro͡/S.tqK^[KOԟW5ISNS wdsGɖNi\dhr$׬R-T* J-0z'Pt 4Š4$j=cZؼ [۠65~cz!A$lQq-]  Ja[\8ӬF D9|Zpt߇nÏw~MOL4ֻ~ kŖbr,a=78vod,ʓ'G@qv4[~:|սj$8}85Mwz XLgPUR(< [|Ew[wbhZ&.N.2qjM2̲̔v7Iے%Ve̯t+$z֋e#qƊQc}!0X:-9ܬ_?ͮ[Ôۘ+%!E^mz /W)E:ކ'|+a>=n3=2I>zH5jE7skʕΫ:M*J]K= .4̾ͅAA(y甧#tg1%oCF!$i?}RÈQOZ !+ڬBO.:Kה_Ea9'^GFRTf?n2QOؘٺ%#lv_A` > l\,_R"=D&a$*cҗl*"aϽj R4^ՌdEaJ|)ۍάR`)2eG̈́ic 㳨HF#TlnHBTOv0ݡr-ʆ&r?gj.ϴ͈B5ZduT`M냝cQi5ޕ_??6D4@?O>9aIl{1Ps񸋐2=[&Pܾ-"nsH v*(2=/ w9\Fʖ6l(΢\!GpA&l/ܳJ_=8^S]貐O3g\S`7TW\j̾) /.0J '|)Q65I#iv r: Ē,_ң6[TI7GXXX! )兎 ɶޘ{x_~w=zԐH@imѵ$CS; !j[H_L*bm{ RՈp͹id)bLOB~ʛ.F,.8GkjXVjv/ ~VM֗=r=& ֯S{a4 }ވOfXTO/Z,~kZ~zHB bGdE7f2( %lm 7=1AZqwľ nA!C?U%UӑE0@9o0SjMZ2Dy|t?<~jęaz(Ve# ҔZ~JIYΒ@#4|9_Uϻc O3a519brY=r;bDΟx)|4 ΉYY<*cL8m)tm끠fCM""|d}ҽ/rP!l*tIH=J4އWvH9{XǏp .Fs{.LfC#v5Th%BeXekBPfg#%(Y'`LjKK+@Xw sw@hh﫺|d5Ü@ҐK,g"\i.# ͎nIbQsoaaaǍmnSpԮ'ޏFA&VW*JW޹?õ΋qC{XY*^r}o>} }=%lاkSoסtbPfr=Ə8$^pL_xd4 <܀}n<3t?&1lm* , _@uL2Mhcoh:mcV'4#ϯS+kʧ IVЁ5d7; DT˾T /eHjDt*@vT )yR2Ϡca_ &7 #sc39{-4*WubN<;b7j&M6ų x;4: LK28D1Huwl#q8fԓ E _PR$:ҠHUa~]b(ngB#4׬K\mFrV-$s@r@SDk ˖DbΉK3d]hXTQIϬgS=hAI) F)r'I*.^53|L}vi7E$P0!`Ky"ӗ&kcRTP'%ެm9 OϏBhze #@o$#N8hrknk4dNMN`xMmLń k/V ? (|Sb*mɜ4ez_@٥O`5<8YLNnP}!8.a[q3$FXݖ3{nj;{TiJ(og {~z=HmkF\ (mAm5an폔ԄA[i5"?-{xT&n>z4>F<G{ջ }i ¡mob3Rcf9Ok[}CM9ɼ)8YM3턣V,#bL:~ Y{gᚫe_ߒ[$wSճhorx2;/gHFSC U2"tl]rNtw\"`װʿ=3-U:/MGmDK]E=L4I9PBy;I']#r9'zAh{gR+yW<9Ȓe].SYd3]gABI v1L-fjJ{_nWD;ׅ ~tX,Ll:ꙛ3=/G[asBxdvLד5e<z$ v:ہ ٯӽ]s.H0lT>7m:F0/Mӥf_o47鐃O)/Ǖ{F24+ecG X ;?ąln pgT*,z0?糈h 04|H 2|>L}9^i2UM?7 p~5@ʏ׏%2U5 `@O-@~(6aڏd) D5#ֽ.=jn#BϿxFP=!t{ew$$4.pKƕ'w h&6Ϩ(J|E&2jNlp \aF^yݙy҆P)Tua$xjO;u 7#R=>7|t.y/ˇ8w wtMZIUyiC"Pͅ&{}<-.,ShP6IExɨ"]\w84fYn m;j"m`\tD >z<ߨ#n}1# [gY# ҵz/xiY vGZ#Rlӈ9qI+{{ӼC .3W@[,$25w? *< wBq+`f}솲 endstream endobj 47 0 obj << /Type /FontDescriptor /FontName /GCRABF+CMR10 /Flags 4 /FontBBox [-40 -250 1009 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle 0 /StemV 69 /XHeight 431 /CharSet (/A/C/D/E/F/H/I/M/N/P/S/T/U/W/a/acute/b/c/circumflex/colon/comma/d/dieresis/e/eight/equal/f/fi/five/four/g/h/hyphen/i/j/k/l/m/macron/n/nine/o/one/p/parenleft/parenright/period/plus/q/quoteleft/quoteright/r/s/semicolon/t/three/two/u/v/w/x/y/z/zero) /FontFile 46 0 R >> endobj 48 0 obj << /Length1 1503 /Length2 7424 /Length3 0 /Length 8433 /Filter /FlateDecode >> stream xڍ46ѣ`Dމ^CaØa F^މQCDх$ JOr=k}ߚff{~Y {:JTt@(LnE  HO(._$P<]ĥ$@0(") PyC]6$`WA"NΨc Pr  8@rݞP_)dQ(wiAA$FOjrٙ;!![ {Fx$pC;'>_ _ ; ;0@_ _DqAa [Au%Ct@BQPدpsQS"!cf]_#v]hEusb@ PBJ@΂қC~Bܷ#M@O7BzAE $CP{NO[7OP4 x=!ַ#0WPSEX!)+#~Q@JR !;WBԟN?{u\7߹cKYC+M[ `V^["nTsȟ; CBn@ {POu(6˟~_K!OW/vY/"Cjp׆ @H$ȗx+$a11*! m{G׍J~[RAߖ-vnxA?)_mofA^BAI ? *O 8,"d]»|Mogr/ .IҸksCWߕ޼us{^TGa珀+dNC?+527Q `ݎ٫^%IbPLq3nX6ܩ!7{R6^d7CxM:}}`Y; KHpŌJ+:6:KZFS tm9Uh uغ3!.߶9r 4 6Ӹ2\ѼeU7v{O>>LQ̈Pjﲠo'ș*/ňYA]4|O6);5 7#mhMCbwgFg*[בVJ1T;}6~}O!g4U;rIMkWSBZ۞+;FϜ7\xQ7)E? *ќvΤ14gWw~:1V?ë:&9bW0.AOX@:0C_!"ːX~`A#5`90͝q>pBJ|}^K$ͩ5Xr-8xZy/rXa8ũ raf7T:[L`ף%+Y?xhqix[I=ʏš3 CǑy< iWډFP"N'5.d1vD|MFwQVUٌ1r?q|iNܟ}vuS$rlH@i(yFKYi51Wa웮Q`]v]0HlO Vh.UZnfO)aᚓT[ʁ@3cx^<_[Ig6}~0VZK6*>-c/ r${em6Fv1WHN."XE}nX2ڐ@oZ/>Д6C9#QE/&*x$S8g#2檌&SQBP(W.9̯1fIgNM^tE`dQ2Y2UFP梩$v#y:j] ThLxdl;ͬ \lRX|W~WLuZ5ʗuīIL-i0ZԤ멞 Ɲ6mS0ƳMQ bv! 3&zoQCt{-(`̍Kޤ{ܵn+.<띹=$㉏cL!m?F.(tFSvG&F'q.Y!F xD^TifQ3ŰSS TToD* H•U>iR+%9 ~ /7_ES^dqvG"PI VTX,^Jv7=:oZ=,V3{e;WbFV}\j_YD<$鍎tU)s0_H&t,D29)H |9ԳX|d{0u NӾ\V/Sj(ڬ(d#IЗ;x6>ĥNd+4v,Jr{~0O-jt MEѽKA5Мc7PxQQA/Y߱u^lw}۫wVn쒷)#.JarCMHX2BK=b Y",Fry qCzv ikU)lufGÑ6t@g1HMhfV)~+8Z)892 &RO"+V$6'W+vse*~w9uܲ@K *"qTՇMbjвZA&Dz{NcOр*Wi3v_=pH#vJqQ{;)֬ͥ1C0'7Sjt{10Xq% ̻Wbn]%'{3=Q6EfOS݋T:f 79  5bU9R k)Mɽ+'$<Ȋc^|Vt'PQQ-o3xVS!ro'%w;6$X=U '{T @~`wB(Nش^US(7݌\G5Q3.btM W`MIoּ-ݱ*K~p2;{@/5:Gq8fBU'-o/z\W9NΪՀ|ѝH5xgMN#aP$qGK´ 󍤴 WVFQ".f;tQIJaE /y?䢛j;zzXjAA4z-ܕbEqM=e1J;Zuͧ%|/~md.UVAB=ZsJ", ~;պޫx?Q4FpxĽ#`pbǣR}ȶC\ 4630ɦJg>Vta>R,(nV AIX ~ֵThG5){cAe<&laCW֖ߖH-G1;E#!:}*zJ/hmc\8萦| E$ͽ@YշR2cz+K{YBh`} ~`٢N;*yÄ́Bx*5RD <丑2kaNo0Qd{C\A6P,e@B-:/V, H1kֱY[vP-$4z =3NB[0?tz'.rS{70 {P‰ehlEjXɌuwJ:;쌍uۗ/M=.Iq=F7骠 n*Pב>出#~j|&=Pwt <,,fyl'F_  F)lj+;F}f4zdmu&,dp|E ?0){R+KUI. nFnAu}݁tt_5gNn4(怊7;ٯ)셾U&cg^܁'ntcB*^|h:t8ѻ\Er0Ex$1b YvYx!T½R%-aeDsWĭ`ŏF}7 Vn _%@;>; o9w65I9`6& WPűXOC-:=}b<2pϼpbvNh>yhF?~NM;cn ;Ý^wzޏ~pW*,yXF^VHxԟ?|"T9PIXUL ،g}X'G=I8`R貕.a襌e`Aӓog^Vo\',ֶp b2Q‹8_^X RM;_-Y%ەv3ip }3ԦICr^cgcp2=0H-Cֶ,X Lxuc?%b0W&]s.rBvfΙJf]n6xkj%.2$@~Z?gz|K]Dr(Avȶ7水! XYyQ[͇/YI~uͤv/.4~2A 7*.~6Gy2m_ĝqR(*64cRN4 4ѱHL&+`z&V46zHbKI!FS~*Q Ƴ;k&vWv!CɹJ9lVv&bҹϝ\VR9Q`R)"myBmzٚzAXrRVKF"J¼za61NSHMY酪20nLKWL~Q^l%ՔN&rT۷0l\E֯WX>/PS`+)5x&w]Q1#{wJ0w)7F̛%TL[eZ Q yV5d.CM EGvTd,!_i[ۗLl9)ٔJM] =q,s\kD_n^KvpWw2F'lq bn &,$Xo*{ ;X_@+!xeD'n\B>UʱD##{2JNo) OP(\Y@(,z*| 75|o\?)jƸTǗi7ojnvw'qU}r#DSTK}Cz bww6 '&ALM(':. : j"'Ԍ6}٪Ҕn+n>ŠPW%$LG>I_ʲ5wa6"μy@բ02#cB|@ߥt3Zi;3] qネ]8q|NP>mըL/m fop)bd>C2EBXgB^mh,D *߬}JT)Rxg^VrJI3 c˖lgc-zU`Q#X;jQHm$x!JF)):xтN:>X4EDGsOYiĵ_]CiG? %#`ZJp_)XܻD 3 ReyT{Qf8Hɔt:C{ ș| @lL@^Z^A&+ :K´`^:aB(/f!&+:=Q̳a/e2y?R )=Jӿ+TN.K]4y94?<޽Mcdfed"̬ 6gHntBЮ];e pFߵXbpa"tPL߹:\MS+e.B0 k}8) Z짦}JNRʥ4[2cK[a<\+\"d]{qթ2IX1`zsFkVӷPI un>.pE<+6e2S--flx.m.(m#a-wf3X~!첈/ cUZh)6C'vEmUBm{C]~~}⌁֭(j",Qx nsI/J)^ffhpAjSO=uKKrRϬLWaC2!ƘI6f9}I=͐;UEa)z_ZQRg@qsx.,S [sȈ}]Rc;[,5:ZY ib*u3n:FX%:d[؈#*#Q[ob8Xu4ܧAܻd{Y$?= \#c;xTXҽn&tuGŭæx.獷_Tɦ~Ar~#+ZH9a "^7^>,)۠r% V;C):|VXϝqB'R&t,,Mi:%*v9e#܍nK l~nV! I5aV1н']_\?S>JF,mae [ 2A?N;N4s;j_P7 :[Tcz~o5muEm0dBHVj(ε"zM(_ʦ`Un;`\xlQEC0{!QƊ: ZSOS7ܬwD' ix! endstream endobj 49 0 obj << /Type /FontDescriptor /FontName /HCOSKL+CMR12 /Flags 4 /FontBBox [-34 -251 988 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle 0 /StemV 65 /XHeight 431 /CharSet (/J/a/comma/n/one/r/two/u/y/zero) /FontFile 48 0 R >> endobj 50 0 obj << /Length1 1663 /Length2 9684 /Length3 0 /Length 10760 /Filter /FlateDecode >> stream xڍP\.;i$xpwwn5h,!Cp ;ᑙ3sWWhյ%a YԍS ``9c0\\0п \@nO2i ';p q qr99csH[x*E svڹ='Ɋ%(;@r[Y@*nv SF+ G rLܜ@OOO +V vh\A. kПq`0ʵ`6n. l>yCA.-elwCpA,`-*sy,ֿ -]aO`G '?*Jh,=W+++waNYj-@@P7WI]@VO sP'/`Zn ;2ya#x999y g;%oSN0'S  j}o[,A`(?џ ?]^#'q8?<u4Xo$ `wu _Up,S_gk7KDZsrZ=p?3?$Gm;zeYw'z?wVd vVi$#UVYI?: \o;'6p}b*wJq,\\,18 zZEk90'S{ RE ~nPo$ >YZ~ A<S$vNvO?O2 h/_PJWzr|*_)S^A_3rwqyؒq@^ +Yp}Uhu'ö;fvV[/YW].%R:6e.i|kP#44'1Iz>KTPSk=8; 6Ud.Gx-USm8|v[c }${Nqp4Ce s7v*4c/)GV X_573>eܮdT/|%wSI|>E5p q=(fWe2U@>\z oڹ GA;mA 3ihP’9 /]ϸ*Nf-9Va0 /gsҚvl'ƥKVgoU}J,En17t6̎4Qh3ӖfrXaW1*wcE*t[sކrV'1iW΂$ @ kpͰz3{/w/Y6&[V_FR)x:a&z/-0{lK7A>6Se"Uvפr¦]=Ccهf1mBwd}K)'d>[(eVLUP kWl@ʩjgefp=^_dT25G3ߨ~FV~i=ZъKO>oϣiTdnX|"4tfq*ZL;F6+?|!\~nU?xsn>)6)G\qG$ܳ.lS 5񷞈{#X ÓSHڗY84FSPAuSAJwvQl/tz/h%7D/SiH:\;z1Tn|lI{&gږ5 \4{_툿jl2%+u&ld88}W6?%JV^EIj;5/}P2[r~#^:2rҳp1i{_BG-0&'o ay^s_ FWBL{5_AY4EF\m3 mJ\'wH+-u/?k{ o!>1RYt+KP-@A/b ~0uX+jm@ʂ|uܴڋ#a="ks{ި o7"G4(1?ﶥ?1q- :m~\Fsxym+;يӧ1Ř1%a N N݇ CH[={Jd*Y Io\ !a&˝>c$" ,(x޽QTDv6m^}%̳szBO%F (lo۰ݗwmSUuJ7X9EdKXmEkXfn<[ I5Y@̀L8nW2bq+,@^p9 )k2~ B4(;~nP!Tz$ SIkHh 1`:hf>Sr_]zm?Je4E+o>o-~סxLvJsc#]fo٤9ʄF\ Zʠlxc>}beѽu$$h^, ?vy^ nK\E$(1}u!պc`;?Yx#"^uA(82ULNM'B]i/Loig3Pָ 1_-0S%8Er:aXЋg<+ңCXTC5[at/\?-ȱ[,{hhM䞈܃}s`1>MLF+ֱTy0}{`nJSdF$o]vYMyհtB3$TޕP*ʞ@M6FXٗ{|LJq&Z<mECKoaZN8o>%\͆Xi^˙ٶ ᇐḘ"|לa&/SuCF' U=y21R&wlw|g߆p(cD.= 0ZQ!x`Xyj ؏GցmYHhBwM(খw:54H}d&÷_jҧ3E&6$ ˡ(*S;G|$۠]"o,]2%YU2@W&@FɥlTwY~{7|V^fCf!d Qx^) z<FW$F$[!}.C9GDI$ l jVil.(OF?ꙜK{jkimcupG})φPz]Zj.miIOfos&b3su_hBK>c:bC ^@SS,!)Րɉ_dyޡLko+:G޿rcQsMHp0; E$L"L#Yp1\S >xR:nx6REV[rg= dQ خ+q?,XPVu`dӰ /n`<Ž$|/Yemiy*Zr1s?*Z7q5޹_w=9YL@tMT2csBN}dlyAk#sG(ljS'C)_4Tgj;Ygr/+eȕf*%g ,+jT^f9d?',#z^V WFͪK,zftt"SwpL+GΟz]}b4ߌS3ڪ9ic|YJ,(|wG~40\d!%/ͅ"3!E"N[}2JaUг{t*ZGWѲd1/2Ii$EP*n,>E " @ok7QU K5-F3>jgNbuۜV / [&py%USoFgO~z{G* ,c^^BW H {Z:$7fsu^3J..ܜ[@\??HJ혝Jɥե!4iB1ᅂ u-(Zꝴ .2 ۑtLv'YxuMTon_JF8vȷ!_dy}3O7g'#{_l9]%SQoDY_B4? x#wܞ;m!c5'/u3CUW"L{+61{K2[LFcniꝔ>}fiiT 7Gxw\lҜ>B`._'qN,NQJ1zfהeE[)d!K $}D-EBgSH^Ż,q_a>D%hH9۽&u5N+Gߪ#vt 2(W9XSIW&6⇮c_G/Ҵ!,+=FfBaz~vF)RfΏ`^sao@5njn"hL.?V"UXXp?aȸ|vWɿؓ\K5Tـ{jti.b~֭^)*l*ӆUJ^pJ.ut$`^s1p4SnfODQTןQ ~7v1QM{xw2,$iDf8զ*3jh0_ \PK"-b>2;TOW vC>&-DTQ\EadCCDyXp |. cξ3v}=sERINZhc "<#_e)TEoZ{hl5LX/&f}%URpنHڟ ]2,3~ '.hLꋑ LQX姥}>Fa#鳪HuW\]!&򊤱Y0ह%-zSi1, PkWNcM\Tx#_>+Q2(<چ]he~/R,r$jNswn) ;9F"ȳX _=JWX&5,@ jkXn.8Yl?jUσ0KJ}S.gG y/ї{Z2ɄGvon#* M$Ff|ʗi*"XqX7O@&kjg;ag~-#gPGr469IkCFIBǣ*wp)j7lS06zX}@;ȶ%NQ7ȥG΁Ub֑.^^*k3}[m, Q;Q$x7VxT)f/Ymºk;})xu1GmEr *%xC_}?Pl杖{|~ʃc,>|յ_!Ʉ/b| [ Ι9E[壗sBvQK¤ArQq44="p?" 8jzLXHE$=8 y+]֠n.D vD{[^&3,aE'W1L(NHbyy"sEE~/RH3>;3S9(E'2-ݨA눅{-"kW :\r yFi_!aŕвꉨ(rsMt\ݜ3W6?ƕJ <$ ZeLE ѥc)[|'2jfY*ixqV?yq3]0/؝@ C]ϫs"ϗt !*Tʴz->?b%M= D1} raRm[DفArf Xmg& -J;\3W k4+Om_ 80q~t)?OnSweNLƳOc}?nK7U#pR%skC.+ M}֡;Gqs)t TJ;DXk5VD&bq&Rt<%]ے6)|׎2'"-D!PH:K/UçbN`LBA{7oڱZܧޞ9VH^(K=rKʿW6J ٰeE>xTn-II%=٥]r.ﺦsJ37TSG%7"*i_)iwN򍙆$Ryek:5 նl(OҮgD;u4 j֠>A/~Sd Z(1޲NZhd6qɐD;>{&{S tr|sF+xGS%r 2-Qr`2֘[_^O2IӮؓV8F/Q!OX)xNlQoLHZ{/˷5hf@YmC1**CvB$`[|b}:jLyβ}PFWdS5ZQ69-!SNWC-ŴGӚgy+Tzk)T&v);[fc·qCL= DHџu;e&+N/׳PJ!F6"Jn1"yó,Dk'U?."wa}InOQɢU P]0͔~(L^dWnZ{ٿ`Kyj)2S`[NV7u=Gý{~\Gw!ֳZ=!B<* cI ,rΉK >JDZ?~ຨ. 3ޞ7j?YK}bB3N44㊇U5&8imߺ0bެ ZGu4𰹍2tWQt?Kl%aT" V M6Zdt+MJ5OV}0Xwc%*?`y;io_^!FfCahe'Ϡr2hf0WZ>ϴKm\L+a;_v+JUEr,1g1_o잫RM>VޤLB0W^hIq\{\=K̭2c9ٰ<53 +ms-uK܂xlJ3Cކl/ >wJ#30~H]gVUH{V"2g`K"W~R9?[DVpc>Ԭ/#LxyqeἮ;JcKiǫ>)1cX ^_LBч)TQVNjVGW͐SkҁY{k  o \&Nq·^h҄IEd XByy &~JRЪG`Gظ| ,0izȆ5Egڰ&X!A)zk\fsz2e|>gpNA_;cDMĈX}JOHn[̍1/bjml m˵4*Y]1%6Ԝ?kwιDNa7ޚLrRBVˤآ4;Sj\:.T#sQD^.~eJϒPg{^ ,]aOWQj[EJ MRK" 9<;9]5fQcv݉ MZ i~j+QkR**ɵ}c+Z̈6-m rCN\YI ; vMQ);1vuz_<em=MY幹_R# SD^015n}q_BYY@Rqeq^l|݌*h"j̡D",޻YӺb|Vs(rOy]û[/T~br4eam+ )Ds(~i?z endstream endobj 51 0 obj << /Type /FontDescriptor /FontName /OORDWG+CMR17 /Flags 4 /FontBBox [-33 -250 945 749] /Ascent 694 /CapHeight 683 /Descent -195 /ItalicAngle 0 /StemV 53 /XHeight 430 /CharSet (/C/H/T/a/d/e/g/h/hyphen/i/j/k/m/n/o/p/r/s/t/v/z) /FontFile 50 0 R >> endobj 52 0 obj << /Length1 1375 /Length2 6042 /Length3 0 /Length 6984 /Filter /FlateDecode >> stream xڍVT$F4f)()]Rc  ( Ҋ(4R* ͝}s9|;>L𢉹+A$E@L@%!)# Z!~H Z5 ӄfF4 @"T^ b&, I4$ "=p,:p /PC!H8 p!# cH.!zp>`p``$ '+H`C`vc 1I `#6ǸaX@x#܀!pcl@k4Tpy Dv DnHopMP`h_0o? Cz\ j_HW_aCBj`P(U& V/4&svC]~D#}zYDe @ @=[ ~+Ą>" ~#] \ppGAG'ncAuxP[w濗 ֲ6TU /!%HHB(TJ ' ߾zh7 X”Up_"?ccE" ov+GVha(w_z^qa @5]Hjp0"Op5AGn`H4P?tVUiR Ǹbba Š 7Y%X\B{a O9(FN(`CTp,@P oV#A8hb r7j\JÂD$FC:4Y3=6O Z»'WSLB͆@レoUuPqKX.ZEy7 _3g ,z;h\΀D<ǣ|8 JQ ݽa3^d1PBݬ݃ѐO-Z88yHw]«}ėNKj!r LBf^N\d ٥cnNw&~%_yWG_TRJޞ UH 5զ3zF]C滈,mD2+tS;W pv,q~^-Q:Ly-p: ն%%'ȇO{R*{Eq)")飷y[8yHx/%9oܱ{:sϜ:]O%<J%uѺӔ|2K+oҔyx^FD;/9ޣHWrVrK jmjOucۭS-1&=E`N[ h{5]YbǥResؙЬd \=Is}ϳJgˬS:^  M-Z<<) ?/';{DJˆ)e`*ȫ-s]uT݌GֳI%ʙ Iiw>o-ҳrnn\=əF4_ MYEյ_3<۔Yq.DGr ZcI#XʪM]_g7P[n瘸JA؝_[v{_LMb0năzW0kxJqv,@ {[aZ/H'݇AmekCd1;[WShX; RIwd% m 7P3TjV"|[)禬- v?=Ú/*y3W vD 3<q.t;oS*c :-rH^=~h69SMqNCPAG5aHbQ~8߻f`ٵ!{ϷHsrtN.b#]џWN >T.a"=Su1z|y*;Wfk(3c⫧?!B{)0:Q'춅DhȘu=9" Nʚ{dwJ]DR~ϕVPQiގ:ݼGkI~Ad rS&_݊bJY#DZV)eq ݬ[ʮ|+ڋ[3 Bp{, 2gyKCHs쵈8W3w}N6p8g0 b|))k2u͇雸!=ZÍĽQw:VO{[`=-?v$lK\QA{.2a}bD͆dRk!{Ujb"C*wO=h5N*$%ce>ހz$mu_~! gqGꝀ I,Ʋ(vs?us[ᛋyt4"w^j39#n=@qdTBrPSbJeVֹ̺&CHr}P!| M58[doIkk Îنbwn<»{Sh4|DI7їCF .۷> {4qNiNJ3D) %3@yvnrK̠ƫ1jRJ-*oZ+AN=5G?}%B4@M{;aSRvɳ׆K)v}a;R?2%dHn68 TjNn٩TmܐqMFV ~:Dy?-3IwUis2M_~C%ֿ96= vbUSUݩ֑ dS.{[>cHlG>uOʐxv&F~Rhn.ZTU{f5V5ٶ#:WRϚom?ɳ,6bm,H=>eNQ̗ڞo9 $Ell&3DpWw{/Tu͙ia!ͯbo{8Nue:7B)4N_W*w_3F/n\5"#.ޒ`('E7otaOCȲhgc}e /<5ء gtW.c;#5]N7W.24ވ;?|;WNUs4o励s*- 4֢\2Kb)?E|Xπ" "?jݫP;i5 蕛'iKtJ r{k 0Fεz_h$p;g 1ҫ̧*QPpiر,Kc0s:h{LGG$񉷦KKU@_T^'=j c_~kHb'-qtƻ(c֖dNAKX[ߚapG5NV *>43pt|AhOv=n.7ݻoYDZ$K;{e_ǗF0oq'jCDB*`ZiSݤ{[*j.穂lr ya&Κw(²L~)eWkD_*W%}})Gsڻ>?~YZ2ye9Gpĭy.18g!G2)I+JurO1/J}?x2JW6甒d -3%nG)#tL8xiG{z/E LuTCTĽR MǎyDL.(SCqEN ׊)ePg?ZK_3nyw" FzlfP]'5M0/`eFw)dm*<$Uc3`1!T|JP$B,I2<\q_˩|^P`xTFugYѵf/D S(D)W_{ R>L!%í%-Ŵ-)jK C+)BGhoS)cb-)WY3 Q̉,w4b/H[gdnWxvgsw7oŦ5vܔa ruIM'i52[^|>{ß.ܾUqSGv:vt9~XA='%Ω*PfZ.pYx/;kxٶTڐフd}d& Jl֐ױ:Xj1{r=_ۗ^Wڄ0|9z%IWWLS01.+JNiRcjQY |4| XSDV\ڃ^ȩ!/e]UoȜM .ޜLtx"V]fɻI3kd`]3YpM"J&mF!w$y{U^u )%.5nauMtʖMG?4Ӥ![c{G9Zְ^z5:SXrwz){`2`Pr@.V93#xע`cGC~2 . Pae>n'vr"T݌sg$y]:cKb92,= lNAHfϜk,6'].,CDb^M {9WFx 'T_tM듖]>=pfՏK qu}zF%#^l1U_6V2M8,eg8? VXaltFVS<f+L@nR'`h$fb9mj5>q0I әlBjs~L>n;4?=_칃V "k=g k?%ҳQÛz$zȱfoCMTj_EÚ8n@&$ot}k@fm.j{'" XaA)Yo1Z7_kFab%#biteЬAԓy%"ɮ5֔rїw[adi}ˍ>}`KE bǺWnNclfDe_H=bOɭo xeN4ŪEh %ߏS8e|t!7W)۫QzMΎ>/uk endstream endobj 53 0 obj << /Type /FontDescriptor /FontName /EVFLBD+CMR7 /Flags 4 /FontBBox [-27 -250 1122 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle 0 /StemV 79 /XHeight 431 /CharSet (/equal/one) /FontFile 52 0 R >> endobj 54 0 obj << /Length1 2397 /Length2 15039 /Length3 0 /Length 16454 /Filter /FlateDecode >> stream xڍuTťŝ$k)VܽXqwע.|{+k%yfw%Jb c4&x`cdac@Vh?,AvH82I#+= l` 8rHX޳Av@'$j  32e:Z-'TA&@XY]]]YlX@"LWK@tt~ P4 5@o* j l,MvNFv@GU9{d LXvdi `fi|V`FvF6NW{##K#W_ŔF9'C'GK{,Yy-hvB#jYڙNٞU('֫p6X>D5oO{=5;:=o04vHf)pt谽!;ozsf qCѬʊjI8 `xyH?T ;B_. =})^3ll&o/aǼoL661bZڸ:uxz] j@SKgʁ^BuYx[:I[M,&bkgciT9Yjll{5u:R_WO39n;Pqps<_<XY@Wk3#X%~FV/UAv >? zQ^A\V?=ze9XZX:8#-mk8+);k$ƎF&@_b- ^Ki~d-  ӚuS^3sk$f.,AΎ2x7֟"qh/ƫ_j/5׼kQbձ[_ޜ?!x}KKGu?k=mU'b88@S%*W_54 9.d[8էאp|˿k\5n_'WO@ǿk:n;_q h0 2 j#reQ~q&Bbo]Lĕsŗ)4d!M=4dHT45x <֛`,(p#!ES3n(/}'Z"#X! _[{HK? k,7=.f,Q?qG+\t pfGw:D \}jLU+>qom;d'SAD6 J*aG^eܖBI+z"c A(Vfb#Z艬e1{r1{Q JbMzbi"9?QJFQK wÜk'(k\R_S袋bEIWۏ5{ nj7R?,eP1-r# Mhx1`C@ϻh)a}Tc!uQ=)^S=[ˋV2']|b!/uT]0E 3SQA܃Cݎ {\},! Fk.L7>參׾0UlN(yط%+,%t{`&H=XI1U-!H?9ѱcQ>H&WHPUƺJwaPxJ;(G2؅?WTv(qMZ`)Q7h0W32 %R+VFݠ+JÉq3PY!qQ=|.*/*.+Rm]?[q5YL m9Xԉ=BzڋqDPڥ)HnQ2BzO>ϲT)QUt#l7$d㱢D8ݔm0*6s 䈉.q˪G$|ѽhwdR3x/kOfmvYRfaFhޜ4st!/Q=jZko@UP֓JJ<JMzlRSeH?2؝ȕhƩ43zqq{RD`†3Phض{[6l'Br^>a%M\h%ϐol3zc]7\haU l`#&A&Ɋߘ9|QY;q@x9y ̾0;ICx;Z@=ˬ_D1"+ech9y!G9$]=&c۝XWyR'N|QY8[b]㙲ޮfDŽGFqT^̘ 5YIo{LRJT4(='wja[{dLf q _8ڨG7Dl%*#br>K4J3=@bh|4&=|U 1ZZ U ^M'k "Si:c'jOGOi7 )_]4RÆyEk6gYM5>+G =m=U0i|ܲ˖Dg.惗kY[Y$cwt ~ Se8Aӧ?=1 ǨM9Ie7qeE܊#wryisSZ?ڰ NzɔHRAC>>gμB l>@cL5)mf'r2}Ա7u5.HnN\!Ô!G]t,.UJ3.V <,jdD"ZȉYdaŷ)UCgۼW4yFNɆ7'EJe3Ytz{n:%,eP&85 `p$ҲHZ`x?S+,YOqd<½*CТ5Cμ}3Κܠ݁ȐHF͕0l0=g"0IS2JOuQU8\郣em~+JQB0 6Wk";c _q(R9ҾzS;Ra)$n<_7|*f*FeU)Xk1v" bM+S8Inl犿T.YYbQȓ9d[<4&ܔbֽ}pVu1)^/}e~3 C%`be7$/=o6-5twjghڈx-eSE.Up+0O"I0j;/HdR Kvj6o]nFAVom/Z)(R9TK'ɺ殼i=;c2 9Q}dWwmԒ$]cA;]|YP) 0䱼F_ 51N| h.]/2FHW| E/k98wgN:zJ"/䭴l6ְK0Z[̆uE.2ŁJS}Ѳ*F+C_tA3GMry!j@~HoD0+riL9fn&{Wxby('t}r /5 {@Kp@LbSeHo?;÷ y|h(yBLqIE( JI(\qŘ +.?nZO@K+G? &I *+ݟZR[#6hL+0'{7/WI1T Mabry85[F89b>M^W؋>4b8qj9k&v5jlc=3ey^ˑnjhϳti)#/*K [z2(1,#%~OHf܈Hb"3+H| P'5 \#UPgLbHN}Q%nǡ$w~H/+.~{?yDDWƊ֨q\T1>ΐہ(vv\*o-[eX՝x̿k)Z>x8{>K2fK7\tJm5w+쳼bze)jVyr)<-dDK.M>,s:`a̐$j juu2#͕Px*i+%k3 \P1NF9o*Ϧ i6rakq,"Fg7pd&Y(6s2Q<{c4Mlf#\ (T 򹣅2$?Ef`)ş/O'ai^SĆ ^*v2 "sRW(ľ:rfav{nñw?%KKH HS@QSqrꨨP\@2}Zs\|7,1 W 2u0px' n4,?Jn5 %24'g η,!6k4J)Q }f7q8T-ҬV&wBhw:@et} t,{fa0JuKSR) 8x8uoUs{B@<@eJB_ݸQc d ZUB~Jj =EܴpcuM$Yaj|u 7৐M\HTeb/IܼN'6DzH}5+h!t<"ļoŮ`9s譞uefW`(wmO/=wi?znڹu!snyZaeD,պiP0zpCQS vB?@zP D̋}}_AM;?`LT'Bvާ\A2M )؀qrmLـ4!,'}ݝj E{4҆rCB3>'̓\{.V̝$b&JXYtao㠵kF cdÇ8Jߨ>`)`!L ֖p <ԏЗ8^Oq^[~dO2$rKP N~c0;VZ. by ,;-)בŸc7-N5EDNԯe C \֫gdyVWj0qԎ -Ƅ>crRYi6.v-:qT{/}&8P[۴t9q%a]A;m(Fn AD_${Hy>m{ ]ϱMڢ$}<3)j.pMQ/&b,63VޤQ Kp %m) vw#h-!$(dPB$3ץocpMe]E@Mo:~)!t,47/88=D5O~1^q:ZU`M " \_8q^[k$N⮲h-E~;6DUΟx0}XpP-?F2:e -O>~gml76fdZ)0>Y n}P;\Ž̈j?ɺg{c*F7!Ԇh1ړ' .'Щ~.^TjYN/#p'-`ƸeΨz3#⟨h=,HH-<4e/˥yY߱>^7Xp.0%?jq4[~վu'6Udm{N7rZ.B'\2~>J܆i gQ&Zzbu#`9ۆD.9#oֳ*gayUU -21[I@NdMwh8igY-Վjo_ϸQMuJڃ(RKD%~.PXxA[]AOcFaWOx^N]ϒ~P)0r'z\6OQLjIF[m t&b9x}O},~oRzXcDA{+rܤFk8/īsȹOfhHYzBi6M |lb'A: zG w,7,s{g70LfC{%` s.,jzYFBi}|۾'8Ћe6Tbv\iRz 5vR̘dA+~V[WMXa,}ҺF"ޚfOv^ҝ2{KkND|!Pa× GC>/MW?#HW*bW.MsO2 %LCb_J5lNҼb闟̠2w9׮O!yhzK, Xe@"?f0;!/EŗR%V株W/7EvZ[:}[j|Mc];GZ}87c ήSwq"?02XI W 7_>p e++1s|S5c˛,RIf탨s 7t/ҖӠ~BRR{G}tl*MߺY˪ƛn\aůl .zσ܍kQO}4%KM(2Dp`YD=)14ܾ>>u3܀">FCݘm\1{̒Y:'oGI#ErQhD[.RAyGJ8a.v{~6KḮ_+p{{*IW[ĕfR 6QM/q%R`#+ۥ; bӳj7 Aeȁ-hab($9úDbPe꯮?"hWycQA&K^(Y:SWq~gSXZZyrl{M\.H3ASIba5:2Cg][I昵E qhP;oVjh2ŝ2~ؖ[:poU›Vr U j 8}Ya]o8\AyoIk12GgO QߦB1'LfPHR^`-kV 8ӫ+'2AҙO8Y 9:iK׺~7f &͡+dZ:D&yb8Jnks~8\:\D1l(X8@:;*\dFP§7M%NvYv)n iddMpt-_#r.*ߙLқ{*7gz^8%{DZ!eXWTF6a[?"'Ε(@6ŞFӬ:G$ᒒ\?1;t٣1t4Z%(^ /\ߤw4FlFBN%倝ikXWoM4ke!,[~rISssH#PRe&hFJmliA4c[0A#Ǭ'_>%! []IJ;>ƾY^!*{g=s8ϺM8g2[s 3TV 1xUJ;1ZnBH-biɖ#6_ۑoWòeHh3{|.k?[Сwi_(wxX)G{d[@ĝSc ^?uba0-ӫcuӜAKY2K`ށU77^I%B[keUO\p"N?R̕N=Guy`Ƀ15(l?C)Ysp9L/pf7,1o]@wZ@אҬ"'"(?'Bdg:[+wxpxu?|M5>g-Fcwԓ%]XZvF=y++y e,OKFy8h~Mhj&lЂᰑ PT)o1dӧUϹ!zm[?Ń1D$iav6Hצ&nN35W ebRN١t؀n؈u-\9=k?4aIc.Q z\!2mVрw lzs5vux™M8 pNd}ـVp`ۧgJ<9 2:b˅Rhp\RiVURN|$3|ݴF DFR6x+Ȗ ?4z +mDpG)B]-m'b<!5uG$Og%,#!wtE.)Y<] tY ;9x*G$i4k 6ey1r [UK@#&-gzID;6&&Fmg>},J /LŃj!2_/*%7s*w3 zxS]aDŽ@qq4ѵ])d$, !jq1Gb7ۚJ *wPj.yGjaۻY s/mh*JL96lf9:{}{ }&4$#ǣU*TrƲDe2M9Z;!_ZLV_JR:Ă.;~qs>^SvxͶ9LJ,!x_=Yľ`^`df0zncBaԻ#_uRVm}s8*DpɰlMDnt;[$m Wi4ghc^?"W~T*FYFmʹZ{IN>HgXJSt) u6]Vzk u1'3J̀о 4boxh=ߵzNeIR > endobj 56 0 obj << /Length1 1466 /Length2 6544 /Length3 0 /Length 7541 /Filter /FlateDecode >> stream xڍxTS6ҤJׄ{hB$t*Mt頀(U@ EAz/"ʍ~~Zgy白p(9"HZ$X PD&0пq"s DHC Fc0U0CC"pHIHa Po"K 9HEġ91} @RRJP/.Pw̎0`huA=|}}(A<?vCQP/#W};OiDS/ 0"Po# ` 0""E9Hp!~;!C8`p(@]W`8 ap;u0@]T> F `_5 9f5 @~ B0/n/" Go!39C1@ .B60615z =N20'((^4sEa4 C;:: bueQ#7wL--Uu/2( ,@ 8@BB 8`؟(vdpxJqlLfok͕j1sP[dFN=];5߹Ȋ}=dum/LoS-؏`ϕZ?mn"QTڬ)ɹگPXbg*Il%Q8ߧےDUn?S7x ;Y_ɦ(8( pY] ~}8j~>}d?` KI~%vœWM]eǓ8b\k֩!sOQjv-\Д⃩&V>C)rRJ ʅ7˥K,P5K$[emב0NA=2}.mhi7jKj2Hbf@YeN  %1Q%*y<.<rqj"Z+Z?j8:aDZ$=9) Wc(񳐥[%dWM OFp+ѥf"wEjG?W[n=o@jh&wڽڐ$gwҎKZOsf_ѥ6v`QwR|,/Nra(-Y&dqFF9ߩ>+0AxcۆWoTGET N>fպrM?S2Y]dx+r߭D+e470hW`Ⱥz9'DxiT|Eu|q'JU9ɂOk^Bw}:eU٪5gN1VI-5Ru!'R%pMTҺ0Ů˦,u p㆜D}Ob 323Ԫw A1<$>i/y8f]}YàPq7K3"*!cg !> l.fez ˩3>h AU Tb1#XzI(QitDOdI5Pbjc!aqeq3ʓq[ UkEYY+;3QN\*'+v/^(@X$S \7tbD hV)ΘR??"-na% ıg;|5:5ungɱ $<=q32Pʊ-O6zo({`n~&ÄP&q+$HI8K\YbeJ<+nyވ@Hp`DbT#lbpaat`%~E8֡ [Q>ò~1Mz@D"tKa{]Ot!O6+3~W/d1g58'|x%~F^VW,?cFTW}PqM 6 _֭c-W-y;ݝ*qYbhi"~+%88z1~#-Ú{W EcO 'cH9]͒:OOy2{}XX {^@x#iXYڤ|QS%5.%wUs7}F곲[n =Kc³@l{mXd ۽ QzV瑅yA>wn=H*.`MSk<~r'E3f]C+MhvԜJö&x0q~AM#P6u|_f-Z8jDUWݾw @J(K=@)w]Oz]!}Iݞ{A-7XEȾ-=\6( ,GWԿ]mVZKkyӁw֍j(2 C1?4mx V$:vbGӱ\hx$al =@ٟa U= ۷cN6%J]Mz6,{sVO>I>}ݚ}C*fۺibP/Akr_f2$3~iGH}3J?VAB~ >P/=Z9pUC{8"aMiqUT`$tA_ ϫ&vcb@Jy8ά1ϐXS7] )y>*[_2"irϗ "}3GNA[Uջ8O!UE`m ;wFSt/[f-EZgSwcS3GU{Q[Un1`q!UL1$[øg)sS~=[wdQ {$G**H&WJq ^0o wNyqp6v~ڴ='+iAwtT{xVVúH%Y բYePV]ob摻Nfq;aWAr٘3bA=x[l/e,Sy=BkV Q K|&N9̨i|2D"-^82 ,@.a 1B]H CBf= u+avG;J!"e+F],؏ԊZi\(}oؑ8OuՋ)gm)W^|9v4Lvgh#~Ktq腡{LOˬ?LX=+\1dgL0eֻW:G urt8޸;Q)'k,ʭ87(;ܡأϩ$3yKַ/CpRkIsͭij߇f\ei]DI;0:V{aO yE٣'u_. tF': *3##cnԛVZIp_d짩77 4^<]dv6i6F ZMdӓ=eW/:wlΠq?pC]-{_9lPCgХ~u3֐NL )M&TFZU {QSY 4c}1!Y8|P}a7" [[B$/|gy4Dg"0WojQDCbBޱ7i z* ;I3oZ܌TB[fI(h%PjZ Esff""En2)b BBr5Qa*8lI:}J^upOg tðw# S9%h23ogW״: 0>c 7 \v[5*7543GMe_ZXi '\ԲP~|J)ЍNM313 [|2st+)xy\JKF-kV.uT~t*nn-t* b+k8=H!*ҍs)~lug)&F3.Gf},jѠST oD3_V]bu-zȾK٭{t'\L,N$զzU{>$WW= e0[2\UƱ,ĎٮO|s)sR`9 㦁ڟV [#4eAGJf`R8J!bwkL!3x6P86'f KUxqGhiioGd{vT/MR+9m1}=^|BޥbO&)YƩV[f9P5w`CmO3itI`#Fpw#ٟ.&s0bB>sRQaScq7a{8!9'kp pze2z<&vǡ$ ؜84Nh⵮{U ukCk3c͞.7ƚlt^ ntXe׷NmZ f.%Uz=9X~kYG;n1qX^`J^ְYO[H5τ"8WgvXMGd+턮NsW>yzqPN[?gْkI F'x4}g'"_r鏗lKQl"~*xaTќܳR -mӮ r Z-Cy9,ap-N싙QAZ Gm՜EͰ Vv-vp~%O5Aj92" w>p̞>xi;6c{E]|vZk g endstream endobj 57 0 obj << /Type /FontDescriptor /FontName /TXXDJK+CMSY10 /Flags 4 /FontBBox [-29 -960 1116 775] /Ascent 750 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 40 /XHeight 431 /CharSet (/braceleft/braceright/element/minus/similar) /FontFile 56 0 R >> endobj 58 0 obj << /Length1 1374 /Length2 5974 /Length3 0 /Length 6920 /Filter /FlateDecode >> stream xڍtT.(ࠀ0 -) C0t7RJH HJHw *8޵]7߻w}U[WaUBQ >~q(__]r @0\P0 S8  @" Qq~~?Hqf !PW"vyfkBoW' zPr 0v! 0(v(8vrC m<`(;.tZ~ ;ALGз!lP`$8 P+ n EЛTZP߳@[] @N` n 9BZJ|(On vtE`# 9$;+ sFE>eE< GOBsp53 UU AEDPbE  'qF8lC@`6P+ @!ݠ~>;AP+- Nvtjg|$`ʏ7spG/PGYϟCx|xAއ HF jU6?ݢ__spɥ@ ![Ko 7;;N0GhPhh 67ǴPkgUQ`dh1aJ0O6 #?'C_t?8h]NA羊pE`$Eď065@>8.g D :ByW7$Zv4 N# ա*e=x7FVZD 8f^ة+O=.JT>>}mӬ#3h1Y%س&w̛;pb`MyF~|)?D;nlu2yp~%cMfDfaE(nO~bE.c/L3{{RO_?)VcJ죧NTw*_)c۩z M(bEb&"n65 pK{.5r9!;^E 'ϔk7fGlYQz}tC9F.*4:❛`wt +ͫW,@c?}4NAA'hs&]do 3hZ@i0>銆啊iPH rj9{ĪNy[@ѐz+Jef_>*12VG%!#E6Zuc|7*bVQu> \{42F*K2ܫN }j*nvYgy@TP7zi~ޛNnYźCdLIZ΋|c)R<ϗZHn0pƦ?E>x{D=d$b4SC\N^l}ٜ]%JT#/.H')0#$D %9pu͚hb$=u_ Y],|g&2E^jP6% ֧rz6(cN;XKRXy%ęCڷn|G[.ob%q9x1E$%iw/W)ϕPp{6fq0ȍx5F0\+ /ۯ[M]،ﰿd-M[2Os'^fjV;ADp7:QF6e;#T#PhހZl6)koObM'\SAkNN4U@lL_`&O |E]0ެٛ'ng6z(x_r%iӉ0NlDσFUpvle=Srv(XMXxAZ˃'&] j[tdsUL?⏭L~=7o_TTe(y@jDFLloq;,Y;V=OCd>S4 F0~J>}+q\ogqHL6)Wf%OP9&ᐃ|crqOd}HmR3.IӤB}`|:󭝺o2&K&_ncL/P :}ǵ* Hݎ.+tIPlnS.|gv*NK_]H9ӄ ?ٰ@ʸ,g{&Sk.w|-WR(؈q&Vgghzz~O]KXʵF/oW$]LP3ã'qxtn"VIՍ+w+HۖSYͣS?`.ORn rں])"+Ӕ[p%efTK5 ׂ_!u2澽4')3_hroSD=c`Sh%dk$m3v|tpP6q \6[9~m =+C#W*RiC꺀pvH M6Cs`ºSOӥh @ :޳BYd<::ؾqMoUiVK>F,fr]zg̎U)<!?iZh]4wS}'4p( o(ߦxAC"y&&cMꗃD] 1}@ӑs$ 9ާ v'Lݚ$/(WISXnvIm5G~j 4gڲ H&uˬHfjyajxiӻV0"M$U,JVƒZٹ'O U6|͈3YX}$iUM݈(I]ힾτps2ռT$婀V )} ]wKK1k#cq_G`ZIfx|^~`DSV^zzv+yՉe&^IF\]ڷ7qX_Y$V.rN/n~zX=|ׄuӜglrʠBNVXh {| ]kSV]U^cGJؿt9_pQ";­\i8Rxu5,,@s#֥wa!3C+ܗ(z׃aS|I6F]ȲO\s' :в[1L2Z A}^J7ǚSB#=G; uYi}_NX*S1a9>;jߡ+TF&,zVgu\]8y~dnVG,:F" a͡9kRUЏ;s}mۥӢc1s]k OkYb~\p4^=/3%]ưAEnDzٹό `OwfJ]>ʊ*oD8m5&fh x+]ZPVFuYFD7cghiH'V*%@9Ƨ#uL %{k:ZbÎ 7R2xs) 2ܾb\~aVQ{uĞjcF^Ìsc }ԵBbb%@LioȘ/84Xg3bѨ| Y0h-3wHԈJT'BU1,(x:'=ihl]C^S1֬Q>Nd&;iy}\ ɼ5(<[WFT["yCg;]hBKY)o0) Nwj0JqwzK6Y3do7P.'i ߥ<'S';U 枽] oz: i*<qΡgtCO$,4l)ʼn )^U#'$d_ ϶QjkT?va \X;g^d"2fht 8켊~z.sݩ`󐞬OC:?/(3&Ȫ7 {<@KE<"^-#Ma#!9 xJAj)EߞnPn˓{0 ^ :+H}jڣ v7՘R0W#*+ԡB;ӹ23[cn{er7~~$VbwB?Fhz1FcnqZ?K'~ϊ4HDq-tlLH8ue+m]N~@]ɬQ$ڨWm+)yweуVxמ7w=_ixPQNS&뮴G"frj^WSӠJIu-%m();>uʃsf|=Ț/9Hwh9~Sdc&ݠFK bw> R,ц- w-ݬ 1QRC]lx΃1yAu Walna./8s7bBMe="dEEfN@5TZpwkfthG^31ev<\Ou"&Pr "H[N2mډHN>>~hWSm!MAÒҎX,Ufʾw:i9sAE<ʲm\Yc%:5Xw)GO@Q 8/MNfNFGz DZܰnzJbչTRNXE#X*!~R&r`R=$L(=C*$POjiK:{vDr_nZ!>~A,ehm9A#?fm;V cPS]Ka*w?&h;i*;>D@#MNkkk?z!w:mG+yeVl\Ee:-bY, G_&2jzvUGJ F#m"صtC^Υ&|!bIpkfm% FжU:(ƍif(Q8#\3ruzZ 3:oNxKŢr=CaSrQඦsd5gE)͢9@ {A/Q)cYM)6i"Þuno endstream endobj 59 0 obj << /Type /FontDescriptor /FontName /QGAUXS+CMSY7 /Flags 4 /FontBBox [-15 -951 1251 782] /Ascent 750 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 49 /XHeight 431 /CharSet (/element) /FontFile 58 0 R >> endobj 60 0 obj << /Length1 2037 /Length2 14165 /Length3 0 /Length 15411 /Filter /FlateDecode >> stream xڍP c@pwww: $w$;+9*սw$SQcڛ\YX,v&6DJJu ?vDJM3ގ q'˛M卨hosXXXXl,,!;$L@"@H)nty;?4fV^^n '@dv @ r4..|L&LNB w%@ rrI(؂- n vC x3؀@vo!v@t@d/¿ 7t+`33{[;Ol(K)0x0LMlML6&oK7H~)>g3'33/ykPdW}`'[=}vvA`;_2v`GWĿ9o&?6 r<,:@/_o{ / pqrzLA`;? w{XƏ?M+f֑V(Fou{9lNvn/]?"e*K)@o.%h> '7w+ߊ\ml7x6.o;h v*`Wu1yQ; 6,U.fƿ b e0rYo# ;{=%c89x"M''m dgxS 0wBJx̒Elf?荩_SjY-0AoqmZ_aA\oCx+,s?"rۻ:#bV!t77oloK'3[۝O1o~VBiǛ6Wx7-!?rѝߞ?o:3X:7E.x7I ۛ ?տq@NJ?3o,-߿e@ ҢU}HQBw)9] ZF%.TTڜu~mIkegF>OF?fpEE|}4 {(]yPU>cݹJ{4 UL-~ܫGzX:OY`iօmf3oT.$[w-~kJ͹_sb[ MwYI̺\Z&!R_|z ,6NK ́9jtǨݥ?+ #F8<6`uOyo! n_m[xwV%).>qPvrAd/pꝠt e~bs6:\Ә#lyjBD E.6"fG_ƕh̞ ǘWbI4ܡKs8'w6ZqQE^qF0h!g#ՙ!f#4VgnXS\$}Aˊ?PX/e*)e#Nac >[osI~^+{HnYVC߁ђA:#GRfvVl[] f ȱOwy9Q}|q;(GɻG%e'= RejqT=5P65,VT/ɭTuB\l{/,CSݒ~I/Ub+HR=_)t8ċؐt2>S҄zAX8-Dt>T$yEǒCƬ1 D#Mj5m1<5 PF䆊w4*~ކ0!v,ue[¼G 2% Rꫭ,E:#l9od[΃cR %zMF ƯE0p1Իv2 ]IqƘk7ہ7e$40:m{7=Ue')NChO{9eߖKiY{!~Z%i<)8,-&^ږ{h,%L[5\uPP4Ř>}h(% xſڄfG"Kd%:4.Vh?DW !aґ n^ef=vsN'm?^je9J( uuy2N|A{bn9֥\8U[?>Y/]cV szl=8$SݾIΗCEiwn+dEtͦk"І=c$sPѦ!VZZO9/*^ &1siS'&w-L{^b1kk&o8^sx 'HCJN€ox#&t7=nVN5N'*![Zf2XcK~W-j"g(.qpcD{JFW{m+Tyuo@rB;%G8(v!0KldQNKQYN쬧1b3 4R5|1EJD10 R$AɯHel Ga\0–j Z킷)9@_ nS./|$h'Y{jX"q?P1mhQyI}:HmfH!xm*7=5guEz:ڙ> 2&[z,v>+0M]t$8”m!Qj= =<$D/`lݒ6Aڊ!>dD9˵(A4!zh6f촂IԻO*{rf$ªv|wCqjL[_}=;]iO*ҝ*lyiL2o2)f*JǿJ˃a0i){˾%`gLw@2V=gkXJyos5@nȗ:.'[Rˬ#1SoGk.pM<$„60u۝6mG|*t]#Q|NxSقc׊53TyW$eR9T#sD+LcƮkz#IJ("B”H^/3󥪭]v+[wԬ/7if4ӣi+2~mU]h^g4=?)c)6ceN|C%:n37ksjE=KOԩ T۽08"Dq.8o=^>bj$ZsݳOy.^`r˭.^܅|mTTMG@vlT}Wґ(oe5^ j4T GIJ^lc; |j3,-Q,GLZı㬹zQ̯3N:ʹdfRym p;c sziISi!m?Wrk soCA'Tb<5[ؼ$}9k-I{| b)z^=}q+՝; HvE8Ho[B *`'u'wt}Q͒΃BG֤\|#w"tΞRك978o(@XJS!", B)k8C)Ul۽?8:^!zƤTHDl1? ;ZۯT$e=\UtUցKʟr ܺOBʰ tE+zҭSQn_Yoڅn]qbjc^OƜ]KԺf&4bawB<ÑC$}+R.o-ܸ1!E%.LSd7&Ҵz @=hTkcS)G)m8q_h^^Jz*KW7<.Hݷ Wk֧)-G;@zR*kz hok6ݮA1%0T9 dTHwoBo-<"jH^ y w9xM'gGS:nqǦYx*P֝%샗%cZ?yԼC@{ #$#\{l#{8+Jp\<{$Z< s?FyQw_ƃWt.kGJmFR6'$-)Dx16$UAkB0/q~.W&<OJG޺gHkpoX<, }ݺңk^yKnw4ZR=s\*'1IX2Bk#p/O4ƄAfCn0qAk1)2Vny.a@ОѣܚV16<վ_a=wiq#%Ŵ- "XՙZ9xk8]uaLބ28E3VJzn9BM^*S>Qtp.W jtqF7dczUz aU,wMч><"g =7SG7kR]eJ[ʆޣ߉ ndC8`A„HfeI 2' PrŔVK|ý TΊX 3:Z!03ngƤR6G;rh V{21 Ε,L-5k-X [rpr@P"k[gt-_b7;@dO\y- s}/c&qv "ђѦ(aT E>г_[gχ7ɐ^2㫟)RDŽTэ6׊[X b.Qe;k"pQb~sUr9`~g*/鱱j!3d%=خm y mMxBS1ո&<|_@C-L#=noN  0j;eE3%Yiw;4F7Mr־K519l&&XX tEZic'q V𡣿یuK`;m:%y=<_J'zٰm嵠Gcgkh8C92 [A i8D <6dcEfil;TC R 5P= egY%&;\F 9<'U<*1 @NŕXEDs56AIJ;W KU~r$#᭶&3Mz;N[Jils#o'KC^Trt[ ȳԌutrqϻpŒ X&0$FZwIU_6_NHU\|l0TfRtK 5%i LN?!dM; *_fRCYusbPrOگFƙ.O[lznRu75AbNPstHµsH$GOh,8yyvo'5r!h7\cH˙]Д['YkmеGٚf1@) 99 JY*UjcL-Dm ! .*f{R#vg`TMKd(༓KHu4nn܄Mvf"lra4RGCM \#/"D}ZRmMzȳֳ9&8CQKflYgۑ}!cE2op͡;qϯDazNڷ]Eg )/+;geݽ})KѵXeᛤ9 KXf-18YxHzaxcy2zG̳/~R=nlpb7 ar4{R@7jU/ ryZ$ ={XJَӖ0@ uk<+jw)K`^oq뜈JWY#\̸u9!ӝar*,\}+G{d]s`B QZFzF]Ť~"SQlQY L~H03vBF7GhE[~$O}6>E0ޮH[l=W{ yETu1KTsst$"N2}jx{/%zOe"09Hs@ _ 7[ܡ2h܄dc9xщ;SKRܒ"X ʘ@/F'Ψceg`(& Lb3qۀ3N`<"K7N&=jخeνyW:4F RM 䔛е+ǫHwᐊq\g7f{-=);qet$ҭz A&bݞbxZUڈ\3&>c-/ :ٯlNLNgm?!bfаuj!,Y܈_g!*rK7GKF-kARMǍ|n=˼OOA^u 1FP 8Qyye'BwG!M&}~Ĵoe._ֱ`.M^<{:Ue EWl|>fp\ PB*|eD_)^:ޟbC+qKv >YCO; ,Hy:Is:e$A8D±٣1 HqAe79!#Bc?K,F~2Ό@Ƒ= ϻ%*ѯ9.ڱoSh׎\S 'igusEC.ruPQ[O!j.B[.us/b_9;ږԤF$-Aw?OH>QRǙֻ0Ė9( N %/<3WP~G :%՗o {Wl%e Cdǽ 3lr[6^+ӵ4yΪEV$Aq;UxnU[+ [dOL17J+M<{s+h6"%G͒c1ϓ3>4_Q}@5]QZ` ,u9Yֱ~:*"_ϭ{~ys__zW~d7WaMo &cZS7 sREnFwViRrHĊvb&s6?ԗY*"ssrkôTIa3"tE~й!U. q͋%!mMׇ]Y)yi\80P}mjj+0 @i^uzDX8aY7j`D̥/ܘæ¤ =ix9?ڞac|n*A qlVwLb>ҳR,5_;*E74Xä5cEv EM^gfu8g@i^B?W'ę"-aZ=jK.;">NO(S6%͒v~Gi:G?CSO 9,8dNXP I2a$T4/?M[Lߕ A1:jxN6~2]1^5w҇y^=/7XnRDGF\N>UCύ\G.gn# */!wzl*͈116mV|=iW]*l&M$EǺ:}:=8dcCN⪇r Qٍ|8X Jrj5+ݷ ]˟ +h7&R.-vZ -m=A)@ olE+^DGQҎ?ViIMk+;["rG^-,b ufq)՚KҼPp:u It x$ ^Fv釃ꏁBt?pJQݏAظ툇}thsnrIҔiO<4e=wR;'[C?ϼ@hS alk`9nYF&Cܛuhgsjg4,;:^q n^~.ΊRV N-VC <Ɣys=] v}^k*.hki6"P#:=fdE<@!AɠʶيioMz`2Z/GzZ\mo*!aKqK&;opxFݕaƸF3"*S}ZVK%W+8 ۚvۚ5TٹK @!`&4bи# i ) wwG}œȐ;VOΑJޔg6_G_ ]DyE> QH?YFC1MG#FI7RDFb45M눂F\ ; [IB^(*8CP&c縢_1{(͐.bL7QuAg!qB&G2}jꂒz2 78 .YtM݉5hhN7^Aǿ冎˛|>zVS^/U|Z9{j1=VA~(gOX! xzHs\Zݛ8lEiB}^g5{Y1/Abm ۵lNQҾՓE! J&#I#<U$Z {Hv# }!$&C{2X&-CmRVDEfŠ &8$tT慎y}ma8/!m^[l5R/F2;Y0HK@EzƷ8WI D OSOI =zA}k 8m;M}V*AS%5dZ!%f`U؉;E5<.{H[d%"OܬH;o.;RLr+O_"݉0^ֲ҄w^$/7r_%"yMv\(XHZG?|4JY~W'RL%Ougm>&RV??M} tmm0bda=\؛!*5vךj ;& LtqNCf!3H} 1Z&Nj]Vb2c`Pl{"y"!⏥)3jb/p=xz wp)e#12BvO*U;Ϳl&ܢUHyuJ屫]΀P6>|83+&)\('w6j O6&MEu% G^I5(ywepm^;hăW=k?i+PdPL}-ϼ_l.gǽ#` 5dQ}L>Nz)FG_S# MbtJZ}ȁ=tI2 yf۱[aJ$Σ ,vbA Yq`U=7 !~%(mu='BŴ1D`Y lfe2l11tX5 {2x*(B(IoܝtKY9Ո?9:֥W^t>x-e՛pGX3d.T~C/j?P#A骘8cKxgteU KGDe1zC#d-g5-QR. Ei6'' > B#Q$t6< =R-fWQK c'X<,s~'&JK؄/MiBQ.)V'h r}ށ`]>bjAzqsㅷg6cC# cE0cY6tOY\} ghOCl.TaPze .'Eĺ( 44ɦwƂ0ujΒ1†RNi  endstream endobj 61 0 obj << /Type /FontDescriptor /FontName /YGTVQB+CMTT10 /Flags 4 /FontBBox [-4 -233 537 696] /Ascent 611 /CapHeight 611 /Descent -222 /ItalicAngle 0 /StemV 69 /XHeight 431 /CharSet (/C/E/H/M/R/S/T/a/b/c/colon/d/e/eight/f/five/four/g/h/hyphen/i/j/k/l/m/n/nine/o/one/p/period/plus/r/s/seven/six/t/three/two/u/v/w/z/zero) /FontFile 60 0 R >> endobj 10 0 obj << /Type /Font /Subtype /Type1 /BaseFont /IXNPPI+CMEX10 /FontDescriptor 39 0 R /FirstChar 80 /LastChar 88 /Widths 31 0 R >> endobj 7 0 obj << /Type /Font /Subtype /Type1 /BaseFont /RDUKTV+CMMI10 /FontDescriptor 41 0 R /FirstChar 15 /LastChar 121 /Widths 34 0 R >> endobj 22 0 obj << /Type /Font /Subtype /Type1 /BaseFont /ADIOYN+CMMI5 /FontDescriptor 43 0 R /FirstChar 72 /LastChar 107 /Widths 26 0 R >> endobj 9 0 obj << /Type /Font /Subtype /Type1 /BaseFont /UHPUZB+CMMI7 /FontDescriptor 45 0 R /FirstChar 69 /LastChar 115 /Widths 32 0 R >> endobj 6 0 obj << /Type /Font /Subtype /Type1 /BaseFont /GCRABF+CMR10 /FontDescriptor 47 0 R /FirstChar 12 /LastChar 127 /Widths 35 0 R >> endobj 5 0 obj << /Type /Font /Subtype /Type1 /BaseFont /HCOSKL+CMR12 /FontDescriptor 49 0 R /FirstChar 44 /LastChar 121 /Widths 36 0 R >> endobj 4 0 obj << /Type /Font /Subtype /Type1 /BaseFont /OORDWG+CMR17 /FontDescriptor 51 0 R /FirstChar 45 /LastChar 122 /Widths 37 0 R >> endobj 11 0 obj << /Type /Font /Subtype /Type1 /BaseFont /EVFLBD+CMR7 /FontDescriptor 53 0 R /FirstChar 49 /LastChar 61 /Widths 30 0 R >> endobj 18 0 obj << /Type /Font /Subtype /Type1 /BaseFont /QNWTNV+CMSLTT10 /FontDescriptor 55 0 R /FirstChar 34 /LastChar 125 /Widths 27 0 R >> endobj 8 0 obj << /Type /Font /Subtype /Type1 /BaseFont /TXXDJK+CMSY10 /FontDescriptor 57 0 R /FirstChar 0 /LastChar 103 /Widths 33 0 R >> endobj 12 0 obj << /Type /Font /Subtype /Type1 /BaseFont /QGAUXS+CMSY7 /FontDescriptor 59 0 R /FirstChar 50 /LastChar 50 /Widths 29 0 R >> endobj 17 0 obj << /Type /Font /Subtype /Type1 /BaseFont /YGTVQB+CMTT10 /FontDescriptor 61 0 R /FirstChar 43 /LastChar 122 /Widths 28 0 R >> endobj 13 0 obj << /Type /Pages /Count 4 /Kids [2 0 R 15 0 R 20 0 R 24 0 R] >> endobj 62 0 obj << /Type /Catalog /Pages 13 0 R >> endobj 63 0 obj << /Producer (MiKTeX pdfTeX-1.40.17) /Creator (TeX) /CreationDate (D:20210112140102+01'00') /ModDate (D:20210112140102+01'00') /Trapped /False /PTEX.Fullbanner (This is MiKTeX-pdfTeX 2.9.6100 (1.40.17)) >> endobj xref 0 64 0000000000 65535 f 0000002865 00000 n 0000002753 00000 n 0000000015 00000 n 0000146456 00000 n 0000146317 00000 n 0000146178 00000 n 0000145759 00000 n 0000146876 00000 n 0000146039 00000 n 0000145619 00000 n 0000146595 00000 n 0000147015 00000 n 0000147295 00000 n 0000004783 00000 n 0000004668 00000 n 0000003021 00000 n 0000147154 00000 n 0000146733 00000 n 0000006164 00000 n 0000006049 00000 n 0000004908 00000 n 0000145899 00000 n 0000006896 00000 n 0000006781 00000 n 0000006278 00000 n 0000006988 00000 n 0000007225 00000 n 0000007611 00000 n 0000007949 00000 n 0000007973 00000 n 0000008067 00000 n 0000008141 00000 n 0000008442 00000 n 0000009041 00000 n 0000009651 00000 n 0000010288 00000 n 0000010717 00000 n 0000011199 00000 n 0000018399 00000 n 0000018644 00000 n 0000029349 00000 n 0000029626 00000 n 0000038277 00000 n 0000038505 00000 n 0000048716 00000 n 0000048958 00000 n 0000069773 00000 n 0000070233 00000 n 0000078785 00000 n 0000079030 00000 n 0000089909 00000 n 0000090170 00000 n 0000097273 00000 n 0000097497 00000 n 0000114071 00000 n 0000114554 00000 n 0000122214 00000 n 0000122475 00000 n 0000129514 00000 n 0000129739 00000 n 0000145270 00000 n 0000147374 00000 n 0000147425 00000 n trailer << /Size 64 /Root 62 0 R /Info 63 0 R /ID [ ] >> startxref 147647 %%EOF sampling/inst/doc/UPexamples.pdf0000644000176200001440000023005313777316641016406 0ustar liggesusers%PDF-1.5 % 3 0 obj << /Length 976 /Filter /FlateDecode >> stream xVKs0WV3%[w&=$mfK;990__C~ɐڃXIo}h/'g tГBd(p((r&sν]5mƪ|ciM7=w+ ;ږ430.&fp-bG/VJB1t2@ѸC\U'+>o!Hȉ8hQ ~(=%%|%@%q4oN=jق:H, >cD] qsf|GQC0 S=UK$@ߔĩ^gAj|`Ґ5Fpg'ZSP,c~dblRXӖyEy]- o,.sֵ]Y_kņ#aM>y5';f[-6c'MMjN\!G:VnZg04ew0Tn@1y8gӘ4۫tmw1W$c+VخƩY/fgY7{6 )]Zv!r8&!M8hn4c{MoS@*Z`}6>6 ΨP&b? O6EPp~cIAC?lS-SsDDꊲvֈ!S&_ykSZtиUm7xa궦xrBΰْ#h]&k\1+{J'P#bŁ2A{gٷ> endstream endobj 2 0 obj << /Type /Page /Contents 3 0 R /Resources 1 0 R /MediaBox [0 0 595.276 841.89] /Parent 8 0 R >> endobj 1 0 obj << /Font << /F34 4 0 R /F19 5 0 R /F8 6 0 R /F43 7 0 R >> /ProcSet [ /PDF /Text ] >> endobj 11 0 obj << /Length 1665 /Filter /FlateDecode >> stream xXIoFW@jpS 1TAqD˂ER}p%{ov}'T4ߌƲJ qc=?fBl\/ 54t`3Ow?à .,gV;8'KD*S :wbg(uyuuʔ|{,Ci·]ZwG>QqRd1)V -6<b)@:GP ;Ն|fŲLA"Bd)9-(Y~K6m$VCf#vEo J(i7cyY˴q}hx-@q{t\əhV6n,Pr%ɮt#[^4GTU#rMaV)Xxf;];r)G~Z :ʳi$,(v{9It~< VhtUW[/Y!hvG]&A$x ]qk!B|TF-1-(FѾzc^؆L|}٬Kq:GީyJw﵎ |QM0gxMˊg&Yjd_ &d - Ȅl6'xײN3xq&`%5'`>].[]ϗLf ȃvkH&lnʭhM:ši*h|82JGT(.7,e3~=]_^z%>'i;C#ް`kW VLh!nԓR%=vH Ld\+:n˖HFl.I`." .gTm12JQ.2~~"ݸ &R[afQtT,% k;`_VJYԑMuYC]ԁBJ 4SPERLS;p -&go}s3^SHWK4QFMYE$٪DPD ou!]Yлd\q;' "()Iku<)s-{ϳ U]@0s?[vHt)nk^YY*&`W b8x.Y$Gm fcIс`}'Tߍ/ Ց F6KD95r:7'.>]`Sӝ8D*!r!>öD83s\aVg FtŵB^Pn$݄p]Q~8@qhABGWH]$B/SHč T p_T 3/xv.|h쫎|87 z׮4&i*6uePvr_'aĝF04\4Tyr +.z7'pJF endstream endobj 10 0 obj << /Type /Page /Contents 11 0 R /Resources 9 0 R /MediaBox [0 0 595.276 841.89] /Parent 8 0 R >> endobj 9 0 obj << /Font << /F43 7 0 R /F8 6 0 R /F45 12 0 R /F11 13 0 R >> /ProcSet [ /PDF /Text ] >> endobj 17 0 obj << /Length 742 /Filter /FlateDecode >> stream xWMo@+,ԃ \6J{*= cdRw?Aa^۷3uܸoZ8шek]7hXmv JBOPfimBsFT2{^SX]Ee}FbP9И@ E\:c8^Gӕz!X4mU鄍6W ˗2Owfo}GD$ .bK'"N\M ߱(a%sɨ\1cA(M_q۔R^8[N$4;Gr h̶B#2?4 WbɯC1Xm&;yp&eqf5F+/GY)ǽhHbԅBk*"SuS8r *,{!_ȗ"dwGD5S8p/.Y<+l.s#wgt/s:uPJ@;4&r=.TѦ:eB8TNSU3)-j^#%A|;:kל-5rM]\BbTm}T}ů9KU4Co2C JѤ2QZi/&`,Kɩ$kIJ  endstream endobj 16 0 obj << /Type /Page /Contents 17 0 R /Resources 15 0 R /MediaBox [0 0 595.276 841.89] /Parent 8 0 R >> endobj 15 0 obj << /Font << /F43 7 0 R /F8 6 0 R >> /ProcSet [ /PDF /Text ] >> endobj 20 0 obj << /Length 114 /Filter /FlateDecode >> stream xMM @+ݱ޶I'l'IQiy B@B,&,k_R[r{.j2:8uciTєcX\x endstream endobj 19 0 obj << /Type /Page /Contents 20 0 R /Resources 18 0 R /MediaBox [0 0 595.276 841.89] /Parent 8 0 R >> endobj 14 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (./UPexamples-up5.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 21 0 R /BBox [0 0 468 504] /Resources << /ProcSet [ /PDF /Text ] /Font << /F2 22 0 R>> /ExtGState << >>/ColorSpace << /sRGB 23 0 R >>>> /Length 1266 /Filter /FlateDecode >> stream xXn7W(!0q!eDƬdkק] k^$tYCx|~3_جKDc07s7a78[C1˟wC)6Ə +xRfzOY~Pq }}mfk'҉XȃPKUS 2a(?54 lCb"]Lₑpp=mt]ΣޘmO?VX7C)hŜ'Y_ ta T0Ȍ( 8өx>} 6N 6>ȓlt du=.)(&Ef̊L3ZGF[#*d]PHMp4c FWY2$/fH_0)2cVd`bzJbHVާF-LW̙ZƤ(( 8ϩx&>yC Iq-X3*0ggVNxkDE1X]A b F˓KEա-b3+B]`r"3L{?Z[j|t ^7԰Eg8ǥj\"uq94.p j}sfy7^Ee6^ęW@E Ylŗl>?nG|_EXߞ$v_"ab..+?{N=0 Ho93E|~HD(po_(B[biB֝l9َ/0=] i n֟|a)*>6!IXfC[GT3X_E89.bvc#@[U!n~%<+Ǣ1+& ͪqZ5iyйU<lE#X jȬ%D!%l^' dg!/ endstream endobj 21 0 obj << /CreationDate (D:20210112140119) /ModDate (D:20210112140119) /Title (R Graphics Output) /Producer (R 4.0.3) /Creator (R) >> endobj 22 0 obj << /Type /Font /Subtype /Type1 /Name /F2 /BaseFont /Helvetica /Encoding 24 0 R >> endobj 23 0 obj [/ICCBased 25 0 R] endobj 24 0 obj << /Type /Encoding /BaseEncoding /WinAnsiEncoding /Differences [ 45/minus] >> endobj 25 0 obj << /Alternate /DeviceRGB /N 3 /Length 2596 /Filter /FlateDecode >> stream xwTSϽ7PkhRH H.*1 J"6DTpDQ2(C"QDqpId߼y͛~kg}ֺLX Xňg` lpBF|،l *?Y"1P\8=W%Oɘ4M0J"Y2Vs,[|e92<se'9`2&ctI@o|N6(.sSdl-c(2-yH_/XZ.$&\SM07#1ؙYrfYym";8980m-m(]v^DW~ emi]P`/u}q|^R,g+\Kk)/C_|Rax8t1C^7nfzDp 柇u$/ED˦L L[B@ٹЖX!@~(* {d+} G͋љς}WL$cGD2QZ4 E@@A(q`1D `'u46ptc48.`R0) @Rt CXCP%CBH@Rf[(t CQhz#0 Zl`O828.p|O×X ?:0FBx$ !i@ڐH[EE1PL ⢖V6QP>U(j MFkt,:.FW8c1L&ӎ9ƌaX: rbl1 {{{;}#tp8_\8"Ey.,X%%Gщ1-9ҀKl.oo/O$&'=JvMޞxǥ{=Vs\x ‰N柜>ucKz=s/ol|ϝ?y ^d]ps~:;/;]7|WpQoH!ɻVsnYs}ҽ~4] =>=:`;cܱ'?e~!ańD#G&}'/?^xI֓?+\wx20;5\ӯ_etWf^Qs-mw3+?~O~ endstream endobj 18 0 obj << /Font << /F8 6 0 R >> /XObject << /Im1 14 0 R >> /ProcSet [ /PDF /Text ] >> endobj 26 0 obj [570] endobj 27 0 obj << /Length 149 /Filter /FlateDecode >> stream x3135R0P0Bc3csCB.c46K$r9yr+p{E=}JJS ]  b<]00 @0?`d=0s@f d'n.WO@.sud endstream endobj 12 0 obj << /Type /Font /Subtype /Type3 /Name /F45 /FontMatrix [0.01204 0 0 0.01204 0 0] /FontBBox [ 5 5 36 37 ] /Resources << /ProcSet [ /PDF /ImageB ] >> /FirstChar 136 /LastChar 136 /Widths 28 0 R /Encoding 29 0 R /CharProcs 30 0 R >> endobj 28 0 obj [41.52 ] endobj 29 0 obj << /Type /Encoding /Differences [136/a136] >> endobj 30 0 obj << /a136 27 0 R >> endobj 31 0 obj [525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525] endobj 32 0 obj [583.3 555.6 555.6 833.3 833.3 277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8 277.8 277.8 500 833.3 500 833.3 777.8 277.8 388.9 388.9 500 777.8 277.8 333.3 277.8 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4] endobj 33 0 obj [272 326.4 272 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 272 761.6 462.4 462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 611.8 897.2 734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 489.6 272 489.6 272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 272 816 544 489.6 544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8] endobj 34 0 obj [693.3 693.3 954.5 693.3 693.3 563.1 249.6 458.6 249.6 458.6 249.6 249.6 458.6 510.9 406.4 510.9 406.4 275.8 458.6 510.9 249.6 275.8 484.7 249.6 772.1 510.9 458.6 510.9 484.7 354.1 359.4 354.1 510.9 484.7 667.6 484.7 484.7] endobj 35 0 obj << /Length1 1394 /Length2 6009 /Length3 0 /Length 6960 /Filter /FlateDecode >> stream xڍwX}? i7FtwHH6Jw) " ")!t3yv]9=~zTD"41hX$ T30 ($5CP^ ĠeC@$:@`@{( Xߐ Ϳ,P⎄ D4U`pHG')G ?Ly/w+A@ JAG~y'++&! qŋbp@$ h#p8g@C+Ok^`q x@p IBh<Iف:@#, s9@(_x Dr`W,D;(HS_IB@ !C!HJ*T1BH!(٣0k@04Y:Kp]ߒ wVtQ!9"@) ) 9L`E2I=zc1X /Ax! wJ0G@(;:Ip-CzA$lH c(XTSПeTUxE$ā"R $)A:3-O᫃vY/ l 1$"f]FGQWwEP_v߀qE HԽG  Z"~V*hGE z$^鉀B`Ni[osPH4!y@e#m̅Vk?eiY>q)i xH'IR@o0iM_1 Գ/P #.GJ˿VD'00ꐖJvAyʍ"Ԅ.I';mn93okk$wE5Wqg8M\j${h%["MNw2WuǻD>-%Y7->4!4A{͖Y x!nda5=@G\O_}'@]o,&K(i$Eb[Ckn3&Q~bBGk4i"Tz;73[T j}\QYR Laz&䄈Cݎ` ^p^)0RuC:Mzt|J7{ kMߜ~qiDmХ\ [g:H3~Ƅ΋?9 5{>@K^w:_D{;vͅýuJfyz1_M<2Fe\ &Md ' f/}C ˓7_Fs8mgXN 9kj2z; |V9ȶe>9oűXҊj% oC+ON̒Q Ql=ԋ)#;) Hհr[5V_0QBW^+wDiZG=;(RdőE}Iki.=G?`Dm9|$hz/>E,Bjw4U"Vw@?KαpfVsz]?~aOyjn uhы9Dwwʊ„Jpp+lىMӆ|lIZ`0Qr=:gֆ4IOU'Ԝc[u@% ͳf&N 8U0uv`U 7``m.Iy?e];WcXru;8ݸ:Nc|3⠔ g=cGF'7~D\gM~+܎YR|]OCeSqIC{K痾Kunّ&ͳ9곙sA3jo muR?Q7NoNj¸k͒0AGqS8t+vQ? ”JJԴ[*c]^(3MCgyq _?д>uUd>3cAQd2eE̥JU2E65Ătb#\!-@YU񈔗1`dk!d=\*|5B^blBׯeٺd\=7|+JZYV-NRH7&PϠQdd:ÜvwҷtM  aR_+Gaz<_Ewq1Gr\WO @UONd}@N>~%6(nkKEq睋+%)Kp唗Fx U꓋E}mTeN̼ bߓ >͉U̒TE]Z5to=*wV+Pkmvja똺5EYl{,֯[HZS*2*;[ -P 'bg[vS/7i] H4|[ysGw4]Xb-;5NŐx۪W]O[[Ãp. h^ !KfOr~vïX5g;>}IV[;w.P_>F":ΧS?`o]:y) GG3OQ }}N R|GIv+앙 R¬2tz.psݠ3_?aO_J_^R}nM" I#W^:bq'sł&T˛ <`6xww]`.`Lв?uـkЍharی:cigq~ c0ߌ_*}+rWLUxɒr6B(xW%"[K4tLSqeFU7^ %D)@V"IP? 4 7rb6y=薦- 1|ƹrvW0w!f6&ϗm 3 f[ M<3~nZhh\Öoy#@ IsB\~NmR䭁1w=oZf|3W$P߸Fe&D|yj΂fD[%OSQ_gjCBd 2xg6{m%+2jv6(==uonq>'UJ=WmX-˶i>VBVØOnm_EPX!c뉇ʇ%'N-yR'a2CX\(Kly`]v4}f.uIBN3(9rՔzEu2rn֞nrڮU*8}{_8txN.&GX)FA۱"W첗Tn޳“) s넻s5Q*1`IJKuH!+Q/z"+,hxTF7X`xfvn^RB]9& ܗ mQu<_8i(G$f }f-~0lZ5Me*`<vث$e"FRu`[XO[cyϻW3kwsgӫh.c3"k%TP1/ÿr:о&G&𫌄.lK\UeJͿ./W\p8^g@~H1L+iO[|G[hqjy+L ӸaM,[t[!=[o% TYx NNky2-?SnS%e=L|]q1bXVVK݂)p{*e2=]8A,<]K1Tm,5 gI `y_lEoY2l19X Vaf mbnGijdnWIL<7fV(:=iE'JS7k^41_k,u;7]{)'ou&_ӆY1zm31\qwņJ't'hUʋ"n2 ~O %Oo.+i\nK6r}:w;A4GVt[Yv*&_ws%uy クϾ%~YzC"!ÌgE`w+,CYR̀ӧz4[7%9e<㠌K < 9+ `!%BKNBYD8,_X5Ok꺢hA@˔+L>GiЊ\ 2UԾѵV#.Y7Kt\|. 얻N鎅R+Fn.;Ը\߭Ӵ!/|c'Ltk4I,In)ʎS3uF+V>q/-,kwӢ6Vk)Y n endstream endobj 36 0 obj << /Type /FontDescriptor /FontName /SFJZUV+CMMI10 /Flags 4 /FontBBox [-32 -250 1048 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 72 /XHeight 431 /CharSet (/pi) /FontFile 35 0 R >> endobj 37 0 obj << /Length1 2244 /Length2 18581 /Length3 0 /Length 19917 /Filter /FlateDecode >> stream xڌP] -wMA7=C %y>};UUƔ1}TI^(argf`ʫ03XX)(,mSh,@<0u9Č@3+ ?v<1#WKS<@tp4p~?j377'ݿ¶@GK#@hjgb t/ j> gg{FF777#[';Gs:@tt*`d 2x rU;3g7#G ]`ci9{LUi9=t{Ed d0%ݝF ӿ l\,m @BX`^s2qwvbpDƿh޻,2Ohvƿ'k syYL*ŞQdɻ `gbbf@w ƿ? w}#acKbk)121ߕf)-c fKowt,$ { 2nXh^?}T%o'ػgd}?% )#~:G?\0W}NN@[!3{? Fg G??ޛ4(n黷?;?{< t;ݱ{}?n@9;`nci4^?\?$f; 'ulS-x4|kMRn{~6HPm_/:##W~ql)C…Tq+^W<:W!\1EP:Co=ƙ;4zL-I kKìjS'9. $A μWYJ{ _1I.] =*KfJbN^2 c'[yGE6( o@3[.3T%7 űsSЯ~_]>}n̟-t#Wy2R+G!:5ҘtK\F!|^E񙷊t{GT7^(tl̠۸q(L(³`7 _R6U0^lTc3{%n/ /fٝ z.d8ӨVog/T&9=h  5=غuhpQ.2ѡ餘.)Qr=gLv&Jj=YFW!-FAU('{潨 V܃_;ɟ=5bj,E2$&߯"jd`=SۤÓ^6zl^tHJmu~W5u7%o3(?X0NETYkrŴosI9V[B$q5Nzuk7|!zbGp{ɹSʠJHZ/9r,`8ts2ЮhHBaMТ`f0R~`(|CBxFAe^q℉O13y<;'5KtX Yb8ߪ޵ov|ccʽamֆ,.׫a~3L9F0ɃMrWcc%w[BAHoiqua>d}Pnr%{5![w8kmcSds%4n-z^_տgϴNTy)/ T5űeN0Kڔ,Ê,M/Y/pQɜDȑT=,L5J6OUI83ѡ|X<ّyJ /Ƶaw2#xt.vU,k.ya32> u#UNq+[-mB;<~wa\M)X;{Q;vNg'ڜY4x;7.TNr@*g:UM`wì=(/)K;an&]E:EPb _Lv!|Ѓ.si @$T+bWt,?Z#y_}?HC=.l0絣@Ncs5łl,(rd+Ԥ9Z[TmbL0Co~zMO %q|b aU9= 3v lNj-hLG(4`./D^5 cW?Yo;yTMW„H;oy>3r!Rd>gM;1Y d˪.m[x MCn ԂHϾM<Ԋ%]yZ :v3v6ȊJ ?&Jp tǴ4pjԔn\_,\Gx p8X֕\'=G bT2A0Z Vf>]o FFBQdPٰk⪜#: 1((+qoСkCmc^ӕdN)qs8qSnW#8.i>(|)>tD"cHs5 a|Em5DpbI.ƯQ͞O%‡)'wH|XTsYpkjP(oTJV*W K>wX<}Ӈqi@Xux ?&.^pr}1-9"MU(,4"LQթ[FKg1FwM5l]7z:# )#K"_7<_ݨ@%+Ѹ|:xt}j(W[lTu.ҺWt͜Fh+v攌u Y_~.X+cTT$ AO9a>I)͔~Rvl&R'z3 wof#PowZO2 M:Ϛ_a,30GW7a=ZF\xE)ana9w%അ,It"u(>o; +@!RR ְ?,c&6`8- [~Z!Mhr`S>!o3{Cc%c U<*-7<;P2߬0+ĩ$b-+;@Ė|VjAw -8ȉ2'iGS{w&?z{`0)'G`3Ұ3ڻeӹx&'O"#0wV4 ]P9 m@_UW#vd/17T >T$6vT$5>}VBvOPӐUX#VJ C\mmuj͒M//eJ-RK`<䎄ga@` e t{ƅ-H񭂵ʨZã}4-f itJ\&zJpG}*3y3$Z/>ϷMڽ1g)FH:Σ`FcI GՍ]%l4#诐/~@Y `O V}!j;[(7.è3]$2NA2lp~elmJTcJ%mt9fZ׉חڴs1{ NJ֐Mg\.+䎗)W.f>&=]/ُ'ty4{ĝ b[nm1?^tx{Nj^6-;  ] 𽡪NHV2?/q1xL>]䣗 "E֎ENuvwA {Y^X?$T玲wC.()6 FP**z@>)=$`乬0lS`p[gOXs/ʿ6Bh;ւs>,õ{N^ƻ4HM`h=z6WTM@<~j4}cbg+-Ȝ5 JS?E+NL8/J@U s~< Ucdq~~p-ֺN4+,ϚzyX,?)MAd8$IfYsIjrjQ@r/gK,:MB.9k*6Z2n\Xپ`&8]σ>Vkgr[p>*`rg!D; zFf |{|Л&pTCLf;U gT1r_mPx "0/tvi&dG}3IDpG*1@$)7得4leAc^wX+ +cefgβ5 lv5d?@uOH)PQaXG}SP T9Z8WxCյ􍯊bCs&YXE2BgUIz BB8ք(u6B 4ѳ{}J&aA{WLzwVb@X*4Izʭ3ϐĐl 'i&F^ XK\v$ GBn~шLJs>g=\cDc9lZԮ`[|p@(jwCoJX<W йt )앛mPň,7m/f=PE`Kӭ7mZHz[&&69Y~@vbw|Ī霬yq%lOXςO{Tn]YS! \Z4wж"zUSg7@}uqf,2u'r@L VdtvgLRmbPJT^aSiQCxz+8ް%Kd,YzUb] I^ޕGs )%.ZS!:!tqyA\rt0,|-{[{7GN- xػMY>Zr;&{<}8T O"j *wvE/ BŸkpejVDx)WFBTi5t1HLjcR"dL$⼱ăP SX;v}b MRʠ]d ]lQJ$}`ޯW'~vI|*'ZS8"hmt^ƒ)h)3&M_ y!] u$7U)v>D/N.-Ӻauu4Fr7vƬ ^H]7TZ7?D'{#xfڦ6Vix,` ) 0ck&<hu"|$hG(te)D M4^u2nKDCSsɒ3+pY&j 7"VxV]|=epfyvqtqs>a?JzWZqVO`yoH\ =OeښYfc̓&v&ފ "莮̖)s({S>]":/f2?)Rr'xz`@bdd4GAQv~SvB]q>5? eK\osH>9:!Tjydj6E`FZ1C U4@mvoA5p)_aaYP3[Mg!}HgTv*UKN1Ġ"x7#|˩ Dauhv=N?e067"A\e?1bުJ'/KP:?PeH=;<s놉Jit]w*Ơ4l7Yb/%^-Apg( XI 5}WK@ff _+f0]3ŠA~3B``OArJjIԔ40w-~y+kC%3egSGڅqYꂗċt3I+]Z=٤ɋ9B66/},{;L*6a~'C6 i`Xfu,0f[#Rq>yڱKs.Oq 1D~m\a* X~K5T 57\4⤠ݦr. e {fif5 >5^J/a˛ sB$j~Dw=vrQX\}<+}~J9[Sm_6}msbq $ϼ&[S_U@A׃^JZBQ|0v/?Z3yϩO{~Yz;;4 kVV܁B6Ӹj"%% 4-bCXN^,ݝS&WsQjHއA!bxBscAV-R+PǟL9^4ppmkzcDDahxθ̲)Y۷Ǘ~BVGW`zBLQ;+t"jvp#8E!ic `ƀ4Tcsxh*˗ -38ZheMH@VNC %F^R:4T^Ng|ڷ6V#,*Q> pxZB]'zRuQ5gYCS٫Cu߽X*3rB1-Pȿ]%+ja6f5V ;l&"anG@\} 3ټ11d6KjUz6OLb Y4'4Ńάoι2!×0>El_CooH`Yʇg^>$Y1Dg䃡$zॶyoLpE~ŗ8! F]R6RICBJOlЀ)쨞oXZ o)vvV?bcnD//@=e#Խgq{636ѥj, oQ0\y5 !h'$794v,k|(<콦f;],@(vJ bUcǘ5<ۯ7,> 50B)yIZF _1|qˇcЙѺS`n[M(V?vJdE$ H¢p‡Ʀ:夢< 1Pȑ=2:XkF9&8W 9-\|m>2!RiK~ۥ0?Nېxˊ_a[gI)PѺ-)wL)kDfT0gS*飮3&o"`2²{kx|ͭEtYq9[ebA/QJ;]b).1_Z W{j{GTt㢪a܂Il65 WNJءAmTw>)Crg3}ܰJY&j\Nx`[: K[@@j8 +4XR' l нh a SG ʔK`ǷhfrNI3m./4Klo-D50KQO+,ۊ'k.-ZdnPf:n!+YMa]-T^OUoGSy[`%t>,U\}Y lM\_Zmfh5b6#{ǝBhЯV {T ]WMzH{hQ9pPۆo}C#5/7EԋE?-['+ țp:߄֬aeYH_:Vr%DR>r':_aBŸ֜T:Cq4bZ'I/3>^Nx]4⤥: I?~QEɏx.>d|_R=0mtĶ`GvSҋU(9C\e}~ml%z1+r ^x"ׄx7~xBJs 9eɥbCgcOϛXonR ލQ"+07s2o, <>3J-eAfQx]„n|uv+S@ZA1v '7)xToK}`EVu뱮b]mFU_Nu_QM [p_ b|Rǘ3=ݼO`eLGŸ=ucpc>f$򓡪pEPKyZ0R#oSM2x8iފv1VįMXQ&.؁RNϧj:W+35q;.J [4]ε^hq:@9|eNfy)k4lE !%Q۴BԈL_L΍ _}xe<|;,<aO rw-\澧˛9h.̭D7Jܡx 2Џ|$r JbJ2cb*4mt|Yճ ҭH{X ?|#"X 3Yɱ/ WY%Qsξ#}HJiLz=weE`h]C3Qoggm WW;cC; Com;t~>#LZ`yRcȑ%arr CHN%! w0 @eO_I*Fgz֊a+@%F6307i$`<^f!"ch&nxLӒCGLf[ !AquR356\LJC36/3u`4sWM\xu Z$-9!*`7< >`&C&Cl8LHoϕNeL+˭[?jfQ=\Kܧ"a5y 3OZH28d4;GӔ-ݕN-+VUJi9pf[|!,.gRX Q-gȍcmpPzDLCiY&)A*r#w 1'Oҋ2+ );<<F)<,?*JgTc#c?Y|Ey-5PtbÏ+qjtn3 kik$agg !9| BzJ1&Y=*v؉cPNп՛:5TʎxB!5TF~%a``Kð#;~L#A}P0%oq/ {3i(3_X]'āո?{u _M$Eǝd/x==41{VBm}v!rN{_kD['9N^\ )UrdLMmd: Vjwp>V-A?*A J +ҙJ%MtWzfҹ@1_QȲmJO|\\ls-bYi¤yweF=I ;i#Yח[qnd{o•Dzu(XRdLγngaY޻f,:":9/@bL5|Aڲ@D/G\6vG[o+z:[b GM0q|kIz La0W'1ZEݫ z}g-ASqP , ̙+9ry[}?4܋j5x!.=HIN0"z["뽔P=muQx>؆kpn6pV%&iH *=ytIzN"Φ7,0_yh0RtNqꑯ)x+&Ur,CZ 8\>/bqU}SҞƀ@6̉g苄dPk$HO]uB]ӣ`㺅Bb[ó6NuRC$Δ|n {nf<ȗ6Χ) N/iL_C#}{e839Ĥ &u Oδmo3=9_` g#S*f4-_||i#4QdŒ?ҳ~_0+<Y[1ٜg{V']Ky٣YU,#Ӭ~HZzfkYX&>+(_I>֢}R,7?)חymdyۍ1Z Zn']}?@'b9I⍋oCjgl/o:@鯶1򟿽4ljl0ǧ$PS$~o.n G"wT2bO2XaUj M27UNRq׊D OT.:vߒ/ٮ 7N0ad=7-x)ᣡSvo[~pj0^Is Iw jw ~@MJͣ1[ 7qJ ~dH7wbT ٪鞓~ʤ^Z/<7lp #0 geDOmbfڢ- _'X2Ri"B0.1e ]dd< Pe u ٖ)h^ĈXͩ7I+z㻖6Ꟍ1Ni9SǙxݱJL-Fſ{t#YdX7P_uvq4,ᵈ{Q_mR9v u\)f*lA* 0B.~#Mm Y7ֻٿҋ3_8zAua E [O4Ym7Va5l g:%Bds(rK4<]bPb5.^vDހsO8-9$ܲh8q Sh?bWgUaXɂNHt:eflhh囅o1SEe#,C$2!߽=(ڃyn*AyV]J4ؘ>xBSX5Zc?߂92ܯ*EǯhkAu^C20"_rQY q=9$r pQ{nWᲘ##cO7Cge˄EE-IY{ZU+S˅1|/}@?; VEu(‚MsoÓr>TcXA655@mѲf[q|bpGU?&Y9aQ-̘^`,K\3fX8vP%%iw:/Hc N9Y5}m$$4b`f6رkIa pv|rgwh2HှV/I^v;gaF„?$B+}WmoH$78{\\6B%n 2e KlW]Fu3VxWwq[6zN`9Î7(̰z)@oV"ן`=ƲOd'ZWvyФrV6BzW%PfF@}%[ Y,4 ojiSq'0(;x'X3g|W8a3{5Tw JNd@uR ~%afn A )0OW]&YeTYkQz4AƓ{ur"=ݼ/&sԼo{I5865'>y-bZMXG&д_ȩzS$g[\W J,(@HٶEWb@-x"8![MRq:#xJZeoLg/axNJ#P>S7 pPƢ<^R>P̈X>p[͡ݒzܭҩ#b*kE&t0U͔caM$@B lN6m&OS :<9隱I" 90ba2CJCjn6ViNFW=w&TѸRߨ^&pY qS[D6 Va~|O4-VL&d%|*tpB<=kpm~f5MLN[V|Q2- 8m_) 0PufzM~3"TE4GrSTD?w#Q\&y+:TuguݍkV5w%e+& 췔 +.Ad “[%k3s"{ZMWrJZŘ3򄶻޽5sO K+>sgCSնR|\ċh`a*ғH850 eo.*^yG'+>IۼUvD6Tk$ksP Xx*]eI P*BFU/` oC'\bG/Qo Bvљ.8. c3@.Q;P:k?KO[֠Lm@= rFQEF֔qRBe "WD6gyE|u- :/1krϚ#_&eZl+v(N5Y::xwѭ xƢ&q@W#&Ij%F߀d ~'ŕ7EF0+_DKL]O"w<76O50C4prط- }\,e [1gmUG|(,ddvSDՎ> n5ΐD<&?z}*@H}tf6cfGcgZ\&__$vBM#Pd2nxq_})V ?mSNmͥZl\-=Sɭ\;XK{i:So6l;G9ضCG|e [LQiB^cU3|9䷛)h x䛅%,h|͉y5{8PnKvyQ D!HGS&˓lXL[8 ݍ#~\; "#u7Z7-~לj5"N shvgc\m[dTq;Vr[>GEǬW'țW= (6~AģmSX՝=1U'y]+@3JkR'=[m) Z7pt7֨ҏⰉhD?#ٷ:DKe*ŝÑc?6$d"&hcݫP WOֱW1׷yy +4nj7}zPd$"I}= 81}5u, endstream endobj 38 0 obj << /Type /FontDescriptor /FontName /QEDFBL+CMR10 /Flags 4 /FontBBox [-40 -250 1009 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle 0 /StemV 69 /XHeight 431 /CharSet (/B/C/D/F/H/I/J/M/N/O/P/S/T/U/W/a/acute/b/c/colon/comma/d/e/f/ff/fi/five/four/g/h/hyphen/i/k/l/m/n/o/one/p/parenleft/parenright/period/q/quoteright/r/s/semicolon/t/three/two/u/v/w/x/y/z/zero) /FontFile 37 0 R >> endobj 39 0 obj << /Length1 1503 /Length2 7424 /Length3 0 /Length 8433 /Filter /FlateDecode >> stream xڍ46ѣ`Dމ^CaØa F^މQCDх$ JOr=k}ߚff{~Y {:JTt@(LnE  HO(._$P<]ĥ$@0(") PyC]6$`WA"NΨc Pr  8@rݞP_)dQ(wiAA$FOjrٙ;!![ {Fx$pC;'>_ _ ; ;0@_ _DqAa [Au%Ct@BQPدpsQS"!cf]_#v]hEusb@ PBJ@΂қC~Bܷ#M@O7BzAE $CP{NO[7OP4 x=!ַ#0WPSEX!)+#~Q@JR !;WBԟN?{u\7߹cKYC+M[ `V^["nTsȟ; CBn@ {POu(6˟~_K!OW/vY/"Cjp׆ @H$ȗx+$a11*! m{G׍J~[RAߖ-vnxA?)_mofA^BAI ? *O 8,"d]»|Mogr/ .IҸksCWߕ޼us{^TGa珀+dNC?+527Q `ݎ٫^%IbPLq3nX6ܩ!7{R6^d7CxM:}}`Y; KHpŌJ+:6:KZFS tm9Uh uغ3!.߶9r 4 6Ӹ2\ѼeU7v{O>>LQ̈Pjﲠo'ș*/ňYA]4|O6);5 7#mhMCbwgFg*[בVJ1T;}6~}O!g4U;rIMkWSBZ۞+;FϜ7\xQ7)E? *ќvΤ14gWw~:1V?ë:&9bW0.AOX@:0C_!"ːX~`A#5`90͝q>pBJ|}^K$ͩ5Xr-8xZy/rXa8ũ raf7T:[L`ף%+Y?xhqix[I=ʏš3 CǑy< iWډFP"N'5.d1vD|MFwQVUٌ1r?q|iNܟ}vuS$rlH@i(yFKYi51Wa웮Q`]v]0HlO Vh.UZnfO)aᚓT[ʁ@3cx^<_[Ig6}~0VZK6*>-c/ r${em6Fv1WHN."XE}nX2ڐ@oZ/>Д6C9#QE/&*x$S8g#2檌&SQBP(W.9̯1fIgNM^tE`dQ2Y2UFP梩$v#y:j] ThLxdl;ͬ \lRX|W~WLuZ5ʗuīIL-i0ZԤ멞 Ɲ6mS0ƳMQ bv! 3&zoQCt{-(`̍Kޤ{ܵn+.<띹=$㉏cL!m?F.(tFSvG&F'q.Y!F xD^TifQ3ŰSS TToD* H•U>iR+%9 ~ /7_ES^dqvG"PI VTX,^Jv7=:oZ=,V3{e;WbFV}\j_YD<$鍎tU)s0_H&t,D29)H |9ԳX|d{0u NӾ\V/Sj(ڬ(d#IЗ;x6>ĥNd+4v,Jr{~0O-jt MEѽKA5Мc7PxQQA/Y߱u^lw}۫wVn쒷)#.JarCMHX2BK=b Y",Fry qCzv ikU)lufGÑ6t@g1HMhfV)~+8Z)892 &RO"+V$6'W+vse*~w9uܲ@K *"qTՇMbjвZA&Dz{NcOр*Wi3v_=pH#vJqQ{;)֬ͥ1C0'7Sjt{10Xq% ̻Wbn]%'{3=Q6EfOS݋T:f 79  5bU9R k)Mɽ+'$<Ȋc^|Vt'PQQ-o3xVS!ro'%w;6$X=U '{T @~`wB(Nش^US(7݌\G5Q3.btM W`MIoּ-ݱ*K~p2;{@/5:Gq8fBU'-o/z\W9NΪՀ|ѝH5xgMN#aP$qGK´ 󍤴 WVFQ".f;tQIJaE /y?䢛j;zzXjAA4z-ܕbEqM=e1J;Zuͧ%|/~md.UVAB=ZsJ", ~;պޫx?Q4FpxĽ#`pbǣR}ȶC\ 4630ɦJg>Vta>R,(nV AIX ~ֵThG5){cAe<&laCW֖ߖH-G1;E#!:}*zJ/hmc\8萦| E$ͽ@YշR2cz+K{YBh`} ~`٢N;*yÄ́Bx*5RD <丑2kaNo0Qd{C\A6P,e@B-:/V, H1kֱY[vP-$4z =3NB[0?tz'.rS{70 {P‰ehlEjXɌuwJ:;쌍uۗ/M=.Iq=F7骠 n*Pב>出#~j|&=Pwt <,,fyl'F_  F)lj+;F}f4zdmu&,dp|E ?0){R+KUI. nFnAu}݁tt_5gNn4(怊7;ٯ)셾U&cg^܁'ntcB*^|h:t8ѻ\Er0Ex$1b YvYx!T½R%-aeDsWĭ`ŏF}7 Vn _%@;>; o9w65I9`6& WPűXOC-:=}b<2pϼpbvNh>yhF?~NM;cn ;Ý^wzޏ~pW*,yXF^VHxԟ?|"T9PIXUL ،g}X'G=I8`R貕.a襌e`Aӓog^Vo\',ֶp b2Q‹8_^X RM;_-Y%ەv3ip }3ԦICr^cgcp2=0H-Cֶ,X Lxuc?%b0W&]s.rBvfΙJf]n6xkj%.2$@~Z?gz|K]Dr(Avȶ7水! XYyQ[͇/YI~uͤv/.4~2A 7*.~6Gy2m_ĝqR(*64cRN4 4ѱHL&+`z&V46zHbKI!FS~*Q Ƴ;k&vWv!CɹJ9lVv&bҹϝ\VR9Q`R)"myBmzٚzAXrRVKF"J¼za61NSHMY酪20nLKWL~Q^l%ՔN&rT۷0l\E֯WX>/PS`+)5x&w]Q1#{wJ0w)7F̛%TL[eZ Q yV5d.CM EGvTd,!_i[ۗLl9)ٔJM] =q,s\kD_n^KvpWw2F'lq bn &,$Xo*{ ;X_@+!xeD'n\B>UʱD##{2JNo) OP(\Y@(,z*| 75|o\?)jƸTǗi7ojnvw'qU}r#DSTK}Cz bww6 '&ALM(':. : j"'Ԍ6}٪Ҕn+n>ŠPW%$LG>I_ʲ5wa6"μy@բ02#cB|@ߥt3Zi;3] qネ]8q|NP>mըL/m fop)bd>C2EBXgB^mh,D *߬}JT)Rxg^VrJI3 c˖lgc-zU`Q#X;jQHm$x!JF)):xтN:>X4EDGsOYiĵ_]CiG? %#`ZJp_)XܻD 3 ReyT{Qf8Hɔt:C{ ș| @lL@^Z^A&+ :K´`^:aB(/f!&+:=Q̳a/e2y?R )=Jӿ+TN.K]4y94?<޽Mcdfed"̬ 6gHntBЮ];e pFߵXbpa"tPL߹:\MS+e.B0 k}8) Z짦}JNRʥ4[2cK[a<\+\"d]{qթ2IX1`zsFkVӷPI un>.pE<+6e2S--flx.m.(m#a-wf3X~!첈/ cUZh)6C'vEmUBm{C]~~}⌁֭(j",Qx nsI/J)^ffhpAjSO=uKKrRϬLWaC2!ƘI6f9}I=͐;UEa)z_ZQRg@qsx.,S [sȈ}]Rc;[,5:ZY ib*u3n:FX%:d[؈#*#Q[ob8Xu4ܧAܻd{Y$?= \#c;xTXҽn&tuGŭæx.獷_Tɦ~Ar~#+ZH9a "^7^>,)۠r% V;C):|VXϝqB'R&t,,Mi:%*v9e#܍nK l~nV! I5aV1н']_\?S>JF,mae [ 2A?N;N4s;j_P7 :[Tcz~o5muEm0dBHVj(ε"zM(_ʦ`Un;`\xlQEC0{!QƊ: ZSOS7ܬwD' ix! endstream endobj 40 0 obj << /Type /FontDescriptor /FontName /HCOSKL+CMR12 /Flags 4 /FontBBox [-34 -251 988 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle 0 /StemV 65 /XHeight 431 /CharSet (/J/a/comma/n/one/r/two/u/y/zero) /FontFile 39 0 R >> endobj 41 0 obj << /Length1 1615 /Length2 9067 /Length3 0 /Length 10112 /Filter /FlateDecode >> stream xڍP\-Jp$Xwwww  4ҍ%w ]C;D䑜sɹWW\cjWbP34H(@ Zb[J rrC!H8L]d.OvJP@`g@  NIS7@ Q%N`+k4Йx~AN`sS@d5\<NŁݝޙd%LpXA '7WeS{_R45.N l8?yB,@N 9E_Lg`caoC~;CL!`lH+x0L! M휡On`;S'ߕO ݞřlE_a,ۃ .Ψ;̟B￁%ba WV-$'ɓy GܚWxMOo%/SPS _%l8|T,.3O'1/tN`k_ eyc|Ye:qqqrx8j ?rK(b>wX'҂tp4afo?$jg[M[Qڃ<6x⬫O[_S_;Vi Vv#YP[EZ Bn3?2}9[zZC-~m;7D$v..7*Z<~s<XBP(/U7xfEcXA@).`=E"CV?S"? ' `u>dJkNNOo? ?yQ!6!b̻cBԻ:ދNHIUANbIzW.D#&3SmC]/!VOB¬)G;Gy\GW^L}2ue#asj_ʦhPeR 0"3{`\\N?1(`{3ZEDEOH w;2I--Y`޻8e=^>p?uAn@͘B7F(cU/"tD=rP=nV{5h'sXlˏ>׳%``ZKN)xte|\=4 ;#zyp0UEdsUx:V3D#T9]T$ I3?/ӑh~JZw3֑/K`?»U;Z:L=/f[gv3%ǖT:gx{xlI޹c=mon郓XBZJҽLw{:1'Luf&k,5-oq,nI`D BH4bsLǖ)eI7^V =HYN~Uު=spCJ#6-7Ꝩe2d3c˴¤דn7~+Y> yQ6\oS cjE1dSILm7}¶o| Ʊ^^G:0s;Fߙ I6qdȆ""p1ijp0P}x;:nVF+S[R{f@v˫S1!F$>,]kOrs"5&𦋕TM׈N^5$_3]9"X?RSжKqb@ğ}pvGz晘%-,Wϐ Ld1rդU=ҶW\sK |@o(zvu2 ÒaihuK!2g+G);׈<3y]p *5pZR,ur:@ﵭAo( kFCş9PZ"`}R0^t~%V>0zпx=aߙ]Db3wU& qVW9OVpy+MR~mQl_fƃ@.(Sݼ'R3 hYH~%R0<1$vd1pSTW(`qv~ٖJz.ﹻWsc-\C6!-]ߨ=**eZutG-Ň2US_X 3iœ g۩x2܃0lp~&'? :~6 ~iS6 >KϪ([ag +Gp aWJi)t mJPZK ; 7lX9JẊ]SWX#CHJ\zA7P6fm&)cqC< 4h=si K.6j%s'cG53r];+o׿%r)&UF4.x}ʓ1G_iR*K:sdy??<$\B/8ir$Zs2efO1?<-sb١0Lz ԅq# |`MvK u^ -Z;Wn17quS¾ɹ%25|eoO2R,Hl:o&@id@yiz"a9"e7\T;;2|Kqz$͞u>8ZnwE54b{AviAμvpxGih#{"BepUܠ4OnX˗/7JP7rt"pToUbAK MA=YjĶ{a9vz"YËJewxDnKFUr)fb$zm7v2)F%J\ԦpQ㧸4Ϻ,oG$ő^J]ઈPʀ>owfzXͶ+@ph}E֕o>bISSnPgK vU\{}.w]VE),H0-ː(9Q;įblKbHY6) #MnR :${uahw̻-6E+"{hEH_Ϻaܘk zٌF4d_4}D"F[ۏSm+EqحoښV*fL2+O*lo6WBYqVzPf>fH\[!2-ɕ0WӊŁfIvqsQ-`J>G -QDvk-֋븉%*fSP_ uĆIh)uմ^| Y /74)RFEƢ΂$ɮ&c?E1eH9' ݪR1e+yEQ&7tjle>e!5tu+cns7&Q?HZ.yѠ`qs&a-sa` ` e*5CZC$BoDb (?䞝1QF)oı6Ρ9fzoykw9(ݦgŶnh& {6_q6ߣc),ߩ™)|"6ItR p'U7Eej`ydJn32uj,4L&-#Hw$0 ]7#l`מųE̓*+>O$BڤbV)YAuT%Wֳ \<*?K (F-1x\U]AP[ |cU^ԟJmѡl %/;Dɜ/b r(/FUک` xӮIeCrtrM%QZ8߉CqW&w'*Pb3,Z{vѴae#1GtdDFn%dJLG͸~<|;prm[Qf\AXVKڈkR7!bS):p2\q*݃w~{Jf5B yYWchE(3^E !֜? l-χFK:&n@S*x^6/o=H3ctGuQAvH 0oʰK+eΚ4#'lK&(Fj:rYLH;ĖmlK K8qzϘi[`I4t]Jő#oj[ څ^U)m*شlZ,*R cVlW^OU,*4ׂC Oz|p>Z;GDl $iw}b35&ks{T,t 1ץ)&KlCMzg=ݫ|4 ^+) Kc^Հ>>„%yK(1-4mHȏaoYL̟`?g4p}v4z&Gl$I3xЪQ*ǨcU4R,-OA?%>zB!EwˆR0Nt%0%q.EOLԤώmCSH3 a9ذBԵItǾ'[1ИMcy^!W#ȭ3)8Ge|܈N<>]ϳ]Y"dvK:`EM;Bwy$YQ;QQkTK ?j<_8m+]DB\j|R87~<J{mw2p۬[⤮d%N)*ҊhɗDKJLa\\K;$c٣G;?[ MHh|m}%V92wY=@؂o7@ia̜M ]ZU†דxAO;Փx(ߋF7kf +u2B h"1@)?Mtk7oD c44d$,[sl_eh'>h* d5˟4IYԃaeTrtmB_ tPyEFCv\{ZǏ%cl'Jyz;a %8ú5{ .$ =߉c,]3vT_MNYO72MyQ&t U-d}sDrUdJCdv ZݨC^ME,n+ٿW[]d"k`O`[sHkq%<]n: C d.۟n9xȥQ$f ~՛^T#,cxa1o\ gZ^ؤSE .;1RD"c 6{VQN7"Hoc:˚FU]sz%@*7 lPTw_$5_RyT]Ib Y~{bRE&PmTzdO6D.llY^AlIxSŶ}{ C}k J&csS dzObr9>pSp-kv(yjB7KKݯ~u+׏GPF¤;)z}ЊSkx^kz{\A7>uXY0X]|-71O(KSZ8+n z=>7n[QCwͰ}t {4R%nЧε}M^&qpLѱL w HnQ#z^k08#7Hi:0}\0.8į}gg$D#Ř!c>K'qs*MPe EhNt=OKg;~M(4ܙ"*n׶KZ^jrd%65)oډ5uϗs֗}f|Ggf&! &Cy*X3MwQe<=guwN^1ߣQ8[z6P<~ZNX䫝XPH;a3[87`h&KQ 7rC7 G $NT2#ak"}F@K|{vsY?%[P?hOW΄_{#$^q=ԥiaT~")߳S^Jz)~Ad-;U.y+g_*>M?^4/ a(F/p]6:͘.m1m1F$~ȷXԼL s'\iO{R>PX]j\Ơ=̝ ō#XG%HbhA? <ֻ4"6^_PX̯F\ێΚk kij:Bϰj*6)}vkE7kͫ k>y ߴmEy`x% i\I^=$CFjjSf.: B;.BbO ܞO"b _L’mf}O"Ef;A/Hh^J uޮU,cϧMыB }amሃa7mӃI_#}bot(Rx3狌aĶ5@ȝmxQ]&O.N>,m47̣MᶀUn Y,njFz`"VM7FpDN &^ O;Z(6=H)G36 ̲q×g veb_c4NA[/չ`37JTlpxpcON#3k.݌6}WllEbׯo₋(o50 ZiC UjqyTG W/E1SFeI,̞NE`BI{W\$:`TY)VGq;'̃QaY֋e]R r as*_ n?> $VߦLHgߝ]yZTcR0 8aKo3Y8.D2Fqe(}\V,9f#ѐ&ش]P[e 6gJpp>R U+XQ\2 Y»;MWKMía 4n'Osx fƼ_RTf{%l q:C=@F,9;,`)Ǒsv o:E|fQ)QG~zciH{GGre54"4|ԍ&R2ڦe3CrH%2-}8{%VH7'!,@,,!t6rg^حָFs*ФVR=돾4*K5 qse 2P{%~eSr=Ɋ_84rn(1\颜E2ZcD7Mox`ч*g, endstream endobj 42 0 obj << /Type /FontDescriptor /FontName /ZBJHMQ+CMR17 /Flags 4 /FontBBox [-33 -250 945 749] /Ascent 694 /CapHeight 683 /Descent -195 /ItalicAngle 0 /StemV 53 /XHeight 430 /CharSet (/U/a/b/d/e/g/i/l/m/n/o/p/q/r/s/t/u/y) /FontFile 41 0 R >> endobj 43 0 obj << /Length1 2426 /Length2 15061 /Length3 0 /Length 16478 /Filter /FlateDecode >> stream xڍeT\;wHc 5hи;w w@ ;wx}ι${=ݳjVҵLIQd 932UXY,,L,,lHTTj6$* %Ȏ#,0rSAvY+;_"ȑ aji gȂNHT {GKs gI 1r3m:Z䍜-Ml Kpvcfvssc2ub9 2,-*@'+W#[1!Q,,Q̜݌h6r3:Te@r)_wˑF&& [{#;K;s (%03hdY oUsON&NLN6ep%LA@;g'⓰t+o@nv^_3Y:e$~́Npc_yV%eSX_H^NF@ O"$VV3hni;X 4BV_dgwEe5M_`dcgprx>H?a*cg/P?@=/xb{6 R_ #[Kp# ^yx)/UM-]lVvfeGl$e4Ut6{Lv6v@%_W fb N ^=Udαqr3#_0%%Elf߈,#¿T#o `V}F`ƿ8c#k'#'l`ƎF&@b#:_1_ dn%IlmGWM\`1r)C;w_/=1 ffK rX0!`_.p:.Xfw.塀kv#mo }: ~Gl[ ?olpaoGp;KrK+=pLw .`Vph_? ؇\r? jnvWwp`O@;\R <4AZ[Ո1Lr߼@bQ.%ȻIΖP҅ #vkg %NxT/ fꜥ0> ?ǀY68jǏNgoAQq!TQWpU`h*lg=r-Ve;|*HuK:;,?t@v1FR]2.A'RP :r+~$IH͟^D+ۻ M~ GIB4s 8*>.=皕99i93fHY!R7$O2T|A3b@hK1ͫMWGOsIhHCj{'@dXGhEYF'S46}%tyX[ܓ Lf\u~uWVyOOǗjyO#ud$xF).?G=|VXIcְ٫ztr?+ Ӣ Z&:F#TlZD/{?cDdA[t9]+(pbE'Mt7udT5Y$n*Z>, ǡ7YM^׷Atd Ka_wyѻІpQ\XWb$nH&3evSŠkjg[2yu?g|x#F6G#m:`5dA&]߇UL8 Qutdpq҆]0b{css''9]V{As#V5?A0OѡV{PgCJ-Q⶷̋+sEiEn%$gBӿW8jͽ V?-V[Sq_&GWz$T4#d@Kk4'h\ti-dt&~k APDQ~WP.d_֧A"eڧuE T d]*WHb-FNW 8m:).}Thoi#n|)D( rHsd΃3kDs5]af, 벮Kt0/ɧDJFg?𡜨n/o AML{*9l釬'bWu_$1aT<\ʰُ2wӁ6XTUnGM`7k?HL.^3V }sk^Uc~1 +šat( )MjO~ޗiҋ ҳ( ~r"Nk1yaCA <,h+ajL2v힕E(埯D+\b!+q\U(U#[A/ǣ;4cÎ'-XGL!aQO zlw]GZ'˞So| OvW Q+ṭuROzhX1 $Rj]E13< nӨGdX@|U0=+wܒștL MLcCI?{2ˈ|0V@Qmf܋ #}/ݔӟU]#W$ۻM0p?4Yr m8[|"hƵe"ԳKWdB0K.||i׋rQ" w)RRwY % K@Ӊx8ͬ1Zϋ/Ӷ)ݺbOHj_ꚿ GeKw=j̡z67 f˔=G3kk+[לR蓦ѯykŰɃ&Ta<}T/ciO-jJҧ vgpjLPR׻?ܳV3`7mۉԲ=I\yLۯwp3侓ZޖY:_2t ͓"%< ʃ/c)cdq͗N 0Of@|~S߱K΋D9;-&O1QAq*LIbk5@ :5PafܱE/nqTߝ6p)-,QEiU )\qk1yN"՚V8B䏾adrݷ)JIDi:A "6h-flC> Ѫ|~;&үءXab 1RaOv Is5\RMFj7nCp}j,I|m\F["~s<_l*H|js9_݄͞^>}$k!-O ^-AeZi^M?6b*gc38,vK[@sDbȍ>sY c_ƗseLXSa<2/h̥<~ 2A%CsP{eBt_S ]µr`'ӥW(@>RihCx5۟H4e%f(?-֒1.;*1)"-' mKPN HP !pcC|%p|3sSđӃRvH8^_s}"QQ5g܏4FYc0 0a'":9MQu/)CM'ߊEda*mw;O*;qL:PEޏ7~_<>@2K/vZ٠W ]ñyDp Iƻ W} %ӴHp[0n6ׯӝ5^%E_:S Vл"Jc]z" Y0]Ay)CNWRAؿ pOeϯpFes, PpHmFl3gwHC]ykݭӽ-hkA1Kӕ|-jʚ@Yf*x}I%_mj.{϶^d4U>e!*#X=//JQ\uVsM3.Ҡ. wsc  4uyS!ovfHg7k*q8Bo'ȀNE^؟6Z:8OZdafȚˎ jg~IAԉIJĞ7$.;% ,#TK_(hom>QMe99۴)6ҙ0Wwyz{LTG&dE!76jdncAu;5ݞ<9))Pr/0zd܎.F%Z71N< ,v=~ =F>sj'?J`3ql)WnzJOF,o\v+gO"M goQ~ _?i!A9 mKE{ f-`iAƩ~A,BW-b LCk!TÑk%h1tt' y_]Ba 8:)g>~,R&v VŸ׉lC -Tܠ g]ݰZ61 44 yObȠgwEwRr*Y>\̏ZR]X#6L䈱1|Z+k%U#Ϡc`sP بRts/$N^uxڋ9+6c8p[ouۇC~joǷSp$y5a9)S}^ҡ֛BؤࢦVmZk<Qy =E0h9:gjzgXw\)JQ+BvnZ,+nRrP47l ٱ߷MY%D`lvvP5SF1<͖='7_q(b-.㬘 PUC3wgi]?MF8.IGdmy8@跽G 4a/'{F0Cɉ4(9\؅FhnRu'!ꌞ^9cܸ *\uAi`AT4.ߐ2Ϫ'C[q3궨8#|S1.mA(_@SuG%*"m]j{4eC-_L yT~{ 7lp>PhaE A57)em#0SSp1s՝q/ŕ~WG30vp_"XzG6r IQsB@ؠKn|4akn"fwKf9R? =yXpe lL}k  rX^MHJ/fOS7ˌPTRd0`7eՅ.rEk N\Ÿ|"?oDr "ĚLK,y7`1҆7*p^9{&7YzB0;GJFiL X}:"")e;N,[ ۯ ;Tx)'N)h4˶m 'ͽ`zn{ȼy@?6]`Sb~W~+\)Y86Ms (}Ȩ3o6auZ0#历Y̥F㧦L4 8A-uE*&XhMOAn{^P_zf@禍:􉐜\z2t&߉tw AF %N7Aۺ ` !n ʶkՒMu MSA_.|Qbp,AG5QMAX. Wi4w'{|HCav6aD#ؕ/JNb20ҖMrCNyȗ"OR]i÷Bqo]>]#Qb`ʷ-ޯy5T4=*/E%'uXǫMfSFc~nur:4Cr6Lpy?v1.Dg)crϬ&14ފEEOD2䦸;ɭ9IK[rVM~z A-cؽW;H 2td@,%ma##il~-2:&2W=C)2lL.݌xce7DLIr3\EopxV- evkuqIXl:(^Jif! ;M\(š/-E Gm`,:U^.TI P#d(鑲taiֶsBϺY]|r8!;P.*zUvݮnt+ې.rL(%}T\G*m9|R{Al؛*DfVHj{U +j \)z2d_EwV,yeAzBk n~-7wQ0lu+ydUfŃlDP9F4UzQK(*ˑڭކ$e(ȸVŏ"O"_0>9x7ʋVwD.vC|B ITrg/#Y0:3kӡEƇ'GKa͡ƚ4"]KP-"g\eltw +c +ñ3Њ$yam (Z{ɴvqe4fXЀU<9F y<ің43-H4JΏUuR]q:ƶL8%HTR5d{mx;i,u:#`Ra윈R.9~N@˟emwVxGUdωo^O r}T#OwÞM6}Њ8Jw6[/vG6R-'ޞBz{_~. 8ͦjYz4V@PՙSKIO5,OGhb!= pdh<](>jwV[5\v@c1wуTBl֝egb.oH&v' /'ałQVjidDO?zkd߫0UfR8puAN6JLUA*ҹ$y4Rv@f|aFk Oޑ h$te=(/vƶ"hr6UlMPhEuG~jS^1W_6AOU#7tRvXW4J)"3wJZǁ}fB t2!3N@%eKGsqDZZd24O(1TrzN(G=E@E73bCi<)1լXK7x@ֵ/-MLx]?gm㊒L^L+2c,Dچ&wVz,%P<ۤ,c-T vs,h7pm "ą$nj0NE ӥ0Wy}'ay5t͠a?]>yöʖRk:5&њбbnLAݫ/gQ;C| i39(Ϭ2 l0x%S6,}+úZ c1/8pחM4v= Ta3gh2,Y'~%*8TӒ"DMVaK*Ѹzu͌uE]MII"X}F7/a񺞒At={[uq 뼋CGD\mnuDdсG(.tViCv O,wM_>hZS4M |Df»eޙEo2+6BkOho}d2vUϓ3bw;ݵ0p c=N {q457v;UM\Py@Qdˏi|G5mBqOְl;RkȤYүuWjk5pQD>%.U~Ͻ-b1 Yw:r9u>seXː_z@- y[ɰdw#ܥr3~l~="zOȆjB[N%EK¼Qt ć8-z_R}#@dI&,ӗ)x(A"P ?QbzgA17#& ^6qQL?Kt6ڽ7ג?Թ"Κ]K'xnĹ [0nIUS߿u`N?D(i糦]jJ\NTe:^8A_D=Ifl3$KW/:OU2zh_q } {Au;Ea-3=}GV]ܹG(2W4g Mz]ɔs [u{5ȀsYϔg: ϸ! fJ-{޴rٲΩ&OJQUQ-ho_cLvlO32+Ha F68T#&{Ӭimu4p*"tuZ*qנ;Ұͤw~Z$1mw![\D7'f@^*R2{k{AEHu^IW\Wpؘß4N/]/.5 xb6ZO{ cDo!N|;Ƅu 8ZI{ M1)qJ Cf旧&Y2`"NV³* 5Z,\ϊQDIlNWt}nO܄Fh}a-rOvupr'ke|jO W᨝g: |֢8;|"Xen*l;|k#p4]Zwmw]`q&6u3p:gH7ϧ, DHTB4_=sZd:6lĽbw?!o4%r_k gj(͵zT/P>VZIjLl@]XOԴd%qlN]nOnta~R8^T- {"h_֍Y?ϡ(8V#ψWz0oV 2(Ia}Յ4<'l,s:ȓ9Q1{(H7#%GbA8le @T5ND~ 1 \ޠf9K͂O;Vż- !? bOAR5 RO ot]g8ú)-mH"·/5CN?y9OFI\A۰/'lWal\330׶+$cج;55+2Rϙpx^۰knw6cKɯ\T)'f4;Rp|ƩkϺL#[!-h^ZzecMX(RXG/]29{E,C#&IĞ)t><.:|s!L^JW2VC63tܑᏗA FW)_<|қutcSߗQSF)_g;Wg"79D6vIX2O7W3 >8]%ዌ EVҹ;Za\&gk˥\(!< T{5F{h8|i ;z6D2gtܹ:ҫb ? 598g_HÐvWJe9=Ku z"ϗSl ,*FHB Q\u؆RWʄW X,aRVgq%2=[B\O8668JGrg8kՊ -x}'ߟrA }mEFٗA ꓙ0v3"yۦXHZuU^jhA-EPl[Dsױ~8@ n5('B6k>iAj=*@a蝛$hg1t1iW-@Qo߫,'nE>6$ #n$sJ{a` (d&Ndu6XY & Fm&۸7.!Q׃`958`X^1rc"Ooؚ2)_b#µ#U-c4OF9~BTFZy%ŵ^IL5jšVaw)>"{zb 1w5'rMsO@ \o3k4TN/5B~UF9U],BZd^_'C3n6WWKa[IT`v>0f 6N;vH>5=^[ouZESgu:Alo G5~kG |Y ŎAĞg9R5G' BlI:Yt:^S2ǢˡB(~jWBŤicbTLxvee3MF4J}fih`%ƸUXja9{wPscMN]ux8>$lXchG:'29uLŀJ&8™FeXxbq B8J>xVW "<%vkqfýBkw7lpY"P-޼XY-cߙ$vĻ=I0||雤€AB +V+~fYjSWΤPM9p1.` A*g) c+ږ}sY/T/`ᔬJfKL.才.*we!Fz=吺\Nfj$Y0&}vد}: /Z!Dkw$yr@ɕ-x ;ڹs+)+,Adbɣb)~ 9:-2_zja@*=F@!:){]}b'ا敽{T2pAcmk"+*TmtpqDÎzB|ʩxICtˍ*AGŽ3@ZXV;whDWCJW\i.HZIՀ8_+P :/ʌ.0n ?/Z%l٩ cjLʼn&H`U,g_+ae$cӮX]\ǘ-asmdAwRLE3*/42s?i}7dɦ 0Rl&9RİI) gqCZzN3d !uaG>sNr%kLe;0ER?Fd^m Żw i\W2P9qͮE-Q|`=  %L_8Y̼Q 96ȧṛ#y~F_1x8-!{vh k`wub  Agߟ3+s_qz.0ᕙ 0UR:P [7Vu9>l)>7ʃm;4 ؊TYj-Iw_|NgYUƁj},i)sxsPM5¿(ع!N)gwKt`rc>b݌Ah(u'\5w}<4ъzY0r/@1z~*8HlOKq`N0:V~"!E}H|1HľmKW|/R:}ψ(+0@}Mc+2(m '4 ^(L >Uѩлv-G5ՈM5gOt\i~/h lX(!3:9XS^jݪOm$rS1GD冫Z{uBH3L2Oӏ.nn7pAoݖ4]8 endstream endobj 44 0 obj << /Type /FontDescriptor /FontName /BMOAJV+CMSLTT10 /Flags 4 /FontBBox [-20 -233 617 696] /Ascent 611 /CapHeight 611 /Descent -222 /ItalicAngle -9 /StemV 69 /XHeight 431 /CharSet (/C/E/H/I/M/N/P/S/T/U/a/b/backslash/braceleft/braceright/bracketleft/bracketright/c/colon/comma/d/dollar/e/eight/equal/exclam/f/five/four/g/greater/h/hyphen/i/k/l/less/m/n/o/one/p/parenleft/parenright/period/plus/q/quotedbl/r/s/seven/six/slash/t/three/two/u/v/w/x/y/z/zero) /FontFile 43 0 R >> endobj 13 0 obj << /Type /Font /Subtype /Type1 /BaseFont /SFJZUV+CMMI10 /FontDescriptor 36 0 R /FirstChar 25 /LastChar 25 /Widths 26 0 R >> endobj 6 0 obj << /Type /Font /Subtype /Type1 /BaseFont /QEDFBL+CMR10 /FontDescriptor 38 0 R /FirstChar 11 /LastChar 122 /Widths 32 0 R >> endobj 5 0 obj << /Type /Font /Subtype /Type1 /BaseFont /HCOSKL+CMR12 /FontDescriptor 40 0 R /FirstChar 44 /LastChar 121 /Widths 33 0 R >> endobj 4 0 obj << /Type /Font /Subtype /Type1 /BaseFont /ZBJHMQ+CMR17 /FontDescriptor 42 0 R /FirstChar 85 /LastChar 121 /Widths 34 0 R >> endobj 7 0 obj << /Type /Font /Subtype /Type1 /BaseFont /BMOAJV+CMSLTT10 /FontDescriptor 44 0 R /FirstChar 33 /LastChar 125 /Widths 31 0 R >> endobj 8 0 obj << /Type /Pages /Count 4 /Kids [2 0 R 10 0 R 16 0 R 19 0 R] >> endobj 45 0 obj << /Type /Catalog /Pages 8 0 R >> endobj 46 0 obj << /Producer (MiKTeX pdfTeX-1.40.17) /Creator (TeX) /CreationDate (D:20210112140120+01'00') /ModDate (D:20210112140120+01'00') /Trapped /False /PTEX.Fullbanner (This is MiKTeX-pdfTeX 2.9.6100 (1.40.17)) >> endobj xref 0 47 0000000000 65535 f 0000001181 00000 n 0000001070 00000 n 0000000015 00000 n 0000076139 00000 n 0000076000 00000 n 0000075861 00000 n 0000076278 00000 n 0000076420 00000 n 0000003139 00000 n 0000003026 00000 n 0000001281 00000 n 0000009567 00000 n 0000075721 00000 n 0000004564 00000 n 0000004177 00000 n 0000004063 00000 n 0000003241 00000 n 0000009221 00000 n 0000004450 00000 n 0000004256 00000 n 0000006154 00000 n 0000006297 00000 n 0000006395 00000 n 0000006430 00000 n 0000006524 00000 n 0000009316 00000 n 0000009338 00000 n 0000009812 00000 n 0000009837 00000 n 0000009899 00000 n 0000009934 00000 n 0000010324 00000 n 0000010946 00000 n 0000011375 00000 n 0000011615 00000 n 0000018694 00000 n 0000018915 00000 n 0000038952 00000 n 0000039356 00000 n 0000047908 00000 n 0000048153 00000 n 0000058384 00000 n 0000058634 00000 n 0000075232 00000 n 0000076498 00000 n 0000076548 00000 n trailer << /Size 47 /Root 45 0 R /Info 46 0 R /ID [ ] >> startxref 76770 %%EOF sampling/inst/doc/HT_Hajek_estimators.R0000644000176200001440000001051213777316616017640 0ustar liggesusers### R code from vignette source 'HT_Hajek_estimators.Snw' ################################################### ### code chunk number 1: HT_Hajek_estimators.Snw:22-26 ################################################### library(sampling) ps.options(pointsize=12) options(width=60) ################################################### ### code chunk number 2: up1 ################################################### data(belgianmunicipalities) attach(belgianmunicipalities) # sample size n=20 pik=inclusionprobabilities(Tot04,n) N=length(pik) ################################################### ### code chunk number 3: up2 ################################################### sim=10 ss=ss1=array(0,c(sim,4)) ################################################### ### code chunk number 4: up3 ################################################### cat("Case 1\n") y1=rep(3,N) cat("Case 2\n") y2=TaxableIncome cat("Case 3\n") x=1:N pik3=inclusionprobabilities(x,n) y3=1/pik3 cat("Case 4\n") epsilon=rnorm(N,0,sqrt(1/3)) pik4=pik3 y4=5*(x+epsilon) ################################################### ### code chunk number 5: up4 ################################################### ht=numeric(4) hajek=numeric(4) for(i in 1:sim) { cat("Simulation ",i,"\n") cat("Case 1\n") s=UPtille(pik) ht[1]=HTestimator(y1[s==1],pik[s==1]) hajek[1]=Hajekestimator(y1[s==1],pik[s==1],N,type="total") cat("Case 2\n") s1=UPpoisson(pik) ht[2]=HTestimator(y2[s1==1],pik[s1==1]) hajek[2]=Hajekestimator(y2[s1==1],pik[s1==1],N,type="total") cat("Case 3\n") ht[3]=HTestimator(y3[s==1],pik3[s==1]) hajek[3]=Hajekestimator(y3[s==1],pik3[s==1],N,type="total") cat("Case 4\n") ht[4]=HTestimator(y4[s==1],pik4[s==1]) hajek[4]=Hajekestimator(y4[s==1],pik4[s==1],N,type="total") ss[i,]=ht ss1[i,]=hajek } ################################################### ### code chunk number 6: up5 ################################################### #true values tv=c(sum(y1),sum(y2),sum(y3),sum(y4)) for(i in 1:4) { cat("Case ",i,"\n") cat("The mean of the Horvitz-Thompson estimators:",mean(ss[,i])," and the true value:",tv[i],"\n") MSE1=var(ss[,i])+(mean(ss[,i])-tv[i])^2 cat("MSE Horvitz-Thompson estimator:",MSE1,"\n") cat("The mean of the Hajek estimators:",mean(ss1[,i])," and the true value:",tv[i],"\n") MSE2=var(ss1[,i])+(mean(ss1[,i])-tv[i])^2 cat("MSE Hajek estimator:",MSE2,"\n") cat("Ratio of the two MSE:", MSE1/MSE2,"\n") } ################################################### ### code chunk number 7: HT_Hajek_estimators.Snw:140-149 (eval = FALSE) ################################################### ## data(belgianmunicipalities) ## attach(belgianmunicipalities) ## # sample size ## n=20 ## pik=inclusionprobabilities(Tot04,n) ## N=length(pik) ## ## ## sim=10 ## ss=ss1=array(0,c(sim,4)) ## ## cat("Case 1\n") ## y1=rep(3,N) ## cat("Case 2\n") ## y2=TaxableIncome ## cat("Case 3\n") ## x=1:N ## pik3=inclusionprobabilities(x,n) ## y3=1/pik3 ## cat("Case 4\n") ## epsilon=rnorm(N,0,sqrt(1/3)) ## pik4=pik3 ## y4=5*(x+epsilon) ## ## ht=numeric(4) ## hajek=numeric(4) ## for(i in 1:sim) ## { ## cat("Simulation ",i,"\n") ## cat("Case 1\n") ## s=UPtille(pik) ## ht[1]=HTestimator(y1[s==1],pik[s==1]) ## hajek[1]=Hajekestimator(y1[s==1],pik[s==1],N,type="total") ## cat("Case 2\n") ## s1=UPpoisson(pik) ## ht[2]=HTestimator(y2[s1==1],pik[s1==1]) ## hajek[2]=Hajekestimator(y2[s1==1],pik[s1==1],N,type="total") ## cat("Case 3\n") ## ht[3]=HTestimator(y3[s==1],pik3[s==1]) ## hajek[3]=Hajekestimator(y3[s==1],pik3[s==1],N,type="total") ## cat("Case 4\n") ## ht[4]=HTestimator(y4[s==1],pik4[s==1]) ## hajek[4]=Hajekestimator(y4[s==1],pik4[s==1],N,type="total") ## ss[i,]=ht ## ss1[i,]=hajek ## } ## ## ## #true values ## tv=c(sum(y1),sum(y2),sum(y3),sum(y4)) ## for(i in 1:4) ## { ## cat("Case ",i,"\n") ## cat("The mean of the Horvitz-Thompson estimators:",mean(ss[,i])," and the true value:",tv[i],"\n") ## MSE1=var(ss[,i])+(mean(ss[,i])-tv[i])^2 ## cat("MSE Horvitz-Thompson estimator:",MSE1,"\n") ## cat("The mean of the Hajek estimators:",mean(ss1[,i])," and the true value:",tv[i],"\n") ## MSE2=var(ss1[,i])+(mean(ss1[,i])-tv[i])^2 ## cat("MSE Hajek estimator:",MSE2,"\n") ## cat("Ratio of the two MSE:", MSE1/MSE2,"\n") ## } ## ## ## ## sampling.newpage() ## sampling/inst/doc/HT_Hajek_estimators.Snw0000644000176200001440000001167313214675503020204 0ustar liggesusers\documentclass[a4paper]{article} %\VignetteIndexEntry{Horvitz-Thompson estimator and Hajek estimator} %\VignettePackage{sampling} \newcommand{\sampling}{{\tt sampling}} \newcommand{\R}{{\tt R}} \setlength{\parindent}{0in} \setlength{\parskip}{.1in} \setlength{\textwidth}{140mm} \setlength{\oddsidemargin}{10mm} \title{Comparing the Horvitz-Thompson estimator and Hajek estimator} \author{} \usepackage{Sweave} \usepackage[latin1]{inputenc} \usepackage{amsmath} \begin{document} \maketitle <>= library(sampling) ps.options(pointsize=12) options(width=60) @ Consider a finite population with labels $U=\{1, 2, \dots, N\}.$ Suppose $y_k, k\in U$ are values of the variable of interest in the population. We wish to estimate the total $\sum_{k=1}^N y_k$ based on a sample $s$ taken from the population $U.$ Assume that the sample is taken according to a sampling scheme having inclusion probabilities $\pi_k= Pr(k\in s).$ When the $\pi_k$ is proportional to a positive quantity $x_k$ available over $U,$ and $s$ has a predetermined sample size $n,$ then $$\pi_k=\frac{nx_k}{\sum_{i=1}^N x_i},$$ and the sampling scheme is said to be probability proportional to size ($\pi ps$). Under this scheme, the H\'ajek estimator of the population total is defined by $$\hat{y}_{Hajek}=N\frac{\sum_{k\in s} y_k/\pi_k}{\sum_{k\in s} 1/\pi_k}.$$ S$\ddot{a}$rndal, Swenson, and Wretman (1992, p. 182) give several cases for regarding the H\'ajek as `usually the better estimator' comparing to the Horvitz-Thompson estimator $$\hat{y}_{HT}=\sum_{k\in s} y_k/\pi_k:$$ \begin{itemize} \item[a)] the $y_k-\bar{y}_U$ tend to be small, \item[b)] sample size is not fixed, \item[c)] $\pi_k$ are weakly or negatively correlated with the $y_k$. \end{itemize} Monte Carlo simulation is used here to compare the accuracy of both estimators for a sample size (or expected value of the sample size) equal to 20. Four cases are considered: \begin{itemize} \item[Case 1.] $y_k$ is constant for $k=1, \dots, N$; this case corresponds to the case a) above; \item[Case 2.] Poisson sampling is used to draw a sample $s$; this case corresponds to the case b) above; \item[Case 3.] $y_k$ are generated using the following model: $x_k=k, \pi_k=nx_k/\sum_{i=1}^N x_i, y_k=1/\pi_k;$ this case corresponds to the case c) above; \item[Case 4.] $y_k$ are generated using the following model: $x_k=k, y_k=5(x_k+\epsilon_k),\epsilon_k\sim N(0, 1/3);$ in this case the Horvitz-Thompson estimator should perform better than the H\'ajek estimator. \end{itemize} Till\'e sampling is used in Cases 1, 3 and 4. Poisson sampling is used in Case 2. The \verb@belgianmunicipalities@ dataset is used in Cases 1 and 2 with $x_k=Tot04_k.$ In Case 2, the variable of interest is TaxableIncome. The mean square error (MSE) is computed using simulations for each case and estimator. The H\'ajek estimator should perform better than the Horvitz-Thompson estimator in Cases 1, 2 and 3. <>= data(belgianmunicipalities) attach(belgianmunicipalities) # sample size n=20 pik=inclusionprobabilities(Tot04,n) N=length(pik) @ Number of runs (for an accurate result, increase this value to 10000): <>= sim=10 ss=ss1=array(0,c(sim,4)) @ Defines the variables of interest: <>= cat("Case 1\n") y1=rep(3,N) cat("Case 2\n") y2=TaxableIncome cat("Case 3\n") x=1:N pik3=inclusionprobabilities(x,n) y3=1/pik3 cat("Case 4\n") epsilon=rnorm(N,0,sqrt(1/3)) pik4=pik3 y4=5*(x+epsilon) @ Simulation and computation of the Horvitz-Thompson estimator and H\'ajek estimator: <>= ht=numeric(4) hajek=numeric(4) for(i in 1:sim) { cat("Simulation ",i,"\n") cat("Case 1\n") s=UPtille(pik) ht[1]=HTestimator(y1[s==1],pik[s==1]) hajek[1]=Hajekestimator(y1[s==1],pik[s==1],N,type="total") cat("Case 2\n") s1=UPpoisson(pik) ht[2]=HTestimator(y2[s1==1],pik[s1==1]) hajek[2]=Hajekestimator(y2[s1==1],pik[s1==1],N,type="total") cat("Case 3\n") ht[3]=HTestimator(y3[s==1],pik3[s==1]) hajek[3]=Hajekestimator(y3[s==1],pik3[s==1],N,type="total") cat("Case 4\n") ht[4]=HTestimator(y4[s==1],pik4[s==1]) hajek[4]=Hajekestimator(y4[s==1],pik4[s==1],N,type="total") ss[i,]=ht ss1[i,]=hajek } @ Estimation of the MSE and the ratio $\frac{MSE_{HT}}{MSE_{Hajek}}:$ <>= #true values tv=c(sum(y1),sum(y2),sum(y3),sum(y4)) for(i in 1:4) { cat("Case ",i,"\n") cat("The mean of the Horvitz-Thompson estimators:",mean(ss[,i])," and the true value:",tv[i],"\n") MSE1=var(ss[,i])+(mean(ss[,i])-tv[i])^2 cat("MSE Horvitz-Thompson estimator:",MSE1,"\n") cat("The mean of the Hajek estimators:",mean(ss1[,i])," and the true value:",tv[i],"\n") MSE2=var(ss1[,i])+(mean(ss1[,i])-tv[i])^2 cat("MSE Hajek estimator:",MSE2,"\n") cat("Ratio of the two MSE:", MSE1/MSE2,"\n") } <>= <> <> <> <> <> sampling.newpage() @ \end{document}