distributional/0000755000176200001440000000000014560702732013314 5ustar liggesusersdistributional/NAMESPACE0000644000176200001440000003631514560645377014556 0ustar liggesusers# Generated by roxygen2: do not edit by hand S3method("$",hilo) S3method("[[",distribution) S3method("dimnames<-",distribution) S3method("names<-",hilo) S3method(.DollarNames,hilo) S3method(Math,dist_default) S3method(Math,dist_lognormal) S3method(Math,dist_na) S3method(Math,dist_normal) S3method(Math,dist_sample) S3method(Math,dist_transformed) S3method(Ops,dist_default) S3method(Ops,dist_na) S3method(Ops,dist_normal) S3method(Ops,dist_sample) S3method(Ops,dist_transformed) S3method(cdf,dist_bernoulli) S3method(cdf,dist_beta) S3method(cdf,dist_binomial) S3method(cdf,dist_burr) S3method(cdf,dist_categorical) S3method(cdf,dist_cauchy) S3method(cdf,dist_chisq) S3method(cdf,dist_default) S3method(cdf,dist_degenerate) S3method(cdf,dist_exponential) S3method(cdf,dist_f) S3method(cdf,dist_gamma) S3method(cdf,dist_geometric) S3method(cdf,dist_gumbel) S3method(cdf,dist_hypergeometric) S3method(cdf,dist_inflated) S3method(cdf,dist_inverse_exponential) S3method(cdf,dist_inverse_gamma) S3method(cdf,dist_inverse_gaussian) S3method(cdf,dist_logarithmic) S3method(cdf,dist_logistic) S3method(cdf,dist_lognormal) S3method(cdf,dist_mixture) S3method(cdf,dist_mvnorm) S3method(cdf,dist_na) S3method(cdf,dist_negbin) S3method(cdf,dist_normal) S3method(cdf,dist_pareto) S3method(cdf,dist_percentile) S3method(cdf,dist_poisson) S3method(cdf,dist_poisson_inverse_gaussian) S3method(cdf,dist_sample) S3method(cdf,dist_student_t) S3method(cdf,dist_studentized_range) S3method(cdf,dist_transformed) S3method(cdf,dist_truncated) S3method(cdf,dist_uniform) S3method(cdf,dist_weibull) S3method(cdf,dist_wrap) S3method(cdf,distribution) S3method(covariance,default) S3method(covariance,dist_bernoulli) S3method(covariance,dist_beta) S3method(covariance,dist_binomial) S3method(covariance,dist_burr) S3method(covariance,dist_categorical) S3method(covariance,dist_cauchy) S3method(covariance,dist_chisq) S3method(covariance,dist_default) S3method(covariance,dist_degenerate) S3method(covariance,dist_exponential) S3method(covariance,dist_f) S3method(covariance,dist_gamma) S3method(covariance,dist_geometric) S3method(covariance,dist_gumbel) S3method(covariance,dist_hypergeometric) S3method(covariance,dist_inflated) S3method(covariance,dist_inverse_exponential) S3method(covariance,dist_inverse_gamma) S3method(covariance,dist_inverse_gaussian) S3method(covariance,dist_logarithmic) S3method(covariance,dist_logistic) S3method(covariance,dist_lognormal) S3method(covariance,dist_mixture) S3method(covariance,dist_multinomial) S3method(covariance,dist_mvnorm) S3method(covariance,dist_na) S3method(covariance,dist_negbin) S3method(covariance,dist_normal) S3method(covariance,dist_pareto) S3method(covariance,dist_poisson) S3method(covariance,dist_poisson_inverse_gaussian) S3method(covariance,dist_sample) S3method(covariance,dist_student_t) S3method(covariance,dist_transformed) S3method(covariance,dist_uniform) S3method(covariance,dist_weibull) S3method(covariance,distribution) S3method(covariance,numeric) S3method(density,dist_bernoulli) S3method(density,dist_beta) S3method(density,dist_binomial) S3method(density,dist_burr) S3method(density,dist_categorical) S3method(density,dist_cauchy) S3method(density,dist_chisq) S3method(density,dist_default) S3method(density,dist_degenerate) S3method(density,dist_exponential) S3method(density,dist_f) S3method(density,dist_gamma) S3method(density,dist_geometric) S3method(density,dist_gumbel) S3method(density,dist_hypergeometric) S3method(density,dist_inflated) S3method(density,dist_inverse_exponential) S3method(density,dist_inverse_gamma) S3method(density,dist_inverse_gaussian) S3method(density,dist_logarithmic) S3method(density,dist_logistic) S3method(density,dist_lognormal) S3method(density,dist_mixture) S3method(density,dist_multinomial) S3method(density,dist_mvnorm) S3method(density,dist_na) S3method(density,dist_negbin) S3method(density,dist_normal) S3method(density,dist_pareto) S3method(density,dist_poisson) S3method(density,dist_poisson_inverse_gaussian) S3method(density,dist_sample) S3method(density,dist_student_t) S3method(density,dist_transformed) S3method(density,dist_truncated) S3method(density,dist_uniform) S3method(density,dist_weibull) S3method(density,dist_wrap) S3method(density,distribution) S3method(dim,dist_default) S3method(dim,dist_multinomial) S3method(dim,dist_mvnorm) S3method(dimnames,distribution) S3method(family,dist_default) S3method(family,distribution) S3method(format,dist_bernoulli) S3method(format,dist_beta) S3method(format,dist_binomial) S3method(format,dist_burr) S3method(format,dist_categorical) S3method(format,dist_cauchy) S3method(format,dist_chisq) S3method(format,dist_default) S3method(format,dist_degenerate) S3method(format,dist_exponential) S3method(format,dist_f) S3method(format,dist_gamma) S3method(format,dist_geometric) S3method(format,dist_gumbel) S3method(format,dist_hypergeometric) S3method(format,dist_inflated) S3method(format,dist_inverse_exponential) S3method(format,dist_inverse_gamma) S3method(format,dist_inverse_gaussian) S3method(format,dist_logarithmic) S3method(format,dist_logistic) S3method(format,dist_lognormal) S3method(format,dist_mixture) S3method(format,dist_multinomial) S3method(format,dist_mvnorm) S3method(format,dist_na) S3method(format,dist_negbin) S3method(format,dist_normal) S3method(format,dist_pareto) S3method(format,dist_percentile) S3method(format,dist_poisson) S3method(format,dist_poisson_inverse_gaussian) S3method(format,dist_sample) S3method(format,dist_student_t) S3method(format,dist_studentized_range) S3method(format,dist_transformed) S3method(format,dist_truncated) S3method(format,dist_uniform) S3method(format,dist_weibull) S3method(format,dist_wrap) S3method(format,distribution) S3method(format,hdr) S3method(format,hilo) S3method(format,support_region) S3method(generate,dist_bernoulli) S3method(generate,dist_beta) S3method(generate,dist_binomial) S3method(generate,dist_burr) S3method(generate,dist_categorical) S3method(generate,dist_cauchy) S3method(generate,dist_chisq) S3method(generate,dist_default) S3method(generate,dist_degenerate) S3method(generate,dist_exponential) S3method(generate,dist_f) S3method(generate,dist_gamma) S3method(generate,dist_geometric) S3method(generate,dist_gumbel) S3method(generate,dist_hypergeometric) S3method(generate,dist_inflated) S3method(generate,dist_inverse_exponential) S3method(generate,dist_inverse_gamma) S3method(generate,dist_inverse_gaussian) S3method(generate,dist_logarithmic) S3method(generate,dist_logistic) S3method(generate,dist_lognormal) S3method(generate,dist_mixture) S3method(generate,dist_multinomial) S3method(generate,dist_mvnorm) S3method(generate,dist_na) S3method(generate,dist_negbin) S3method(generate,dist_normal) S3method(generate,dist_pareto) S3method(generate,dist_percentile) S3method(generate,dist_poisson) S3method(generate,dist_poisson_inverse_gaussian) S3method(generate,dist_sample) S3method(generate,dist_student_t) S3method(generate,dist_transformed) S3method(generate,dist_uniform) S3method(generate,dist_weibull) S3method(generate,dist_wrap) S3method(generate,distribution) S3method(hdr,default) S3method(hdr,dist_default) S3method(hdr,distribution) S3method(hilo,default) S3method(hilo,dist_default) S3method(hilo,distribution) S3method(is.na,hilo) S3method(kurtosis,dist_bernoulli) S3method(kurtosis,dist_beta) S3method(kurtosis,dist_binomial) S3method(kurtosis,dist_categorical) S3method(kurtosis,dist_cauchy) S3method(kurtosis,dist_chisq) S3method(kurtosis,dist_degenerate) S3method(kurtosis,dist_exponential) S3method(kurtosis,dist_f) S3method(kurtosis,dist_gamma) S3method(kurtosis,dist_geometric) S3method(kurtosis,dist_gumbel) S3method(kurtosis,dist_hypergeometric) S3method(kurtosis,dist_logistic) S3method(kurtosis,dist_lognormal) S3method(kurtosis,dist_na) S3method(kurtosis,dist_negbin) S3method(kurtosis,dist_normal) S3method(kurtosis,dist_poisson) S3method(kurtosis,dist_uniform) S3method(kurtosis,dist_weibull) S3method(kurtosis,distribution) S3method(likelihood,dist_default) S3method(likelihood,distribution) S3method(log_cdf,dist_default) S3method(log_cdf,dist_lognormal) S3method(log_cdf,dist_na) S3method(log_cdf,dist_normal) S3method(log_cdf,distribution) S3method(log_density,dist_bernoulli) S3method(log_density,dist_beta) S3method(log_density,dist_binomial) S3method(log_density,dist_burr) S3method(log_density,dist_cauchy) S3method(log_density,dist_chisq) S3method(log_density,dist_default) S3method(log_density,dist_exponential) S3method(log_density,dist_f) S3method(log_density,dist_gamma) S3method(log_density,dist_geometric) S3method(log_density,dist_gumbel) S3method(log_density,dist_hypergeometric) S3method(log_density,dist_inverse_exponential) S3method(log_density,dist_inverse_gamma) S3method(log_density,dist_inverse_gaussian) S3method(log_density,dist_logarithmic) S3method(log_density,dist_logistic) S3method(log_density,dist_lognormal) S3method(log_density,dist_multinomial) S3method(log_density,dist_mvnorm) S3method(log_density,dist_na) S3method(log_density,dist_negbin) S3method(log_density,dist_normal) S3method(log_density,dist_pareto) S3method(log_density,dist_poisson) S3method(log_density,dist_poisson_inverse_gaussian) S3method(log_density,dist_student_t) S3method(log_density,dist_uniform) S3method(log_density,dist_weibull) S3method(log_density,dist_wrap) S3method(log_density,distribution) S3method(log_likelihood,dist_default) S3method(log_likelihood,distribution) S3method(log_quantile,dist_default) S3method(log_quantile,dist_lognormal) S3method(log_quantile,dist_na) S3method(log_quantile,dist_normal) S3method(log_quantile,distribution) S3method(mean,dist_bernoulli) S3method(mean,dist_beta) S3method(mean,dist_binomial) S3method(mean,dist_burr) S3method(mean,dist_categorical) S3method(mean,dist_cauchy) S3method(mean,dist_chisq) S3method(mean,dist_default) S3method(mean,dist_degenerate) S3method(mean,dist_exponential) S3method(mean,dist_f) S3method(mean,dist_gamma) S3method(mean,dist_geometric) S3method(mean,dist_gumbel) S3method(mean,dist_hypergeometric) S3method(mean,dist_inflated) S3method(mean,dist_inverse_exponential) S3method(mean,dist_inverse_gamma) S3method(mean,dist_inverse_gaussian) S3method(mean,dist_logarithmic) S3method(mean,dist_logistic) S3method(mean,dist_lognormal) S3method(mean,dist_mixture) S3method(mean,dist_multinomial) S3method(mean,dist_mvnorm) S3method(mean,dist_na) S3method(mean,dist_negbin) S3method(mean,dist_normal) S3method(mean,dist_pareto) S3method(mean,dist_poisson) S3method(mean,dist_poisson_inverse_gaussian) S3method(mean,dist_sample) S3method(mean,dist_student_t) S3method(mean,dist_transformed) 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S3method(quantile,dist_logarithmic) S3method(quantile,dist_logistic) S3method(quantile,dist_lognormal) S3method(quantile,dist_mixture) S3method(quantile,dist_mvnorm) S3method(quantile,dist_na) S3method(quantile,dist_negbin) S3method(quantile,dist_normal) S3method(quantile,dist_pareto) S3method(quantile,dist_percentile) S3method(quantile,dist_poisson) S3method(quantile,dist_poisson_inverse_gaussian) S3method(quantile,dist_sample) S3method(quantile,dist_student_t) S3method(quantile,dist_studentized_range) S3method(quantile,dist_transformed) S3method(quantile,dist_truncated) S3method(quantile,dist_uniform) S3method(quantile,dist_weibull) S3method(quantile,dist_wrap) S3method(quantile,distribution) S3method(skewness,dist_bernoulli) S3method(skewness,dist_beta) S3method(skewness,dist_binomial) S3method(skewness,dist_categorical) S3method(skewness,dist_cauchy) S3method(skewness,dist_chisq) S3method(skewness,dist_degenerate) S3method(skewness,dist_exponential) S3method(skewness,dist_f) S3method(skewness,dist_gamma) S3method(skewness,dist_geometric) S3method(skewness,dist_gumbel) S3method(skewness,dist_hypergeometric) S3method(skewness,dist_logistic) S3method(skewness,dist_lognormal) S3method(skewness,dist_na) S3method(skewness,dist_negbin) S3method(skewness,dist_normal) S3method(skewness,dist_poisson) S3method(skewness,dist_sample) S3method(skewness,dist_uniform) S3method(skewness,dist_weibull) S3method(skewness,distribution) S3method(sum,distribution) S3method(support,dist_categorical) S3method(support,dist_default) S3method(support,distribution) S3method(variance,default) S3method(variance,dist_default) S3method(variance,distribution) S3method(variance,matrix) S3method(variance,numeric) S3method(vec_arith,distribution) S3method(vec_arith,hilo) S3method(vec_arith.distribution,default) S3method(vec_arith.numeric,distribution) S3method(vec_arith.numeric,hilo) S3method(vec_cast,character.distribution) S3method(vec_cast,character.hilo) S3method(vec_cast,distribution.distribution) S3method(vec_cast,distribution.double) S3method(vec_cast,distribution.integer) S3method(vec_math,distribution) S3method(vec_math,hilo) S3method(vec_ptype2,distribution.distribution) S3method(vec_ptype2,distribution.double) S3method(vec_ptype2,distribution.integer) S3method(vec_ptype2,double.distribution) S3method(vec_ptype2,hilo.hilo) S3method(vec_ptype2,integer.distribution) S3method(vec_ptype_abbr,distribution) S3method(vec_ptype_abbr,support_region) export(cdf) export(covariance) export(dist_bernoulli) export(dist_beta) export(dist_binomial) export(dist_burr) export(dist_categorical) export(dist_cauchy) export(dist_chisq) export(dist_degenerate) export(dist_exponential) export(dist_f) export(dist_gamma) export(dist_geometric) export(dist_gumbel) export(dist_hypergeometric) export(dist_inflated) export(dist_inverse_exponential) export(dist_inverse_gamma) export(dist_inverse_gaussian) export(dist_logarithmic) export(dist_logistic) export(dist_lognormal) export(dist_missing) export(dist_mixture) export(dist_multinomial) export(dist_multivariate_normal) export(dist_negative_binomial) export(dist_normal) export(dist_pareto) export(dist_percentile) export(dist_poisson) export(dist_poisson_inverse_gaussian) export(dist_sample) export(dist_student_t) export(dist_studentized_range) export(dist_transformed) export(dist_truncated) export(dist_uniform) export(dist_weibull) export(dist_wrap) export(generate) export(hdr) export(hilo) export(is_distribution) export(is_hdr) export(is_hilo) export(kurtosis) export(likelihood) export(log_likelihood) export(new_dist) export(new_hdr) export(new_hilo) export(parameters) export(skewness) export(support) export(variance) import(rlang) import(vctrs) importFrom(generics,generate) importFrom(lifecycle,deprecate_soft) importFrom(lifecycle,deprecated) importFrom(stats,density) importFrom(stats,family) importFrom(stats,median) importFrom(stats,quantile) importFrom(utils,.DollarNames) distributional/README.md0000644000176200001440000001311614475774237014613 0ustar liggesusers # distributional [![Lifecycle: maturing](https://img.shields.io/badge/lifecycle-maturing-blue.svg)](https://lifecycle.r-lib.org/articles/stages.html) [![R-CMD-check](https://github.com/mitchelloharawild/distributional/actions/workflows/R-CMD-check.yaml/badge.svg)](https://github.com/mitchelloharawild/distributional/actions/workflows/R-CMD-check.yaml) [![CRAN status](https://www.r-pkg.org/badges/version/distributional)](https://CRAN.R-project.org/package=distributional) ![Download count](https://cranlogs.r-pkg.org/badges/last-month/distributional) The distributional package allows distributions to be used in a vectorised context. It provides methods which are minimal wrappers to the standard d, p, q, and r distribution functions which are applied to each distribution in the vector. Additional distributional statistics can be computed, including the `mean()`, `median()`, `variance()`, and intervals with `hilo()`. The distributional nature of a model’s predictions is often understated, with default output of prediction methods usually only producing point predictions. Some R packages (such as [forecast](https://CRAN.R-project.org/package=forecast)) further emphasise uncertainty by producing point forecasts and intervals by default, however the user’s ability to interact with them is limited. This package vectorises distributions and provides methods for working with them, making distributions compatible with prediction outputs of modelling functions. These vectorised distributions can be illustrated with [ggplot2](https://CRAN.R-project.org/package=ggplot2) using the [ggdist](https://CRAN.R-project.org/package=ggdist) package, providing further opportunity to visualise the uncertainty of predictions and teach distributional theory. ## Installation You can install the released version of distributional from [CRAN](https://CRAN.R-project.org/package=distributional) with: ``` r install.packages("distributional") ``` The development version can be installed from [GitHub](https://github.com/mitchelloharawild/distributional) with: ``` r # install.packages("remotes") remotes::install_github("mitchelloharawild/distributional") ``` ## Examples Distributions are created using `dist_*()` functions. A list of included distribution shapes can be found here: ``` r library(distributional) my_dist <- c(dist_normal(mu = 0, sigma = 1), dist_student_t(df = 10)) my_dist #> #> [1] N(0, 1) t(10, 0, 1) ``` The standard four distribution functions in R are usable via these generics: ``` r density(my_dist, 0) # c(dnorm(0, mean = 0, sd = 1), dt(0, df = 10)) #> [1] 0.3989423 0.3891084 cdf(my_dist, 5) # c(pnorm(5, mean = 0, sd = 1), pt(5, df = 10)) #> [1] 0.9999997 0.9997313 quantile(my_dist, 0.1) # c(qnorm(0.1, mean = 0, sd = 1), qt(0.1, df = 10)) #> [1] -1.281552 -1.372184 generate(my_dist, 10) # list(rnorm(10, mean = 0, sd = 1), rt(10, df = 10)) #> [[1]] #> [1] 1.262954285 -0.326233361 1.329799263 1.272429321 0.414641434 #> [6] -1.539950042 -0.928567035 -0.294720447 -0.005767173 2.404653389 #> #> [[2]] #> [1] 0.99165484 -1.36999677 -0.40943004 -0.85261144 -1.37728388 0.81020460 #> [7] -1.82965813 -0.06142032 -1.33933588 -0.28491414 ``` You can also compute intervals using `hilo()` ``` r hilo(my_dist, 0.95) #> #> [1] [-0.01190677, 0.01190677]0.95 [-0.01220773, 0.01220773]0.95 ``` Additionally, some distributions may support other methods such as mathematical operations and summary measures. If the methods aren’t supported, a transformed distribution will be created. ``` r my_dist #> #> [1] N(0, 1) t(10, 0, 1) my_dist*3 + 2 #> #> [1] N(2, 9) t(t(10, 0, 1)) mean(my_dist) #> [1] 0 0 variance(my_dist) #> [1] 1.00 1.25 ``` You can also visualise the distribution(s) using the [ggdist](https://mjskay.github.io/ggdist/) package. ``` r library(ggdist) library(ggplot2) df <- data.frame( name = c("Gamma(2,1)", "Normal(5,1)", "Mixture"), dist = c(dist_gamma(2,1), dist_normal(5,1), dist_mixture(dist_gamma(2,1), dist_normal(5, 1), weights = c(0.4, 0.6))) ) ggplot(df, aes(y = factor(name, levels = rev(name)))) + stat_dist_halfeye(aes(dist = dist)) + labs(title = "Density function for a mixture of distributions", y = NULL, x = NULL) ``` ## Related work There are several packages which unify interfaces for distributions in R: - stats provides functions to work with possibly multiple distributions (comparisons made below). - [distributions3](https://cran.r-project.org/package=distributions3) represents singular distributions using S3, with particularly nice documentation. This package makes use of some code and documentation from this package. - [distr](https://cran.r-project.org/package=distr) represents singular distributions using S4. - [distr6](https://cran.r-project.org/package=distr6) represents singular distributions using R6. - Many more in the [CRAN task view](https://cran.r-project.org/view=Distributions) This package differs from the above libraries by storing the distributions in a vectorised format. It does this using [vctrs](https://vctrs.r-lib.org/), so it should play nicely with the tidyverse (try putting distributions into a tibble\!). distributional/man/0000755000176200001440000000000014560645400014065 5ustar liggesusersdistributional/man/dist_weibull.Rd0000644000176200001440000000322214304314270017033 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_weibull.R \name{dist_weibull} \alias{dist_weibull} \title{The Weibull distribution} \usage{ dist_weibull(shape, scale) } \arguments{ \item{shape, scale}{shape and scale parameters, the latter defaulting to 1.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Generalization of the gamma distribution. Often used in survival and time-to-event analyses. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X} be a Weibull random variable with success probability \code{p} = \eqn{p}. \strong{Support}: \eqn{R^+} and zero. \strong{Mean}: \eqn{\lambda \Gamma(1+1/k)}, where \eqn{\Gamma} is the gamma function. \strong{Variance}: \eqn{\lambda [ \Gamma (1 + \frac{2}{k} ) - (\Gamma(1+ \frac{1}{k}))^2 ]} \strong{Probability density function (p.d.f)}: \deqn{ f(x) = \frac{k}{\lambda}(\frac{x}{\lambda})^{k-1}e^{-(x/\lambda)^k}, x \ge 0 } \strong{Cumulative distribution function (c.d.f)}: \deqn{F(x) = 1 - e^{-(x/\lambda)^k}, x \ge 0} \strong{Moment generating function (m.g.f)}: \deqn{\sum_{n=0}^\infty \frac{t^n\lambda^n}{n!} \Gamma(1+n/k), k \ge 1} } \examples{ dist <- dist_weibull(shape = c(0.5, 1, 1.5, 5), scale = rep(1, 4)) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } \seealso{ \link[stats:Weibull]{stats::Weibull} } distributional/man/dist_inverse_gaussian.Rd0000644000176200001440000000173714304314270020746 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_inverse_gaussian.R \name{dist_inverse_gaussian} \alias{dist_inverse_gaussian} \title{The Inverse Gaussian distribution} \usage{ dist_inverse_gaussian(mean, shape) } \arguments{ \item{mean, shape}{parameters. Must be strictly positive. Infinite values are supported.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } \examples{ dist <- dist_inverse_gaussian(mean = c(1,1,1,3,3), shape = c(0.2, 1, 3, 0.2, 1)) dist \dontshow{if (requireNamespace("actuar", quietly = TRUE)) (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf} mean(dist) variance(dist) support(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) \dontshow{\}) # examplesIf} } \seealso{ \link[actuar:InverseGaussian]{actuar::InverseGaussian} } distributional/man/covariance.distribution.Rd0000644000176200001440000000123714304314270021201 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{covariance.distribution} \alias{covariance.distribution} \title{Covariance of a probability distribution} \usage{ \method{covariance}{distribution}(x, ...) } \arguments{ \item{x}{The distribution(s).} \item{...}{Additional arguments used by methods.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Returns the empirical covariance of the probability distribution. If the method does not exist, the covariance of a random sample will be returned. } distributional/man/covariance.Rd0000644000176200001440000000114314304316713016463 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{covariance} \alias{covariance} \title{Covariance} \usage{ covariance(x, ...) } \arguments{ \item{x}{An object.} \item{...}{Additional arguments used by methods.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} A generic function for computing the covariance of an object. } \seealso{ \code{\link[=covariance.distribution]{covariance.distribution()}}, \code{\link[=variance]{variance()}} } distributional/man/mean.distribution.Rd0000644000176200001440000000117314304314270020006 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{mean.distribution} \alias{mean.distribution} \title{Mean of a probability distribution} \usage{ \method{mean}{distribution}(x, ...) } \arguments{ \item{x}{The distribution(s).} \item{...}{Additional arguments used by methods.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Returns the empirical mean of the probability distribution. If the method does not exist, the mean of a random sample will be returned. } distributional/man/dist_inverse_gamma.Rd0000644000176200001440000000174114304314270020211 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_inverse_gamma.R \name{dist_inverse_gamma} \alias{dist_inverse_gamma} \title{The Inverse Gamma distribution} \usage{ dist_inverse_gamma(shape, rate = 1/scale, scale) } \arguments{ \item{shape, scale}{parameters. Must be strictly positive.} \item{rate}{an alternative way to specify the scale.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } \examples{ dist <- dist_inverse_gamma(shape = c(1,2,3,3), rate = c(1,1,1,2)) dist \dontshow{if (requireNamespace("actuar", quietly = TRUE)) (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf} mean(dist) variance(dist) support(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) \dontshow{\}) # examplesIf} } \seealso{ \link[actuar:InverseGamma]{actuar::InverseGamma} } distributional/man/dist_gamma.Rd0000644000176200001440000000506214304314267016464 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_gamma.R \name{dist_gamma} \alias{dist_gamma} \title{The Gamma distribution} \usage{ dist_gamma(shape, rate, scale = 1/rate) } \arguments{ \item{shape, scale}{shape and scale parameters. Must be positive, \code{scale} strictly.} \item{rate}{an alternative way to specify the scale.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Several important distributions are special cases of the Gamma distribution. When the shape parameter is \code{1}, the Gamma is an exponential distribution with parameter \eqn{1/\beta}. When the \eqn{shape = n/2} and \eqn{rate = 1/2}, the Gamma is a equivalent to a chi squared distribution with n degrees of freedom. Moreover, if we have \eqn{X_1} is \eqn{Gamma(\alpha_1, \beta)} and \eqn{X_2} is \eqn{Gamma(\alpha_2, \beta)}, a function of these two variables of the form \eqn{\frac{X_1}{X_1 + X_2}} \eqn{Beta(\alpha_1, \alpha_2)}. This last property frequently appears in another distributions, and it has extensively been used in multivariate methods. More about the Gamma distribution will be added soon. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X} be a Gamma random variable with parameters \code{shape} = \eqn{\alpha} and \code{rate} = \eqn{\beta}. \strong{Support}: \eqn{x \in (0, \infty)} \strong{Mean}: \eqn{\frac{\alpha}{\beta}} \strong{Variance}: \eqn{\frac{\alpha}{\beta^2}} \strong{Probability density function (p.m.f)}: \deqn{ f(x) = \frac{\beta^{\alpha}}{\Gamma(\alpha)} x^{\alpha - 1} e^{-\beta x} }{ f(x) = \frac{\beta^{\alpha}}{\Gamma(\alpha)} x^{\alpha - 1} e^{-\beta x} } \strong{Cumulative distribution function (c.d.f)}: \deqn{ f(x) = \frac{\Gamma(\alpha, \beta x)}{\Gamma{\alpha}} }{ f(x) = \frac{\Gamma(\alpha, \beta x)}{\Gamma{\alpha}} } \strong{Moment generating function (m.g.f)}: \deqn{ E(e^{tX}) = \Big(\frac{\beta}{ \beta - t}\Big)^{\alpha}, \thinspace t < \beta }{ E(e^(tX)) = \Big(\frac{\beta}{ \beta - t}\Big)^{\alpha}, \thinspace t < \beta } } \examples{ dist <- dist_gamma(shape = c(1,2,3,5,9,7.5,0.5), rate = c(0.5,0.5,0.5,1,2,1,1)) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } \seealso{ \link[stats:GammaDist]{stats::GammaDist} } distributional/man/dist_sample.Rd0000644000176200001440000000140314304314270016650 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_sample.R \name{dist_sample} \alias{dist_sample} \title{Sampling distribution} \usage{ dist_sample(x) } \arguments{ \item{x}{A list of sampled values.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } \examples{ # Univariate numeric samples dist <- dist_sample(x = list(rnorm(100), rnorm(100, 10))) dist mean(dist) variance(dist) skewness(dist) generate(dist, 10) density(dist, 1) # Multivariate numeric samples dist <- dist_sample(x = list(cbind(rnorm(100), rnorm(100, 10)))) dist mean(dist) variance(dist) skewness(dist) generate(dist, 10) density(dist, 1) } distributional/man/dist_degenerate.Rd0000644000176200001440000000277714304314267017517 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_degenerate.R \name{dist_degenerate} \alias{dist_degenerate} \title{The degenerate distribution} \usage{ dist_degenerate(x) } \arguments{ \item{x}{The value of the distribution.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} The degenerate distribution takes a single value which is certain to be observed. It takes a single parameter, which is the value that is observed by the distribution. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X} be a degenerate random variable with value \code{x} = \eqn{k_0}. \strong{Support}: \eqn{R}, the set of all real numbers \strong{Mean}: \eqn{k_0} \strong{Variance}: \eqn{0} \strong{Probability density function (p.d.f)}: \deqn{ f(x) = 1 for x = k_0 }{ f(x) = 1 for x = k_0 } \deqn{ f(x) = 0 for x \neq k_0 }{ f(x) = 0 for x \neq k_0 } \strong{Cumulative distribution function (c.d.f)}: The cumulative distribution function has the form \deqn{ F(x) = 0 for x < k_0 }{ F(x) = 0 for x < k_0 } \deqn{ F(x) = 1 for x \ge k_0 }{ F(x) = 1 for x \ge k_0 } \strong{Moment generating function (m.g.f)}: \deqn{ E(e^{tX}) = e^{k_0 t} }{ E(e^(tX)) = e^(k_0 t) } } \examples{ dist_degenerate(x = 1:5) } distributional/man/dist_transformed.Rd0000644000176200001440000000213014304316336017716 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/transformed.R \name{dist_transformed} \alias{dist_transformed} \title{Modify a distribution with a transformation} \usage{ dist_transformed(dist, transform, inverse) } \arguments{ \item{dist}{A univariate distribution vector.} \item{transform}{A function used to transform the distribution. This transformation should be monotonic over appropriate domain.} \item{inverse}{The inverse of the \code{transform} function.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#maturing}{\figure{lifecycle-maturing.svg}{options: alt='[Maturing]'}}}{\strong{[Maturing]}} The \code{\link[=density]{density()}}, \code{\link[=mean]{mean()}}, and \code{\link[=variance]{variance()}} methods are approximate as they are based on numerical derivatives. } \examples{ # Create a log normal distribution dist <- dist_transformed(dist_normal(0, 0.5), exp, log) density(dist, 1) # dlnorm(1, 0, 0.5) cdf(dist, 4) # plnorm(4, 0, 0.5) quantile(dist, 0.1) # qlnorm(0.1, 0, 0.5) generate(dist, 10) # rlnorm(10, 0, 0.5) } distributional/man/dist_logistic.Rd0000644000176200001440000000360714304314270017214 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_logistic.R \name{dist_logistic} \alias{dist_logistic} \title{The Logistic distribution} \usage{ dist_logistic(location, scale) } \arguments{ \item{location, scale}{location and scale parameters.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} A continuous distribution on the real line. For binary outcomes the model given by \eqn{P(Y = 1 | X) = F(X \beta)} where \eqn{F} is the Logistic \code{\link[=cdf]{cdf()}} is called \emph{logistic regression}. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X} be a Logistic random variable with \code{location} = \eqn{\mu} and \code{scale} = \eqn{s}. \strong{Support}: \eqn{R}, the set of all real numbers \strong{Mean}: \eqn{\mu} \strong{Variance}: \eqn{s^2 \pi^2 / 3} \strong{Probability density function (p.d.f)}: \deqn{ f(x) = \frac{e^{-(\frac{x - \mu}{s})}}{s [1 + \exp(-(\frac{x - \mu}{s})) ]^2} }{ f(x) = e^(-(t - \mu) / s) / (s (1 + e^(-(t - \mu) / s))^2) } \strong{Cumulative distribution function (c.d.f)}: \deqn{ F(t) = \frac{1}{1 + e^{-(\frac{t - \mu}{s})}} }{ F(t) = 1 / (1 + e^(-(t - \mu) / s)) } \strong{Moment generating function (m.g.f)}: \deqn{ E(e^{tX}) = e^{\mu t} \beta(1 - st, 1 + st) }{ E(e^(tX)) = = e^(\mu t) \beta(1 - st, 1 + st) } where \eqn{\beta(x, y)} is the Beta function. } \examples{ dist <- dist_logistic(location = c(5,9,9,6,2), scale = c(2,3,4,2,1)) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } \seealso{ \link[stats:Logistic]{stats::Logistic} } distributional/man/variance.Rd0000644000176200001440000000227214304316713016145 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{variance} \alias{variance} \alias{variance.numeric} \alias{variance.matrix} \alias{covariance.numeric} \title{Variance} \usage{ variance(x, ...) \method{variance}{numeric}(x, ...) \method{variance}{matrix}(x, ...) \method{covariance}{numeric}(x, ...) } \arguments{ \item{x}{An object.} \item{...}{Additional arguments used by methods.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} A generic function for computing the variance of an object. } \details{ The implementation of \code{variance()} for numeric variables coerces the input to a vector then uses \code{\link[stats:cor]{stats::var()}} to compute the variance. This means that, unlike \code{\link[stats:cor]{stats::var()}}, if \code{variance()} is passed a matrix or a 2-dimensional array, it will still return the variance (\code{\link[stats:cor]{stats::var()}} returns the covariance matrix in that case). } \seealso{ \code{\link[=variance.distribution]{variance.distribution()}}, \code{\link[=covariance]{covariance()}} } distributional/man/dist_binomial.Rd0000644000176200001440000000560014304314267017172 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_binomial.R \name{dist_binomial} \alias{dist_binomial} \title{The Binomial distribution} \usage{ dist_binomial(size, prob) } \arguments{ \item{size}{The number of trials. Must be an integer greater than or equal to one. When \code{size = 1L}, the Binomial distribution reduces to the Bernoulli distribution. Often called \code{n} in textbooks.} \item{prob}{The probability of success on each trial, \code{prob} can be any value in \verb{[0, 1]}.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Binomial distributions are used to represent situations can that can be thought as the result of \eqn{n} Bernoulli experiments (here the \eqn{n} is defined as the \code{size} of the experiment). The classical example is \eqn{n} independent coin flips, where each coin flip has probability \code{p} of success. In this case, the individual probability of flipping heads or tails is given by the Bernoulli(p) distribution, and the probability of having \eqn{x} equal results (\eqn{x} heads, for example), in \eqn{n} trials is given by the Binomial(n, p) distribution. The equation of the Binomial distribution is directly derived from the equation of the Bernoulli distribution. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. The Binomial distribution comes up when you are interested in the portion of people who do a thing. The Binomial distribution also comes up in the sign test, sometimes called the Binomial test (see \code{\link[stats:binom.test]{stats::binom.test()}}), where you may need the Binomial C.D.F. to compute p-values. In the following, let \eqn{X} be a Binomial random variable with parameter \code{size} = \eqn{n} and \code{p} = \eqn{p}. Some textbooks define \eqn{q = 1 - p}, or called \eqn{\pi} instead of \eqn{p}. \strong{Support}: \eqn{\{0, 1, 2, ..., n\}}{{0, 1, 2, ..., n}} \strong{Mean}: \eqn{np} \strong{Variance}: \eqn{np \cdot (1 - p) = np \cdot q}{np (1 - p)} \strong{Probability mass function (p.m.f)}: \deqn{ P(X = k) = {n \choose k} p^k (1 - p)^{n-k} }{ P(X = k) = choose(n, k) p^k (1 - p)^(n - k) } \strong{Cumulative distribution function (c.d.f)}: \deqn{ P(X \le k) = \sum_{i=0}^{\lfloor k \rfloor} {n \choose i} p^i (1 - p)^{n-i} }{ P(X \le k) = \sum_{i=0}^k choose(n, i) p^i (1 - p)^(n-i) } \strong{Moment generating function (m.g.f)}: \deqn{ E(e^{tX}) = (1 - p + p e^t)^n }{ E(e^(tX)) = (1 - p + p e^t)^n } } \examples{ dist <- dist_binomial(size = 1:5, prob = c(0.05, 0.5, 0.3, 0.9, 0.1)) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } distributional/man/new_hilo.Rd0000644000176200001440000000137314304316713016162 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/hilo.R \name{new_hilo} \alias{new_hilo} \title{Construct hilo intervals} \usage{ new_hilo(lower = double(), upper = double(), size = double()) } \arguments{ \item{lower, upper}{A numeric vector of values for lower and upper limits.} \item{size}{Size of the interval between [0, 100].} } \value{ A "hilo" vector } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Class constructor function to help with manually creating hilo interval objects. } \examples{ new_hilo(lower = rnorm(10), upper = rnorm(10) + 5, size = 95) } \author{ Earo Wang & Mitchell O'Hara-Wild } distributional/man/dist_beta.Rd0000644000176200001440000000136214304310476016312 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_beta.R \name{dist_beta} \alias{dist_beta} \title{The Beta distribution} \usage{ dist_beta(shape1, shape2) } \arguments{ \item{shape1, shape2}{The non-negative shape parameters of the Beta distribution.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } \examples{ dist <- dist_beta(shape1 = c(0.5, 5, 1, 2, 2), shape2 = c(0.5, 1, 3, 2, 5)) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } \seealso{ \link[stats:Beta]{stats::Beta} } distributional/man/support.Rd0000644000176200001440000000105014304316336016063 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{support} \alias{support} \alias{support.distribution} \title{Region of support of a distribution} \usage{ support(x, ...) \method{support}{distribution}(x, ...) } \arguments{ \item{x}{The distribution(s).} \item{...}{Additional arguments used by methods.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#experimental}{\figure{lifecycle-experimental.svg}{options: alt='[Experimental]'}}}{\strong{[Experimental]}} } distributional/man/kurtosis.Rd0000644000176200001440000000103014304314326016225 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{kurtosis} \alias{kurtosis} \alias{kurtosis.distribution} \title{Kurtosis of a probability distribution} \usage{ kurtosis(x, ...) \method{kurtosis}{distribution}(x, ...) } \arguments{ \item{x}{The distribution(s).} \item{...}{Additional arguments used by methods.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } distributional/man/is_hilo.Rd0000644000176200001440000000035613703764147016016 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/hilo.R \name{is_hilo} \alias{is_hilo} \title{Is the object a hilo} \usage{ is_hilo(x) } \arguments{ \item{x}{An object.} } \description{ Is the object a hilo } distributional/man/generate.distribution.Rd0000644000176200001440000000115414304314270020657 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{generate.distribution} \alias{generate.distribution} \title{Randomly sample values from a distribution} \usage{ \method{generate}{distribution}(x, times, ...) } \arguments{ \item{x}{The distribution(s).} \item{times}{The number of samples.} \item{...}{Additional arguments used by methods.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Generate random samples from probability distributions. } distributional/man/dist_studentized_range.Rd0000644000176200001440000000237514304314270021116 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_studentized_range.R \name{dist_studentized_range} \alias{dist_studentized_range} \title{The Studentized Range distribution} \usage{ dist_studentized_range(nmeans, df, nranges) } \arguments{ \item{nmeans}{sample size for range (same for each group).} \item{df}{degrees of freedom for \eqn{s} (see below).} \item{nranges}{number of \emph{groups} whose \bold{maximum} range is considered.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Tukey's studentized range distribution, used for Tukey's honestly significant differences test in ANOVA. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. \strong{Support}: \eqn{R^+}, the set of positive real numbers. Other properties of Tukey's Studentized Range Distribution are omitted, largely because the distribution is not fun to work with. } \examples{ dist <- dist_studentized_range(nmeans = c(6, 2), df = c(5, 4), nranges = c(1, 1)) dist cdf(dist, 4) quantile(dist, 0.7) } \seealso{ \link[stats:Tukey]{stats::Tukey} } distributional/man/dist_gumbel.Rd0000644000176200001440000000435514304314267016661 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_gumbel.R \name{dist_gumbel} \alias{dist_gumbel} \title{The Gumbel distribution} \usage{ dist_gumbel(alpha, scale) } \arguments{ \item{alpha}{location parameter.} \item{scale}{parameter. Must be strictly positive.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} The Gumbel distribution is a special case of the Generalized Extreme Value distribution, obtained when the GEV shape parameter \eqn{\xi} is equal to 0. It may be referred to as a type I extreme value distribution. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X} be a Gumbel random variable with location parameter \code{mu} = \eqn{\mu}, scale parameter \code{sigma} = \eqn{\sigma}. \strong{Support}: \eqn{R}, the set of all real numbers. \strong{Mean}: \eqn{\mu + \sigma\gamma}, where \eqn{\gamma} is Euler's constant, approximately equal to 0.57722. \strong{Median}: \eqn{\mu - \sigma\ln(\ln 2)}{\mu - \sigma ln(ln 2)}. \strong{Variance}: \eqn{\sigma^2 \pi^2 / 6}. \strong{Probability density function (p.d.f)}: \deqn{f(x) = \sigma ^ {-1} \exp[-(x - \mu) / \sigma]% \exp\{-\exp[-(x - \mu) / \sigma] \}}{% f(x) = (1 / \sigma) exp[-(x - \mu) / \sigma]% exp{-exp[-(x - \mu) / \sigma]}} for \eqn{x} in \eqn{R}, the set of all real numbers. \strong{Cumulative distribution function (c.d.f)}: In the \eqn{\xi = 0} (Gumbel) special case \deqn{F(x) = \exp\{-\exp[-(x - \mu) / \sigma] \}}{% F(x) = exp{ - exp[-(x - \mu) / \sigma]} } for \eqn{x} in \eqn{R}, the set of all real numbers. } \examples{ dist <- dist_gumbel(alpha = c(0.5, 1, 1.5, 3), scale = c(2, 2, 3, 4)) dist \dontshow{if (requireNamespace("actuar", quietly = TRUE)) (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf} mean(dist) variance(dist) skewness(dist) kurtosis(dist) support(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) \dontshow{\}) # examplesIf} } \seealso{ \link[actuar:Gumbel]{actuar::Gumbel} } distributional/man/cdf.Rd0000644000176200001440000000123114304314270015077 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{cdf} \alias{cdf} \alias{cdf.distribution} \title{The cumulative distribution function} \usage{ cdf(x, q, ..., log = FALSE) \method{cdf}{distribution}(x, q, ...) } \arguments{ \item{x}{The distribution(s).} \item{q}{The quantile at which the cdf is calculated.} \item{...}{Additional arguments passed to methods.} \item{log}{If \code{TRUE}, probabilities will be given as log probabilities.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } distributional/man/hdr.distribution.Rd0000644000176200001440000000164214304316336017651 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{hdr.distribution} \alias{hdr.distribution} \title{Highest density regions of probability distributions} \usage{ \method{hdr}{distribution}(x, size = 95, n = 512, ...) } \arguments{ \item{x}{The distribution(s).} \item{size}{The size of the interval (between 0 and 100).} \item{n}{The resolution used to estimate the distribution's density.} \item{...}{Additional arguments used by methods.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#maturing}{\figure{lifecycle-maturing.svg}{options: alt='[Maturing]'}}}{\strong{[Maturing]}} This function is highly experimental and will change in the future. In particular, improved functionality for object classes and visualisation tools will be added in a future release. Computes minimally sized probability intervals highest density regions. } distributional/man/density.distribution.Rd0000644000176200001440000000144414304314270020546 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{density.distribution} \alias{density.distribution} \title{The probability density/mass function} \usage{ \method{density}{distribution}(x, at, ..., log = FALSE) } \arguments{ \item{x}{The distribution(s).} \item{at}{The point at which to compute the density/mass.} \item{...}{Additional arguments passed to methods.} \item{log}{If \code{TRUE}, probabilities will be given as log probabilities.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Computes the probability density function for a continuous distribution, or the probability mass function for a discrete distribution. } distributional/man/dist_inverse_exponential.Rd0000644000176200001440000000164114304314270021454 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_inverse_exponential.R \name{dist_inverse_exponential} \alias{dist_inverse_exponential} \title{The Inverse Exponential distribution} \usage{ dist_inverse_exponential(rate) } \arguments{ \item{rate}{an alternative way to specify the scale.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } \examples{ dist <- dist_inverse_exponential(rate = 1:5) dist \dontshow{if (requireNamespace("actuar", quietly = TRUE)) (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf} mean(dist) variance(dist) support(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) \dontshow{\}) # examplesIf} } \seealso{ \link[actuar:InverseExponential]{actuar::InverseExponential} } distributional/man/dist_pareto.Rd0000644000176200001440000000155014304316335016670 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_pareto.R \name{dist_pareto} \alias{dist_pareto} \title{The Pareto distribution} \usage{ dist_pareto(shape, scale) } \arguments{ \item{shape, scale}{parameters. Must be strictly positive.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } \examples{ dist <- dist_pareto(shape = c(10, 3, 2, 1), scale = rep(1, 4)) dist \dontshow{if (requireNamespace("actuar", quietly = TRUE)) (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf} mean(dist) variance(dist) support(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) \dontshow{\}) # examplesIf} } \seealso{ \link[actuar:Pareto]{actuar::Pareto} } distributional/man/family.distribution.Rd0000644000176200001440000000131214304316335020346 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{family.distribution} \alias{family.distribution} \title{Extract the name of the distribution family} \usage{ \method{family}{distribution}(object, ...) } \arguments{ \item{object}{The distribution(s).} \item{...}{Additional arguments used by methods.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#experimental}{\figure{lifecycle-experimental.svg}{options: alt='[Experimental]'}}}{\strong{[Experimental]}} } \examples{ dist <- c( dist_normal(1:2), dist_poisson(3), dist_multinomial(size = c(4, 3), prob = list(c(0.3, 0.5, 0.2), c(0.1, 0.5, 0.4))) ) family(dist) } distributional/man/variance.distribution.Rd0000644000176200001440000000122314304314270020652 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{variance.distribution} \alias{variance.distribution} \title{Variance of a probability distribution} \usage{ \method{variance}{distribution}(x, ...) } \arguments{ \item{x}{The distribution(s).} \item{...}{Additional arguments used by methods.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Returns the empirical variance of the probability distribution. If the method does not exist, the variance of a random sample will be returned. } distributional/man/skewness.Rd0000644000176200001440000000103014304314326016204 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{skewness} \alias{skewness} \alias{skewness.distribution} \title{Skewness of a probability distribution} \usage{ skewness(x, ...) \method{skewness}{distribution}(x, ...) } \arguments{ \item{x}{The distribution(s).} \item{...}{Additional arguments used by methods.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } distributional/man/dist_logarithmic.Rd0000644000176200001440000000155314304314270017677 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_logarithmic.R \name{dist_logarithmic} \alias{dist_logarithmic} \title{The Logarithmic distribution} \usage{ dist_logarithmic(prob) } \arguments{ \item{prob}{parameter. \code{0 <= prob < 1}.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } \examples{ dist <- dist_logarithmic(prob = c(0.33, 0.66, 0.99)) dist \dontshow{if (requireNamespace("actuar", quietly = TRUE)) (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf} mean(dist) variance(dist) support(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) \dontshow{\}) # examplesIf} } \seealso{ \link[actuar:Logarithmic]{actuar::Logarithmic} } distributional/man/dist_multinomial.Rd0000644000176200001440000000472314304316335017735 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_multinomial.R \name{dist_multinomial} \alias{dist_multinomial} \title{The Multinomial distribution} \usage{ dist_multinomial(size, prob) } \arguments{ \item{size}{The number of draws from the Categorical distribution.} \item{prob}{The probability of an event occurring from each draw.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} The multinomial distribution is a generalization of the binomial distribution to multiple categories. It is perhaps easiest to think that we first extend a \code{\link[=dist_bernoulli]{dist_bernoulli()}} distribution to include more than two categories, resulting in a \code{\link[=dist_categorical]{dist_categorical()}} distribution. We then extend repeat the Categorical experiment several (\eqn{n}) times. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X = (X_1, ..., X_k)} be a Multinomial random variable with success probability \code{p} = \eqn{p}. Note that \eqn{p} is vector with \eqn{k} elements that sum to one. Assume that we repeat the Categorical experiment \code{size} = \eqn{n} times. \strong{Support}: Each \eqn{X_i} is in \eqn{{0, 1, 2, ..., n}}. \strong{Mean}: The mean of \eqn{X_i} is \eqn{n p_i}. \strong{Variance}: The variance of \eqn{X_i} is \eqn{n p_i (1 - p_i)}. For \eqn{i \neq j}, the covariance of \eqn{X_i} and \eqn{X_j} is \eqn{-n p_i p_j}. \strong{Probability mass function (p.m.f)}: \deqn{ P(X_1 = x_1, ..., X_k = x_k) = \frac{n!}{x_1! x_2! ... x_k!} p_1^{x_1} \cdot p_2^{x_2} \cdot ... \cdot p_k^{x_k} }{ P(X_1 = x_1, ..., X_k = x_k) = n! / (x_1! x_2! ... x_k!) p_1^x_1 p_2^x_2 ... p_k^x_k } \strong{Cumulative distribution function (c.d.f)}: Omitted for multivariate random variables for the time being. \strong{Moment generating function (m.g.f)}: \deqn{ E(e^{tX}) = \left(\sum_{i=1}^k p_i e^{t_i}\right)^n }{ E(e^(tX)) = (p_1 e^t_1 + p_2 e^t_2 + ... + p_k e^t_k)^n } } \examples{ dist <- dist_multinomial(size = c(4, 3), prob = list(c(0.3, 0.5, 0.2), c(0.1, 0.5, 0.4))) dist mean(dist) variance(dist) generate(dist, 10) # TODO: Needs fixing to support multiple inputs # density(dist, 2) # density(dist, 2, log = TRUE) } \seealso{ \link[stats:Multinom]{stats::Multinomial} } distributional/man/dist_student_t.Rd0000644000176200001440000000440514304314270017405 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_student_t.R \name{dist_student_t} \alias{dist_student_t} \title{The (non-central) location-scale Student t Distribution} \usage{ dist_student_t(df, mu = 0, sigma = 1, ncp = NULL) } \arguments{ \item{df}{degrees of freedom (\eqn{> 0}, maybe non-integer). \code{df = Inf} is allowed.} \item{mu}{The location parameter of the distribution. If \code{ncp == 0} (or \code{NULL}), this is the median.} \item{sigma}{The scale parameter of the distribution.} \item{ncp}{non-centrality parameter \eqn{\delta}{delta}; currently except for \code{rt()}, only for \code{abs(ncp) <= 37.62}. If omitted, use the central t distribution.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} The Student's T distribution is closely related to the \code{\link[=Normal]{Normal()}} distribution, but has heavier tails. As \eqn{\nu} increases to \eqn{\infty}, the Student's T converges to a Normal. The T distribution appears repeatedly throughout classic frequentist hypothesis testing when comparing group means. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X} be a \strong{central} Students T random variable with \code{df} = \eqn{\nu}. \strong{Support}: \eqn{R}, the set of all real numbers \strong{Mean}: Undefined unless \eqn{\nu \ge 2}, in which case the mean is zero. \strong{Variance}: \deqn{ \frac{\nu}{\nu - 2} }{ \nu / (\nu - 2) } Undefined if \eqn{\nu < 1}, infinite when \eqn{1 < \nu \le 2}. \strong{Probability density function (p.d.f)}: \deqn{ f(x) = \frac{\Gamma(\frac{\nu + 1}{2})}{\sqrt{\nu \pi} \Gamma(\frac{\nu}{2})} (1 + \frac{x^2}{\nu} )^{- \frac{\nu + 1}{2}} }{ f(x) = \Gamma((\nu + 1) / 2) / (\sqrt(\nu \pi) \Gamma(\nu / 2)) (1 + x^2 / \nu)^(- (\nu + 1) / 2) } } \examples{ dist <- dist_student_t(df = c(1,2,5), mu = c(0,1,2), sigma = c(1,2,3)) dist mean(dist) variance(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } \seealso{ \link[stats:TDist]{stats::TDist} } distributional/man/hilo.distribution.Rd0000644000176200001440000000156514304316336020033 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{hilo.distribution} \alias{hilo.distribution} \title{Probability intervals of a probability distribution} \usage{ \method{hilo}{distribution}(x, size = 95, ...) } \arguments{ \item{x}{The distribution(s).} \item{size}{The size of the interval (between 0 and 100).} \item{...}{Additional arguments used by methods.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Returns a \code{hilo} central probability interval with probability coverage of \code{size}. By default, the distribution's \code{\link[=quantile]{quantile()}} will be used to compute the lower and upper bound for a centered interval } \seealso{ \code{\link[=hdr.distribution]{hdr.distribution()}} } distributional/man/dist_exponential.Rd0000644000176200001440000000130614304314267017725 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_exponential.R \name{dist_exponential} \alias{dist_exponential} \title{The Exponential Distribution} \usage{ dist_exponential(rate) } \arguments{ \item{rate}{vector of rates.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } \examples{ dist <- dist_exponential(rate = c(2, 1, 2/3)) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } \seealso{ \link[stats:Exponential]{stats::Exponential} } distributional/man/dist_f.Rd0000644000176200001440000000344714304314267015634 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_f.R \name{dist_f} \alias{dist_f} \title{The F Distribution} \usage{ dist_f(df1, df2, ncp = NULL) } \arguments{ \item{df1, df2}{degrees of freedom. \code{Inf} is allowed.} \item{ncp}{non-centrality parameter. If omitted the central F is assumed.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X} be a Gamma random variable with parameters \code{shape} = \eqn{\alpha} and \code{rate} = \eqn{\beta}. \strong{Support}: \eqn{x \in (0, \infty)} \strong{Mean}: \eqn{\frac{\alpha}{\beta}} \strong{Variance}: \eqn{\frac{\alpha}{\beta^2}} \strong{Probability density function (p.m.f)}: \deqn{ f(x) = \frac{\beta^{\alpha}}{\Gamma(\alpha)} x^{\alpha - 1} e^{-\beta x} }{ f(x) = \frac{\beta^{\alpha}}{\Gamma(\alpha)} x^{\alpha - 1} e^{-\beta x} } \strong{Cumulative distribution function (c.d.f)}: \deqn{ f(x) = \frac{\Gamma(\alpha, \beta x)}{\Gamma{\alpha}} }{ f(x) = \frac{\Gamma(\alpha, \beta x)}{\Gamma{\alpha}} } \strong{Moment generating function (m.g.f)}: \deqn{ E(e^{tX}) = \Big(\frac{\beta}{ \beta - t}\Big)^{\alpha}, \thinspace t < \beta }{ E(e^(tX)) = \Big(\frac{\beta}{ \beta - t}\Big)^{\alpha}, \thinspace t < \beta } } \examples{ dist <- dist_f(df1 = c(1,2,5,10,100), df2 = c(1,1,2,1,100)) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } \seealso{ \link[stats:Fdist]{stats::FDist} } distributional/man/dist_bernoulli.Rd0000644000176200001440000000434514304314267017400 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_bernoulli.R \name{dist_bernoulli} \alias{dist_bernoulli} \title{The Bernoulli distribution} \usage{ dist_bernoulli(prob) } \arguments{ \item{prob}{The probability of success on each trial, \code{prob} can be any value in \verb{[0, 1]}.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Bernoulli distributions are used to represent events like coin flips when there is single trial that is either successful or unsuccessful. The Bernoulli distribution is a special case of the \code{\link[=Binomial]{Binomial()}} distribution with \code{n = 1}. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X} be a Bernoulli random variable with parameter \code{p} = \eqn{p}. Some textbooks also define \eqn{q = 1 - p}, or use \eqn{\pi} instead of \eqn{p}. The Bernoulli probability distribution is widely used to model binary variables, such as 'failure' and 'success'. The most typical example is the flip of a coin, when \eqn{p} is thought as the probability of flipping a head, and \eqn{q = 1 - p} is the probability of flipping a tail. \strong{Support}: \eqn{\{0, 1\}}{{0, 1}} \strong{Mean}: \eqn{p} \strong{Variance}: \eqn{p \cdot (1 - p) = p \cdot q}{p (1 - p)} \strong{Probability mass function (p.m.f)}: \deqn{ P(X = x) = p^x (1 - p)^{1-x} = p^x q^{1-x} }{ P(X = x) = p^x (1 - p)^(1-x) } \strong{Cumulative distribution function (c.d.f)}: \deqn{ P(X \le x) = \left \{ \begin{array}{ll} 0 & x < 0 \\ 1 - p & 0 \leq x < 1 \\ 1 & x \geq 1 \end{array} \right. }{ P(X \le x) = (1 - p) 1_{[0, 1)}(x) + 1_{1}(x) } \strong{Moment generating function (m.g.f)}: \deqn{ E(e^{tX}) = (1 - p) + p e^t }{ E(e^(tX)) = (1 - p) + p e^t } } \examples{ dist <- dist_bernoulli(prob = c(0.05, 0.5, 0.3, 0.9, 0.1)) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } distributional/man/dist_multivariate_normal.Rd0000644000176200001440000000215014304316335021451 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_multivariate_normal.R \name{dist_multivariate_normal} \alias{dist_multivariate_normal} \title{The multivariate normal distribution} \usage{ dist_multivariate_normal(mu = 0, sigma = diag(1)) } \arguments{ \item{mu}{A list of numeric vectors for the distribution's mean.} \item{sigma}{A list of matrices for the distribution's variance-covariance matrix.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } \examples{ dist <- dist_multivariate_normal(mu = list(c(1,2)), sigma = list(matrix(c(4,2,2,3), ncol=2))) dist \dontshow{if (requireNamespace("mvtnorm", quietly = TRUE)) (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf} mean(dist) variance(dist) support(dist) generate(dist, 10) density(dist, c(2, 1)) density(dist, c(2, 1), log = TRUE) cdf(dist, 4) quantile(dist, 0.7) \dontshow{\}) # examplesIf} } \seealso{ \link[mvtnorm:Mvnorm]{mvtnorm::dmvnorm}, \link[mvtnorm:qmvnorm]{mvtnorm::qmvnorm} } distributional/man/figures/0000755000176200001440000000000014406447336015540 5ustar liggesusersdistributional/man/figures/lifecycle-defunct.svg0000644000176200001440000000170414304310441021627 0ustar liggesuserslifecyclelifecycledefunctdefunct distributional/man/figures/lifecycle-maturing.svg0000644000176200001440000000170614304310441022027 0ustar liggesuserslifecyclelifecyclematuringmaturing distributional/man/figures/README-plot-1.png0000644000176200001440000003467614406447336020335 0ustar liggesusersPNG  IHDRHc pHYsod IDATxg`SÀs3)Rv޲%CAQET* Eee"DPE̖B#}?tP$M$}Ҥ9w>9EeYm)=~ "h@<D ]RY͏l?":[!lgz~ښC/'}-~ecwc]/>uRmXw,ܷ#_X/ \oVmB*4s֬Yfˏwc}ߙ}\Y=v`!?/J/=6^GA~x׍܍.y]96VmnjwE@; J@Q#'?ު`#L}/N=go0fQVEg0HįO,X/_d5:vXOsi~TC-l#/˺.B6w8ݳp.-+:ז?COYdho?I_2o2gLFCCv;97T_\/L/:?D[oq=Պ 2G:j/w5) YwӬC{^jf l"dŏjMܒu8S?OL#Sձ?\̵#BL^?dqa-O j^-O~OM.:ւZϟMNwM{J|D'|ɖ3ԞӉѮZ_d_OsԴZ)r+jmtm]GJ_<ةVx`PD-yv_ol 2`d=ESI?].ќѶal3g۩ND`@h<Ǚ]M>tʎf;GH)}nmQ]~w*o`N6'E)|ы팆ʑeY]f\!.x74-8#˹shQxm'+Ug%,9^mh=yyr`]姭rKgօC;>z෷q|fήgBo]w%z[CɿlMNص~R37~.%U9^h}@~_GoaW֢ûow-8wgl3ּw9[8_1uz3x8{V 7EK{At/>emMs⍑BuF c yaQK&yIշ]WXVYʦ/ۊvqz[۪-ʖ'J=Ǿ2gwbxs# rؐzyt5JMvx;Cy 8_좙p)2dY_ۗ?IpH>)r^~Lͽv>'e˲e6FSy7U(#ߘ{U8C]]`aᆺm-wYeYL;puTG Zz2oFS9ǬEWxߏh?ϼ;l)[&72=3Gt.Ηl9K.e'Nv D;;!Vhv;GcKo <7Z̡҆tK  iiAC14R{*^uޜ[}KHޯFկ%Y-!Bxp]9B}o@c~ܰ%M!į!amM5o+6y2xǶsmΟ~6ч:~y+G+K64~o{՞S͏;mɗe-`c!Vzcۆjb-RfkvˣYe}srpe[9 'nvS)/:`vwm=;~Krߠ/ϡX9#-CI߉֫˓IɶT%)(UfmܡZ=̼u&0SA*_߰WƧ2M>球.${EWF׮ij]F>x1S'ΊMK~I򯪎6s,Y[3%!3e=ypV:F!Eݶ`ۮ2kUQ@9ׄ]Ol|{mmG 4_T_Jam|ZݡZE)`GCYmBvZ,P anr/Yb;nL7O^+R˛xiYS{"9I]+:~4W_i.:.uז#(q[9 銝lJ{0;;BqCt:!?W9re=O#EX[V{! 5ԥ]lպ@ )G'f\3ٷ?ݴ;_n[%^9 ~曯~vqC,E ]..Fl؁#^jڄvg95SUĩ\s'IjT+7˹d3Vo~WxxDvՃJon=GM\qyה+Ƕ֪n`3}-l_ =wjU`?suu!ɩgC]Z}onb;~rl#l_t:LJ+6i߸ɼB{XԫSչޠ]J8쿗-[vu{4G_]ձUزM3{w?潷VO |9lK(5al 7^{V TG]9S/7{T[ /{S*"+[ 7dOq?oۿ~ҟN}*Rǰ*FpjScJK+$+6МELo۹^Tp@h`jޗ sn z_eYmX2 1af1(n;^X{8k<*s;7nz߼.,"ݯ>=|o@.n?K\tAR@Ao.4UmɻOۤJH`H6&ܗ _Iۿ!kT0FxGt.Ζl9<1`'-ww]I+%```sЕ~ 80,ƛ^fs%6X:0Poo=hCڊn48>p~MNerzt` d nl@;\):E&X~cT@S`TߖT:9P:$ٕs 7̔ݻ^/wY_1DGo+vPx5WSݳ&\eP~W~u~FP6^]7s%weKhsD4A "h@<D ?C7IIIZl MNN;h4 W>%"""+++==)aaaW\QznƳU%f"++K選YTTTzz.?L&SXXXۙA "h@<D x4A "h@<D x4A "hASK{HG൦]|׎2ɢ(=(nL%Sz-޷y.v >ku/T$<߃=׽@||z( x_排yP3|">1H7P8x$,v>I2J!8GUM3id*^FK{E$5^4B2^@ EOT@AcB^„71 &m =/`( =b( =O`zE=9ʆp PP;J <3(=x xxP"vmʎx@ ֬YSL >e>A +\~~o÷{@<<"E{x%!P??%<#<o<P < ѩDR!|д(y_?#OƹO=/nէw9 ְ- Z3P2|a=yɂUNf3vd*Ňsj.kB9me)'~wz(~}={B uYf;vLK/{t~?pCsYV.?l۶MQӧ(= 6lXiEWPqfv+d9"HI蛌^j?. ;V,Z'QWZa+hBI$$ !ko;)ΆKM|vF߸Ơ4 B8e3bĈlYK-[YYY/^t2 111Z$I> 5hР+sfŢ*_׻7n-,پM崿<#z7/]s_sZxXXؕ+WU'' r;>]~jo;~艓ntzD7iJ3x!Dzz… 7oޜPR-ZL0AndhuK>D/GEEk%z\&)fEOk h6{v:]ZO>cw'Zoȩ[ppO<O(=G M]L?l?xTx!d0¿/r x4Aq?wPR¿BG<$-X CxbGʪD 'wx措ylxdp |(>4T<|`yl2VME4(6!Cax0>!@ | * |@J-#U&xQ2cAx@#(ذaC_ YF!P<>I<(v<>H4v<ʃ(3WvH@x@ux@x@]. 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Follow the links below to see their documentation. \describe{ \item{generics}{\code{\link[generics]{generate}}} }} distributional/man/dist_cauchy.Rd0000644000176200001440000000347314304316335016660 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_cauchy.R \name{dist_cauchy} \alias{dist_cauchy} \title{The Cauchy distribution} \usage{ dist_cauchy(location, scale) } \arguments{ \item{location, scale}{location and scale parameters.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} The Cauchy distribution is the student's t distribution with one degree of freedom. The Cauchy distribution does not have a well defined mean or variance. Cauchy distributions often appear as priors in Bayesian contexts due to their heavy tails. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X} be a Cauchy variable with mean \verb{location =} \eqn{x_0} and \code{scale} = \eqn{\gamma}. \strong{Support}: \eqn{R}, the set of all real numbers \strong{Mean}: Undefined. \strong{Variance}: Undefined. \strong{Probability density function (p.d.f)}: \deqn{ f(x) = \frac{1}{\pi \gamma \left[1 + \left(\frac{x - x_0}{\gamma} \right)^2 \right]} }{ f(x) = 1 / (\pi \gamma (1 + ((x - x_0) / \gamma)^2) } \strong{Cumulative distribution function (c.d.f)}: \deqn{ F(t) = \frac{1}{\pi} \arctan \left( \frac{t - x_0}{\gamma} \right) + \frac{1}{2} }{ F(t) = arctan((t - x_0) / \gamma) / \pi + 1/2 } \strong{Moment generating function (m.g.f)}: Does not exist. } \examples{ dist <- dist_cauchy(location = c(0, 0, 0, -2), scale = c(0.5, 1, 2, 1)) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } \seealso{ \link[stats:Cauchy]{stats::Cauchy} } distributional/man/dist_uniform.Rd0000644000176200001440000000357014304314270017055 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_uniform.R \name{dist_uniform} \alias{dist_uniform} \title{The Uniform distribution} \usage{ dist_uniform(min, max) } \arguments{ \item{min, max}{lower and upper limits of the distribution. Must be finite.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} A distribution with constant density on an interval. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X} be a Poisson random variable with parameter \code{lambda} = \eqn{\lambda}. \strong{Support}: \eqn{[a,b]}{[a,b]} \strong{Mean}: \eqn{\frac{1}{2}(a+b)} \strong{Variance}: \eqn{\frac{1}{12}(b-a)^2} \strong{Probability mass function (p.m.f)}: \deqn{ f(x) = \frac{1}{b-a} for x \in [a,b] }{ f(x) = \frac{1}{b-a} for x in [a,b] } \deqn{ f(x) = 0 otherwise }{ f(x) = 0 otherwise } \strong{Cumulative distribution function (c.d.f)}: \deqn{ F(x) = 0 for x < a }{ F(x) = 0 for x < a } \deqn{ F(x) = \frac{x - a}{b-a} for x \in [a,b] }{ F(x) = \frac{x - a}{b-a} for x in [a,b] } \deqn{ F(x) = 1 for x > b }{ F(x) = 1 for x > b } \strong{Moment generating function (m.g.f)}: \deqn{ E(e^{tX}) = \frac{e^{tb} - e^{ta}}{t(b-a)} for t \neq 0 }{ E(e^(tX)) = \frac{e^{tb} - e^{ta}}{t(b-a)} for t \neq 0 } \deqn{ E(e^{tX}) = 1 for t = 0 }{ E(e^(tX)) = 1 for t = 0 } } \examples{ dist <- dist_uniform(min = c(3, -2), max = c(5, 4)) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } \seealso{ \link[stats:Uniform]{stats::Uniform} } distributional/man/new_dist.Rd0000644000176200001440000000131114304316713016162 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{new_dist} \alias{new_dist} \title{Create a new distribution} \usage{ new_dist(..., class = NULL, dimnames = NULL) } \arguments{ \item{...}{Parameters of the distribution (named).} \item{class}{The class of the distribution for S3 dispatch.} \item{dimnames}{The names of the variables in the distribution (optional).} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#maturing}{\figure{lifecycle-maturing.svg}{options: alt='[Maturing]'}}}{\strong{[Maturing]}} Allows extension package developers to define a new distribution class compatible with the distributional package. } distributional/man/quantile.distribution.Rd0000644000176200001440000000125214304314270020706 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{quantile.distribution} \alias{quantile.distribution} \title{Distribution Quantiles} \usage{ \method{quantile}{distribution}(x, p, ..., log = FALSE) } \arguments{ \item{x}{The distribution(s).} \item{p}{The probability of the quantile.} \item{...}{Additional arguments passed to methods.} \item{log}{If \code{TRUE}, probabilities will be given as log probabilities.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Computes the quantiles of a distribution. } distributional/man/parameters.Rd0000644000176200001440000000134614304316335016521 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{parameters} \alias{parameters} \alias{parameters.distribution} \title{Extract the parameters of a distribution} \usage{ parameters(x, ...) \method{parameters}{distribution}(x, ...) } \arguments{ \item{x}{The distribution(s).} \item{...}{Additional arguments used by methods.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#experimental}{\figure{lifecycle-experimental.svg}{options: alt='[Experimental]'}}}{\strong{[Experimental]}} } \examples{ dist <- c( dist_normal(1:2), dist_poisson(3), dist_multinomial(size = c(4, 3), prob = list(c(0.3, 0.5, 0.2), c(0.1, 0.5, 0.4))) ) parameters(dist) } distributional/man/is_hdr.Rd0000644000176200001440000000035013703764147015632 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/hdr.R \name{is_hdr} \alias{is_hdr} \title{Is the object a hdr} \usage{ is_hdr(x) } \arguments{ \item{x}{An object.} } \description{ Is the object a hdr } distributional/man/dist_hypergeometric.Rd0000644000176200001440000000376114304314270020426 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_hypergeometric.R \name{dist_hypergeometric} \alias{dist_hypergeometric} \title{The Hypergeometric distribution} \usage{ dist_hypergeometric(m, n, k) } \arguments{ \item{m}{The number of type I elements available.} \item{n}{The number of type II elements available.} \item{k}{The size of the sample taken.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} To understand the HyperGeometric distribution, consider a set of \eqn{r} objects, of which \eqn{m} are of the type I and \eqn{n} are of the type II. A sample with size \eqn{k} (\eqn{k= "3.4") withAutoprint else force)(\{ # examplesIf} mean(dist) variance(dist) support(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) \dontshow{\}) # examplesIf} } \seealso{ \link[actuar:PoissonInverseGaussian]{actuar::PoissonInverseGaussian} } distributional/man/dist_lognormal.Rd0000644000176200001440000000443714304314270017373 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_lognormal.R \name{dist_lognormal} \alias{dist_lognormal} \title{The log-normal distribution} \usage{ dist_lognormal(mu = 0, sigma = 1) } \arguments{ \item{mu}{The mean (location parameter) of the distribution, which is the mean of the associated Normal distribution. Can be any real number.} \item{sigma}{The standard deviation (scale parameter) of the distribution. Can be any positive number.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} The log-normal distribution is a commonly used transformation of the Normal distribution. If \eqn{X} follows a log-normal distribution, then \eqn{\ln{X}} would be characteristed by a Normal distribution. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{Y} be a Normal random variable with mean \code{mu} = \eqn{\mu} and standard deviation \code{sigma} = \eqn{\sigma}. The log-normal distribution \eqn{X = exp(Y)} is characterised by: \strong{Support}: \eqn{R+}, the set of all real numbers greater than or equal to 0. \strong{Mean}: \eqn{e^(\mu + \sigma^2/2} \strong{Variance}: \eqn{(e^(\sigma^2)-1) e^(2\mu + \sigma^2} \strong{Probability density function (p.d.f)}: \deqn{ f(x) = \frac{1}{x\sqrt{2 \pi \sigma^2}} e^{-(\ln{x} - \mu)^2 / 2 \sigma^2} }{ f(x) = 1 / (x * sqrt(2 \pi \sigma^2)) exp(-(log(x) - \mu)^2 / (2 \sigma^2)) } \strong{Cumulative distribution function (c.d.f)}: The cumulative distribution function has the form \deqn{ F(x) = \Phi((\ln{x} - \mu)/\sigma) }{ F(x) = Phi((log(x) - \mu)/\sigma) } Where \eqn{Phi}{Phi} is the CDF of a standard Normal distribution, N(0,1). } \examples{ dist <- dist_lognormal(mu = 1:5, sigma = 0.1) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) # A log-normal distribution X is exp(Y), where Y is a Normal distribution of # the same parameters. So log(X) will produce the Normal distribution Y. log(dist) } \seealso{ \link[stats:Lognormal]{stats::Lognormal} } distributional/man/dist_poisson.Rd0000644000176200001440000000316514304314270017070 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_poisson.R \name{dist_poisson} \alias{dist_poisson} \title{The Poisson Distribution} \usage{ dist_poisson(lambda) } \arguments{ \item{lambda}{vector of (non-negative) means.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Poisson distributions are frequently used to model counts. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X} be a Poisson random variable with parameter \code{lambda} = \eqn{\lambda}. \strong{Support}: \eqn{\{0, 1, 2, 3, ...\}}{{0, 1, 2, 3, ...}} \strong{Mean}: \eqn{\lambda} \strong{Variance}: \eqn{\lambda} \strong{Probability mass function (p.m.f)}: \deqn{ P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!} }{ P(X = k) = \lambda^k e^(-\lambda) / k! } \strong{Cumulative distribution function (c.d.f)}: \deqn{ P(X \le k) = e^{-\lambda} \sum_{i = 0}^{\lfloor k \rfloor} \frac{\lambda^i}{i!} }{ P(X \le k) = e^(-\lambda) \sum_{i = 0}^k \lambda^i / i! } \strong{Moment generating function (m.g.f)}: \deqn{ E(e^{tX}) = e^{\lambda (e^t - 1)} }{ E(e^(tX)) = e^(\lambda (e^t - 1)) } } \examples{ dist <- dist_poisson(lambda = c(1, 4, 10)) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } \seealso{ \link[stats:Poisson]{stats::Poisson} } distributional/man/dist_negative_binomial.Rd0000644000176200001440000000404014304314270021043 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_negative_binomial.R \name{dist_negative_binomial} \alias{dist_negative_binomial} \title{The Negative Binomial distribution} \usage{ dist_negative_binomial(size, prob) } \arguments{ \item{size}{target for number of successful trials, or dispersion parameter (the shape parameter of the gamma mixing distribution). Must be strictly positive, need not be integer.} \item{prob}{probability of success in each trial. \code{0 < prob <= 1}.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} A generalization of the geometric distribution. It is the number of failures in a sequence of i.i.d. Bernoulli trials before a specified number of successes (\code{size}) occur. The probability of success in each trial is given by \code{prob}. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X} be a Negative Binomial random variable with success probability \code{prob} = \eqn{p} and the number of successes \code{size} = \eqn{r}. \strong{Support}: \eqn{\{0, 1, 2, 3, ...\}} \strong{Mean}: \eqn{\frac{p r}{1-p}} \strong{Variance}: \eqn{\frac{pr}{(1-p)^2}} \strong{Probability mass function (p.m.f)}: \deqn{ f(k) = {k + r - 1 \choose k} \cdot (1-p)^r p^k }{ f(k) = (k+r-1)!/(k!(r-1)!) (1-p)^r p^k } \strong{Cumulative distribution function (c.d.f)}: Too nasty, omitted. \strong{Moment generating function (m.g.f)}: \deqn{ \left(\frac{1-p}{1-pe^t}\right)^r, t < -\log p }{ \frac{(1-p)^r}{(1-pe^t)^r}, t < -\log p } } \examples{ dist <- dist_negative_binomial(size = 10, prob = 0.5) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) support(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } \seealso{ \link[stats:NegBinomial]{stats::NegBinomial} } distributional/man/median.distribution.Rd0000644000176200001440000000131214304314326020320 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{median.distribution} \alias{median.distribution} \title{Median of a probability distribution} \usage{ \method{median}{distribution}(x, na.rm = FALSE, ...) } \arguments{ \item{x}{The distribution(s).} \item{na.rm}{Unused, included for consistency with the generic function.} \item{...}{Additional arguments used by methods.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Returns the median (50th percentile) of a probability distribution. This is equivalent to \code{quantile(x, p=0.5)}. } distributional/man/dist_missing.Rd0000644000176200001440000000127314304316335017051 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_missing.R \name{dist_missing} \alias{dist_missing} \title{Missing distribution} \usage{ dist_missing(length = 1) } \arguments{ \item{length}{The number of missing distributions} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#maturing}{\figure{lifecycle-maturing.svg}{options: alt='[Maturing]'}}}{\strong{[Maturing]}} A placeholder distribution for handling missing values in a vector of distributions. } \examples{ dist <- dist_missing(3L) dist mean(dist) variance(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } distributional/man/dist_mixture.Rd0000644000176200001440000000115714304316336017077 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/mixture.R \name{dist_mixture} \alias{dist_mixture} \title{Create a mixture of distributions} \usage{ dist_mixture(..., weights = numeric()) } \arguments{ \item{...}{Distributions to be used in the mixture.} \item{weights}{The weight of each distribution passed to \code{...}.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#maturing}{\figure{lifecycle-maturing.svg}{options: alt='[Maturing]'}}}{\strong{[Maturing]}} } \examples{ dist_mixture(dist_normal(0, 1), dist_normal(5, 2), weights = c(0.3, 0.7)) } distributional/man/dist_percentile.Rd0000644000176200001440000000121314304316335017524 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_percentile.R \name{dist_percentile} \alias{dist_percentile} \title{Percentile distribution} \usage{ dist_percentile(x, percentile) } \arguments{ \item{x}{A list of values} \item{percentile}{A list of percentiles} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } \examples{ dist <- dist_normal() percentiles <- seq(0.01, 0.99, by = 0.01) x <- vapply(percentiles, quantile, double(1L), x = dist) dist_percentile(list(x), list(percentiles*100)) } distributional/man/hilo.Rd0000644000176200001440000000163114304316713015306 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/hilo.R \name{hilo} \alias{hilo} \title{Compute intervals} \usage{ hilo(x, ...) } \arguments{ \item{x}{Object to create hilo from.} \item{...}{Additional arguments used by methods.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Used to extract a specified prediction interval at a particular confidence level from a distribution. The numeric lower and upper bounds can be extracted from the interval using \verb{$lower} and \verb{$upper} as shown in the examples below. } \examples{ # 95\% interval from a standard normal distribution interval <- hilo(dist_normal(0, 1), 95) interval # Extract the individual quantities with `$lower`, `$upper`, and `$level` interval$lower interval$upper interval$level } distributional/man/dist_burr.Rd0000644000176200001440000000167514304314267016362 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_burr.R \name{dist_burr} \alias{dist_burr} \title{The Burr distribution} \usage{ dist_burr(shape1, shape2, rate = 1, scale = 1/rate) } \arguments{ \item{shape1, shape2, scale}{parameters. Must be strictly positive.} \item{rate}{an alternative way to specify the scale.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } \examples{ dist <- dist_burr(shape1 = c(1,1,1,2,3,0.5), shape2 = c(1,2,3,1,1,2)) dist \dontshow{if (requireNamespace("actuar", quietly = TRUE)) (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf} mean(dist) variance(dist) support(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) \dontshow{\}) # examplesIf} } \seealso{ \link[actuar:Burr]{actuar::Burr} } distributional/man/dist_inflated.Rd0000644000176200001440000000113014304316336017157 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/inflated.R \name{dist_inflated} \alias{dist_inflated} \title{Inflate a value of a probability distribution} \usage{ dist_inflated(dist, prob, x = 0) } \arguments{ \item{dist}{The distribution(s) to inflate.} \item{prob}{The added probability of observing \code{x}.} \item{x}{The value to inflate. The default of \code{x = 0} is for zero-inflation.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } distributional/man/new_support_region.Rd0000644000176200001440000000065314164717433020316 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/support.R \name{new_support_region} \alias{new_support_region} \title{Create a new support region vector} \usage{ new_support_region(x, limits = NULL) } \arguments{ \item{x}{A list of prototype vectors defining the distribution type.} \item{limits}{A list of value limits for the distribution.} } \description{ Create a new support region vector } distributional/man/dist_normal.Rd0000644000176200001440000000573014304314270016666 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_normal.R \name{dist_normal} \alias{dist_normal} \title{The Normal distribution} \usage{ dist_normal(mu = 0, sigma = 1, mean = mu, sd = sigma) } \arguments{ \item{mu, mean}{The mean (location parameter) of the distribution, which is also the mean of the distribution. Can be any real number.} \item{sigma, sd}{The standard deviation (scale parameter) of the distribution. Can be any positive number. If you would like a Normal distribution with \strong{variance} \eqn{\sigma^2}, be sure to take the square root, as this is a common source of errors.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} The Normal distribution is ubiquitous in statistics, partially because of the central limit theorem, which states that sums of i.i.d. random variables eventually become Normal. Linear transformations of Normal random variables result in new random variables that are also Normal. If you are taking an intro stats course, you'll likely use the Normal distribution for Z-tests and in simple linear regression. Under regularity conditions, maximum likelihood estimators are asymptotically Normal. The Normal distribution is also called the gaussian distribution. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X} be a Normal random variable with mean \code{mu} = \eqn{\mu} and standard deviation \code{sigma} = \eqn{\sigma}. \strong{Support}: \eqn{R}, the set of all real numbers \strong{Mean}: \eqn{\mu} \strong{Variance}: \eqn{\sigma^2} \strong{Probability density function (p.d.f)}: \deqn{ f(x) = \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-(x - \mu)^2 / 2 \sigma^2} }{ f(x) = 1 / sqrt(2 \pi \sigma^2) exp(-(x - \mu)^2 / (2 \sigma^2)) } \strong{Cumulative distribution function (c.d.f)}: The cumulative distribution function has the form \deqn{ F(t) = \int_{-\infty}^t \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-(x - \mu)^2 / 2 \sigma^2} dx }{ F(t) = integral_{-\infty}^t 1 / sqrt(2 \pi \sigma^2) exp(-(x - \mu)^2 / (2 \sigma^2)) dx } but this integral does not have a closed form solution and must be approximated numerically. The c.d.f. of a standard Normal is sometimes called the "error function". The notation \eqn{\Phi(t)} also stands for the c.d.f. of a standard Normal evaluated at \eqn{t}. Z-tables list the value of \eqn{\Phi(t)} for various \eqn{t}. \strong{Moment generating function (m.g.f)}: \deqn{ E(e^{tX}) = e^{\mu t + \sigma^2 t^2 / 2} }{ E(e^(tX)) = e^(\mu t + \sigma^2 t^2 / 2) } } \examples{ dist <- dist_normal(mu = 1:5, sigma = 3) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } \seealso{ \link[stats:Normal]{stats::Normal} } distributional/man/is-distribution.Rd0000644000176200001440000000123514304314326017501 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{is_distribution} \alias{is_distribution} \title{Test if the object is a distribution} \usage{ is_distribution(x) } \arguments{ \item{x}{An object.} } \value{ TRUE if the object inherits from the distribution class. } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} This function returns \code{TRUE} for distributions and \code{FALSE} for all other objects. } \examples{ dist <- dist_normal() is_distribution(dist) is_distribution("distributional") } distributional/man/dist_wrap.Rd0000644000176200001440000000333514304316335016352 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_wrap.R \name{dist_wrap} \alias{dist_wrap} \title{Create a distribution from p/d/q/r style functions} \usage{ dist_wrap(dist, ..., package = NULL) } \arguments{ \item{dist}{The name of the distribution used in the functions (name that is prefixed by p/d/q/r)} \item{...}{Named arguments used to parameterise the distribution.} \item{package}{The package from which the distribution is provided. If NULL, the calling environment's search path is used to find the distribution functions. Alternatively, an arbitrary environment can also be provided here.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#maturing}{\figure{lifecycle-maturing.svg}{options: alt='[Maturing]'}}}{\strong{[Maturing]}} If a distribution is not yet supported, you can vectorise p/d/q/r functions using this function. \code{dist_wrap()} stores the distributions parameters, and provides wrappers which call the appropriate p/d/q/r functions. Using this function to wrap a distribution should only be done if the distribution is not yet available in this package. If you need a distribution which isn't in the package yet, consider making a request at https://github.com/mitchelloharawild/distributional/issues. } \examples{ dist <- dist_wrap("norm", mean = 1:3, sd = c(3, 9, 2)) density(dist, 1) # dnorm() cdf(dist, 4) # pnorm() quantile(dist, 0.975) # qnorm() generate(dist, 10) # rnorm() library(actuar) dist <- dist_wrap("invparalogis", package = "actuar", shape = 2, rate = 2) density(dist, 1) # actuar::dinvparalogis() cdf(dist, 4) # actuar::pinvparalogis() quantile(dist, 0.975) # actuar::qinvparalogis() generate(dist, 10) # actuar::rinvparalogis() } distributional/man/dist_geometric.Rd0000644000176200001440000000354714304314267017366 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_geometric.R \name{dist_geometric} \alias{dist_geometric} \title{The Geometric Distribution} \usage{ dist_geometric(prob) } \arguments{ \item{prob}{probability of success in each trial. \code{0 < prob <= 1}.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} The Geometric distribution can be thought of as a generalization of the \code{\link[=dist_bernoulli]{dist_bernoulli()}} distribution where we ask: "if I keep flipping a coin with probability \code{p} of heads, what is the probability I need \eqn{k} flips before I get my first heads?" The Geometric distribution is a special case of Negative Binomial distribution. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X} be a Geometric random variable with success probability \code{p} = \eqn{p}. Note that there are multiple parameterizations of the Geometric distribution. \strong{Support}: 0 < p < 1, \eqn{x = 0, 1, \dots} \strong{Mean}: \eqn{\frac{1-p}{p}} \strong{Variance}: \eqn{\frac{1-p}{p^2}} \strong{Probability mass function (p.m.f)}: \deqn{ P(X = x) = p(1-p)^x, } \strong{Cumulative distribution function (c.d.f)}: \deqn{ P(X \le x) = 1 - (1-p)^{x+1} } \strong{Moment generating function (m.g.f)}: \deqn{ E(e^{tX}) = \frac{pe^t}{1 - (1-p)e^t} }{ E(e^{tX}) = \frac{pe^t}{1 - (1-p)e^t} } } \examples{ dist <- dist_geometric(prob = c(0.2, 0.5, 0.8)) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } \seealso{ \link[stats:Geometric]{stats::Geometric} } distributional/man/distributional-package.Rd0000644000176200001440000000267514151532232021005 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distributional-package.R \docType{package} \name{distributional-package} \alias{distributional} \alias{distributional-package} \title{distributional: Vectorised Probability Distributions} \description{ Vectorised distribution objects with tools for manipulating, visualising, and using probability distributions. Designed to allow model prediction outputs to return distributions rather than their parameters, allowing users to directly interact with predictive distributions in a data-oriented workflow. In addition to providing generic replacements for p/d/q/r functions, other useful statistics can be computed including means, variances, intervals, and highest density regions. } \seealso{ Useful links: \itemize{ \item \url{https://pkg.mitchelloharawild.com/distributional/} \item \url{https://github.com/mitchelloharawild/distributional} \item Report bugs at \url{https://github.com/mitchelloharawild/distributional/issues} } } \author{ \strong{Maintainer}: Mitchell O'Hara-Wild \email{mail@mitchelloharawild.com} (\href{https://orcid.org/0000-0001-6729-7695}{ORCID}) Authors: \itemize{ \item Matthew Kay (\href{https://orcid.org/0000-0001-9446-0419}{ORCID}) \item Alex Hayes (\href{https://orcid.org/0000-0002-4985-5160}{ORCID}) } Other contributors: \itemize{ \item Earo Wang (\href{https://orcid.org/0000-0001-6448-5260}{ORCID}) [contributor] } } \keyword{internal} distributional/man/dist_categorical.Rd0000644000176200001440000000450114304314267017654 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_categorical.R \name{dist_categorical} \alias{dist_categorical} \title{The Categorical distribution} \usage{ dist_categorical(prob, outcomes = NULL) } \arguments{ \item{prob}{A list of probabilities of observing each outcome category.} \item{outcomes}{The values used to represent each outcome.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Categorical distributions are used to represent events with multiple outcomes, such as what number appears on the roll of a dice. This is also referred to as the 'generalised Bernoulli' or 'multinoulli' distribution. The Cateogorical distribution is a special case of the \code{\link[=Multinomial]{Multinomial()}} distribution with \code{n = 1}. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X} be a Categorical random variable with probability parameters \code{p} = \eqn{\{p_1, p_2, \ldots, p_k\}}. The Categorical probability distribution is widely used to model the occurance of multiple events. A simple example is the roll of a dice, where \eqn{p = \{1/6, 1/6, 1/6, 1/6, 1/6, 1/6\}} giving equal chance of observing each number on a 6 sided dice. \strong{Support}: \eqn{\{1, \ldots, k\}}{{1, ..., k}} \strong{Mean}: \eqn{p} \strong{Variance}: \eqn{p \cdot (1 - p) = p \cdot q}{p (1 - p)} \strong{Probability mass function (p.m.f)}: \deqn{ P(X = i) = p_i }{ P(X = i) = p_i } \strong{Cumulative distribution function (c.d.f)}: The cdf() of a categorical distribution is undefined as the outcome categories aren't ordered. } \examples{ dist <- dist_categorical(prob = list(c(0.05, 0.5, 0.15, 0.2, 0.1), c(0.3, 0.1, 0.6))) dist generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) # The outcomes aren't ordered, so many statistics are not applicable. cdf(dist, 4) quantile(dist, 0.7) mean(dist) variance(dist) skewness(dist) kurtosis(dist) dist <- dist_categorical( prob = list(c(0.05, 0.5, 0.15, 0.2, 0.1), c(0.3, 0.1, 0.6)), outcomes = list(letters[1:5], letters[24:26]) ) generate(dist, 10) density(dist, "a") density(dist, "z", log = TRUE) } distributional/man/hdr.Rd0000644000176200001440000000060613703764147015143 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/hdr.R \name{hdr} \alias{hdr} \title{Compute highest density regions} \usage{ hdr(x, ...) } \arguments{ \item{x}{Object to create hilo from.} \item{...}{Additional arguments used by methods.} } \description{ Used to extract a specified prediction interval at a particular confidence level from a distribution. } distributional/man/dist_chisq.Rd0000644000176200001440000000437114304314267016513 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/dist_chisq.R \name{dist_chisq} \alias{dist_chisq} \title{The (non-central) Chi-Squared Distribution} \usage{ dist_chisq(df, ncp = 0) } \arguments{ \item{df}{degrees of freedom (non-negative, but can be non-integer).} \item{ncp}{non-centrality parameter (non-negative).} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} Chi-square distributions show up often in frequentist settings as the sampling distribution of test statistics, especially in maximum likelihood estimation settings. } \details{ We recommend reading this documentation on \url{https://pkg.mitchelloharawild.com/distributional/}, where the math will render nicely. In the following, let \eqn{X} be a \eqn{\chi^2} random variable with \code{df} = \eqn{k}. \strong{Support}: \eqn{R^+}, the set of positive real numbers \strong{Mean}: \eqn{k} \strong{Variance}: \eqn{2k} \strong{Probability density function (p.d.f)}: \deqn{ f(x) = \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-(x - \mu)^2 / 2 \sigma^2} }{ f(x) = 1 / (2 \pi \sigma^2) exp(-(x - \mu)^2 / (2 \sigma^2)) } \strong{Cumulative distribution function (c.d.f)}: The cumulative distribution function has the form \deqn{ F(t) = \int_{-\infty}^t \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-(x - \mu)^2 / 2 \sigma^2} dx }{ F(t) = integral_{-\infty}^t 1 / (2 \pi \sigma^2) exp(-(x - \mu)^2 / (2 \sigma^2)) dx } but this integral does not have a closed form solution and must be approximated numerically. The c.d.f. of a standard normal is sometimes called the "error function". The notation \eqn{\Phi(t)} also stands for the c.d.f. of a standard normal evaluated at \eqn{t}. Z-tables list the value of \eqn{\Phi(t)} for various \eqn{t}. \strong{Moment generating function (m.g.f)}: \deqn{ E(e^{tX}) = e^{\mu t + \sigma^2 t^2 / 2} }{ E(e^(tX)) = e^(\mu t + \sigma^2 t^2 / 2) } } \examples{ dist <- dist_chisq(df = c(1,2,3,4,6,9)) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7) } \seealso{ \link[stats:Chisquare]{stats::Chisquare} } distributional/man/new_hdr.Rd0000644000176200001440000000117414151532232015777 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/hdr.R \name{new_hdr} \alias{new_hdr} \title{Construct hdr intervals} \usage{ new_hdr( lower = list_of(.ptype = double()), upper = list_of(.ptype = double()), size = double() ) } \arguments{ \item{lower, upper}{A list of numeric vectors specifying the region's lower and upper bounds.} \item{size}{A numeric vector specifying the coverage size of the region.} } \value{ A "hdr" vector } \description{ Construct hdr intervals } \examples{ new_hdr(lower = list(1, c(3,6)), upper = list(10, c(5, 8)), size = c(80, 95)) } \author{ Mitchell O'Hara-Wild } distributional/man/likelihood.Rd0000644000176200001440000000140214304316335016472 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/distribution.R \name{likelihood} \alias{likelihood} \alias{likelihood.distribution} \alias{log_likelihood} \title{The (log) likelihood of a sample matching a distribution} \usage{ likelihood(x, ...) \method{likelihood}{distribution}(x, sample, ..., log = FALSE) log_likelihood(x, ...) } \arguments{ \item{x}{The distribution(s).} \item{...}{Additional arguments used by methods.} \item{sample}{A list of sampled values to compare to distribution(s).} \item{log}{If \code{TRUE}, the log-likelihood will be computed.} } \description{ \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#stable}{\figure{lifecycle-stable.svg}{options: alt='[Stable]'}}}{\strong{[Stable]}} } distributional/DESCRIPTION0000644000176200001440000000421714560702732015026 0ustar liggesusersPackage: distributional Title: Vectorised Probability Distributions Version: 0.4.0 Authors@R: c(person(given = "Mitchell", family = "O'Hara-Wild", role = c("aut", "cre"), email = "mail@mitchelloharawild.com", comment = c(ORCID = "0000-0001-6729-7695")), person(given = "Matthew", family = "Kay", role = c("aut"), comment = c(ORCID = "0000-0001-9446-0419")), person(given = "Alex", family = "Hayes", role = c("aut"), comment = c(ORCID = "0000-0002-4985-5160")), person(given = "Earo", family = "Wang", role = c("ctb"), comment = c(ORCID = "0000-0001-6448-5260"))) Description: Vectorised distribution objects with tools for manipulating, visualising, and using probability distributions. Designed to allow model prediction outputs to return distributions rather than their parameters, allowing users to directly interact with predictive distributions in a data-oriented workflow. In addition to providing generic replacements for p/d/q/r functions, other useful statistics can be computed including means, variances, intervals, and highest density regions. License: GPL-3 Imports: vctrs (>= 0.3.0), rlang (>= 0.4.5), generics, stats, numDeriv, utils, lifecycle Suggests: testthat (>= 2.1.0), covr, mvtnorm, actuar (>= 2.0.0), ggdist, ggplot2 RdMacros: lifecycle URL: https://pkg.mitchelloharawild.com/distributional/, https://github.com/mitchelloharawild/distributional BugReports: https://github.com/mitchelloharawild/distributional/issues Encoding: UTF-8 Language: en-GB RoxygenNote: 7.2.3 NeedsCompilation: no Packaged: 2024-02-07 10:31:01 UTC; mitchell Author: Mitchell O'Hara-Wild [aut, cre] (), Matthew Kay [aut] (), Alex Hayes [aut] (), Earo Wang [ctb] () Maintainer: Mitchell O'Hara-Wild Repository: CRAN Date/Publication: 2024-02-07 13:30:02 UTC distributional/tests/0000755000176200001440000000000013703764147014464 5ustar liggesusersdistributional/tests/testthat/0000755000176200001440000000000014560702732016316 5ustar liggesusersdistributional/tests/testthat/test-dist-beta.R0000644000176200001440000000116313703764147021301 0ustar liggesuserstest_that("Beta distribution", { dist <- dist_beta(3, 4) expect_equal(format(dist), "Beta(3, 4)") # quantiles expect_equal(quantile(dist, 0.1), qbeta(0.1, 3, 4)) expect_equal(quantile(dist, 0.5), qbeta(0.5, 3, 4)) # pdf expect_equal(density(dist, 0), dbeta(0, 3, 4)) expect_equal(density(dist, 3), dbeta(3, 3, 4)) # cdf expect_equal(cdf(dist, 0), pbeta(0, 3, 4)) expect_equal(cdf(dist, 3), pbeta(3, 3, 4)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4)), 0.4, tolerance = 1e-3) # stats expect_equal(mean(dist), 3/(3+4)) expect_equal(variance(dist), 3*4/((3+4)^2*(3+4+1))) }) distributional/tests/testthat/test-dist-uniform.R0000644000176200001440000000125013703764147022042 0ustar liggesuserstest_that("Uniform distribution", { dist <- dist_uniform(-2, 4) expect_equal(format(dist), "U(-2, 4)") # quantiles expect_equal(quantile(dist, 0.1), stats::qunif(0.1, -2, 4)) expect_equal(quantile(dist, 0.5), stats::qunif(0.5, -2, 4)) # pdf expect_equal(density(dist, 0), stats::dunif(0, -2, 4)) expect_equal(density(dist, 3), stats::dunif(3, -2, 4)) # cdf expect_equal(cdf(dist, 0), stats::punif(0, -2, 4)) expect_equal(cdf(dist, 3), stats::punif(3, -2, 4)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4246)), 0.4246, tolerance = 1e-3) # stats expect_equal(mean(dist), 0.5*(-2 + 4)) expect_equal(variance(dist), (4+2)^2/12) }) distributional/tests/testthat/test-issues.R0000644000176200001440000000034614151532232020724 0ustar liggesuserstest_that("is.na() on [[1]] (#29)", { x <- c(dist_normal(0,1), NA) expect_equal( is.na(x), c(FALSE, TRUE) ) expect_equal( is.na(x[[1]]), FALSE ) expect_equal( is.na(x[[2]]), TRUE ) }) distributional/tests/testthat/test-dist-multinomial.R0000644000176200001440000000123114304205073022676 0ustar liggesuserstest_that("Multinomial distribution", { p <- c(0.3, 0.5, 0.2) dist <- dist_multinomial(size = 4, prob = list(p)) dimnames(dist) <- c("a", "b", "c") expect_equal(format(dist), "Multinomial(4)[3]") # quantiles # pdf expect_equal(density(dist, cbind(1, 2, 1)), dmultinom(c(1, 2, 1), 4, p)) # cdf # F(Finv(a)) ~= a # stats expect_equal( mean(dist), matrix(c(1.2, 2, 0.8), nrow = 1, dimnames = list(NULL, c("a", "b", "c"))) ) expect_equal( covariance(dist), list( matrix( c(0.84, -0.6, -0.24, -0.6, 1, -0.4, -0.24, -0.4, 0.64), nrow = 3, dimnames = list(NULL, c("a", "b", "c")) ) ) ) }) distributional/tests/testthat/test-mixture.R0000644000176200001440000000373014406341620021110 0ustar liggesuserstest_that("Mixture of Normals", { dist <- dist_mixture(dist_normal(0, 1), dist_normal(10, 4), weights = c(0.5, 0.5)) # format expect_equal(format(dist), "mixture(n=2)") # quantiles expect_equal(quantile(dist, 0.5), 2, tolerance = 1e-5) expect_equal(quantile(dist, 0.1), -0.854, tolerance = 1e-3) # pdf expect_equal(density(dist, 0), 0.5*dnorm(0) + 0.5*dnorm(0, 10, 4)) expect_equal(density(dist, 3), 0.5*dnorm(3) + 0.5*dnorm(3, 10, 4)) # cdf expect_equal(cdf(dist, 0), 0.5*pnorm(0) + 0.5*pnorm(0, 10, 4)) expect_equal(cdf(dist, 3), 0.5*pnorm(3) + 0.5*pnorm(3, 10, 4)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.5)), 0.5, tolerance = 1e-6) expect_equal(mean(dist), 5) expect_equal(variance(dist), 33.5) }) test_that("Mixture of different distributions", { dist <- dist_mixture(dist_normal(0, 1), dist_student_t(10), weights = c(0.3, 0.7)) # format expect_equal(format(dist), "mixture(n=2)") # quantiles expect_equal(quantile(dist, 0.5), 0, tolerance = 1e-5) expect_equal(quantile(dist, 0.1), -1.343, tolerance = 1e-3) # pdf expect_equal(density(dist, 0), 0.3*dnorm(0) + 0.7*dt(0, 10)) expect_equal(density(dist, 3), 0.3*dnorm(3) + 0.7*dt(3, 10)) # cdf expect_equal(cdf(dist, 0), 0.3*pnorm(0) + 0.7*pt(0, 10)) expect_equal(cdf(dist, 3), 0.3*pnorm(3) + 0.7*pt(3, 10)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.5)), 0.5, tolerance = 1e-6) expect_equal(mean(dist), 0) expect_equal(variance(dist), 1.175) }) test_that("Mixture of point masses", { dist <- dist_mixture(dist_degenerate(1), dist_degenerate(2), dist_degenerate(3), weights = c(0.1, 0.2, 0.7)) # format expect_equal(format(dist), "mixture(n=3)") # quantiles expect_equal(quantile(dist, c(0, 0.1, 0.3, 1))[[1]], c(1, 1:3), tolerance = .Machine$double.eps^0.25) # pmf expect_equal(density(dist, 1:3)[[1]], c(0.1, 0.2, 0.7)) #cdf expect_equal(cdf(dist, 1:3)[[1]], c(0.1, 0.3, 1)) #mean expect_equal(mean(dist), 2.6) }) distributional/tests/testthat/test-truncated.R0000644000176200001440000000410213703764147021412 0ustar liggesuserstest_that("Truncated Normal distributions", { dist <- dist_truncated(dist_normal(0, 1), -5, 5) # format expect_equal(format(dist), sprintf("%s[-5,5]", format(dist_normal(0,1)))) # quantiles expect_equal( quantile(dist, 0.1), -1.28155025885944 #dput(extraDistr::qtnorm(0.1, 0, 1, -5, 5)) ) expect_equal( quantile(dist, 0.5), -1.39145821233588e-16 #dput(extraDistr::qtnorm(0.5, 0, 1, -5, 5)) ) # pdf expect_equal( density(dist, 0), 0.398942509116427, #dput(extraDistr::dtnorm(0, 0, 1, -5, 5)) ) expect_equal( density(dist, 3), 0.00443185095273209, #dput(extraDistr::dtnorm(3, 0, 1, -5, 5)) ) # cdf expect_equal(cdf(dist, 0), 0.5) expect_equal( cdf(dist, 3), 0.998650387846205, #dput(extraDistr::ptnorm(3, 0, 1, -5, 5)) ) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.3)), 0.3, tolerance = 1e-6) # stats # expect_equal(mean(dist), ???) # expect_equal(variance(dist), ???) }) test_that("Truncated Binomial distributions", { dist <- dist_truncated(dist_binomial(100, 0.83), 76, 86) # format expect_equal(format(dist), sprintf("%s[76,86]", format(dist_binomial(100,0.83)))) # quantiles expect_equal( quantile(dist, 0.1), 79 #dput(extraDistr::qtbinom(0.1, 100, 0.83, 76, 86)) ) expect_equal( quantile(dist, 0.5), 82 #dput(extraDistr::qtbinom(0.5, 100, 0.83, 76, 86)) ) # pdf expect_equal(density(dist, 75), 0) expect_equal(density(dist, 87), 0) expect_equal( density(dist, 80), 0.094154977726162, #dput(extraDistr::dtbinom(80, 100, 0.83, 76, 86)) ) expect_equal( density(dist, 85), 0.123463609708811, #dput(extraDistr::dtbinom(85, 100, 0.83, 76, 86)) ) # cdf expect_equal(cdf(dist, 0), 0) expect_equal(cdf(dist, 76), 0) expect_equal(cdf(dist, 86), 1) expect_equal( cdf(dist, 80), 0.259185477677455, #dput(extraDistr::ptbinom(80, 100, 0.83, 76, 86)) ) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.372)), 0.372, tolerance = 1e-3) # stats # expect_equal(mean(dist), ???) # expect_equal(variance(dist), ???) }) distributional/tests/testthat/test-dist_categorical.R0000644000176200001440000000114314406341620022707 0ustar liggesuserstest_that("Categorical distribution", { dist <- dist_categorical(list(c(0.4, 0.2, 0.3, 0.1))) expect_equal(format(dist), "Categorical[4]") # quantiles expect_true(all(is.na(quantile(dist, 0.5)))) expect_true(all(is.na(quantile(dist, 0.2)))) # pdf expect_equal(density(dist, -1), NA_real_) expect_equal(density(dist, 0), NA_real_) expect_equal(density(dist, 1), 0.4) expect_equal(density(dist, 2), 0.2) expect_equal(density(dist, 5), NA_real_) # cdf expect_true(all(is.na(cdf(dist, 1)))) # stats expect_true(all(is.na(mean(dist)))) expect_true(all(is.na(variance(dist)))) }) distributional/tests/testthat/test-dist-logistic.R0000644000176200001440000000124413703764147022203 0ustar liggesuserstest_that("Logistic distribution", { dist <- dist_logistic(5, 2) expect_equal(format(dist), "Logistic(5, 2)") # quantiles expect_equal(quantile(dist, 0.1), stats::qlogis(0.1, 5, 2)) expect_equal(quantile(dist, 0.5), stats::qlogis(0.5, 5, 2)) # pdf expect_equal(density(dist, 0), stats::dlogis(0, 5, 2)) expect_equal(density(dist, 3), stats::dlogis(3, 5, 2)) # cdf expect_equal(cdf(dist, 0), stats::plogis(0, 5, 2)) expect_equal(cdf(dist, 3), stats::plogis(3, 5, 2)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4246)), 0.4246, tolerance = 1e-3) # stats expect_equal(mean(dist), 5) expect_equal(variance(dist), (2*pi)^2/3) }) distributional/tests/testthat/test-dist-studentised-range.R0000644000176200001440000000101213703764147024004 0ustar liggesuserstest_that("Studentized Range distribution", { dist <- dist_studentized_range(6, 5, 1) expect_equal(format(dist), "StudentizedRange(6, 5, 1)") # quantiles expect_equal(quantile(dist, 0.1), stats::qtukey(0.1, 6, 5, 1)) expect_equal(quantile(dist, 0.5), stats::qtukey(0.5, 6, 5, 1)) # pdf # cdf expect_equal(cdf(dist, 0), stats::ptukey(0, 6, 5, 1)) expect_equal(cdf(dist, 3), stats::ptukey(3, 6, 5, 1)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4246)), 0.4246, tolerance = 1e-3) }) distributional/tests/testthat/test-dist-poisson-inverse-gaussian.R0000644000176200001440000000145614151532232025330 0ustar liggesuserstest_that("Poisson Inverse Gaussian distribution", { dist <- dist_poisson_inverse_gaussian(0.1, 0.8) expect_equal(format(dist), "PIG(0.1, 0.8)") # Require package installed skip_if_not_installed("actuar", "2.0.0") # quantiles expect_equal(quantile(dist, 0.1), actuar::qpig(0.1, 0.1, 0.8)) expect_equal(quantile(dist, 0.5), actuar::qpig(0.5, 0.1, 0.8)) # pdf expect_equal(density(dist, 0), actuar::dpig(0, 0.1, 0.8)) expect_equal(density(dist, 3), actuar::dpig(3, 0.1, 0.8)) # cdf expect_equal(cdf(dist, 0), actuar::ppig(0, 0.1, 0.8)) expect_equal(cdf(dist, 3), actuar::ppig(3, 0.1, 0.8)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.994)), 0.994, tolerance = 1e-3) # stats expect_equal(mean(dist), 0.1) expect_equal(variance(dist), 0.1/0.8*(0.1^2 + 0.8)) }) distributional/tests/testthat/test-dist-multivariate-normal.R0000644000176200001440000000246014304205073024345 0ustar liggesuserstest_that("Multivariate normal distribution", { mu <- c(1,2) sigma <- matrix(c(4,2,2,3), ncol=2) dist <- dist_multivariate_normal(mu = list(mu), sigma = list(sigma)) dimnames(dist) <- c("a", "b") expect_equal(format(dist), "MVN[2]") # stats expect_equal( mean(dist), matrix(c(1,2), nrow = 1, dimnames = list(NULL, c("a", "b"))) ) expect_equal(covariance(dist), list(`colnames<-`(sigma, dimnames(dist)))) # quantiles expect_equal( quantile(dist, 0.1), matrix(c(qnorm(0.1, mu[1], sqrt(sigma[1,1])), qnorm(0.1, mu[2], sqrt(sigma[2,2]))), nrow = 1, dimnames = list(NULL, c("a", "b"))) ) skip_if_not_installed("mvtnorm") expect_equivalent(quantile(dist, 0.1, type = "equicoordinate"), mvtnorm::qmvnorm(0.1, mean = mu, sigma = sigma)$quantile) # pdf expect_equal(density(dist, cbind(1, 2)), mvtnorm::dmvnorm(c(1, 2), mean = mu, sigma = sigma)) expect_equal(density(dist, cbind(-3, 4)), mvtnorm::dmvnorm(c(-3, 4), mean = mu, sigma = sigma)) # cdf expect_equivalent(cdf(dist, cbind(1, 2)), mvtnorm::pmvnorm(upper = c(1,2), mean = mu, sigma = sigma)) expect_equivalent(cdf(dist, cbind(-3, 4)), mvtnorm::pmvnorm(c(-3, 4), mean = mu, sigma = sigma)) # F(Finv(a)) ~= a # expect_equal(cdf(dist, list(as.numeric(quantile(dist, 0.53)))), 0.53, tolerance = 1e-3) }) distributional/tests/testthat/test-apply.R0000644000176200001440000001312014304205073020530 0ustar liggesuserstest_that("Recycling rules and output for applying multiple inputs over multiple univariate distributions", { # is a distribution vector of length 10 dist <- dist_named <- dist_normal(1:10, 1:10) dimnames(dist_named) <- "name" # p = 0.5: apply p across all elements of (recycling p onto ) # Returns a vector of length 10 expect_equal( quantile(dist, 0.5), qnorm(0.5, 1:10, 1:10) ) expect_equal( quantile(dist_named, 0.5), qnorm(0.5, 1:10, 1:10) ) # p = c(0.5, 0.9): Cannot recycle p (length 2) onto (length 10) # Returns a list containing values for each p. expect_equal( quantile(dist, c(0.5, 0.9)), mapply({function(mean, sd) qnorm(c(0.5, 0.9), mean, sd)}, mean = 1:10, sd = 1:10, SIMPLIFY = FALSE) ) expect_equal( quantile(dist_named, c(0.5, 0.9)), mapply({function(mean, sd) qnorm(c(0.5, 0.9), mean, sd)}, mean = 1:10, sd = 1:10, SIMPLIFY = FALSE) ) # p = ppoints(10): apply each p to each element of (no recycling) # Returns a list for each distribution with the 10 quantiles. expect_equal( quantile(dist, ppoints(10)), mapply({function(mean, sd) qnorm(ppoints(10), mean, sd)}, mean = 1:10, sd = 1:10, SIMPLIFY = FALSE) ) expect_equal( quantile(dist_named, ppoints(10)), mapply({function(mean, sd) qnorm(ppoints(10), mean, sd)}, mean = 1:10, sd = 1:10, SIMPLIFY = FALSE) ) # p = list(0.5): equivalent to p = 0.5, but returns a list output # Returns a tibble with 1 vector column of length 10 expect_equal( quantile(dist, list(a = 0.5)), new_data_frame(list(a = quantile(dist, 0.5))) ) expect_equal( quantile(dist_named, list(a = 0.5)), new_data_frame(list(a = quantile(dist, 0.5))) ) # p = list(c(0.5, 0.9)): # Cannot recycle p[[1]] (length 2) onto (length 10) # Returns an error. expect_error( quantile(dist, list(a = c(0.5, 0.9))), "Cannot recycle input" ) expect_error( quantile(dist_named, list(a = c(0.5, 0.9))), "Cannot recycle input" ) # p = list(p1, 0.5): equivalent to df(quantile(, p1), quantile(, 0.5)). # Returns a tibble with 2 vector columns of length 10 # Names of p are used in output. expect_equal( quantile(dist, list(a=ppoints(10), b=0.5)), new_data_frame(list(a = qnorm(ppoints(10), 1:10, 1:10), b = quantile(dist, 0.5))) ) expect_equal( quantile(dist_named, list(a=ppoints(10), b=0.5)), new_data_frame(list(a = qnorm(ppoints(10), 1:10, 1:10), b = quantile(dist, 0.5))) ) }) test_that("Recycling rules and output for applying multiple inputs over multiple multivariate distributions", { # is a bivariate distribution vector of length 2 dist <- dist_named <- dist_multivariate_normal(mu = list(c(1,2), c(3,5)), sigma = list(matrix(c(4,2,2,3), ncol=2), matrix(c(5,1,1,4), ncol=2))) dimnames(dist_named) <- c("a", "b") expect_equal( quantile(dist, 0.5), matrix(c(1,3,2,5), nrow = 2) ) expect_equal( quantile(dist_named, 0.5), matrix(c(1,3,2,5), nrow = 2, dimnames = list(NULL, c("a", "b"))) ) expect_equal( quantile(dist, c(0.5, 0.9)), list(matrix(c(1, 3.5631031310892, 2, 4.21971242404268), ncol = 2), matrix(c(3, 5.86563641722901, 5, 7.5631031310892), ncol = 2)) ) expect_equal( quantile(dist_named, c(0.5, 0.9)), list(matrix(c(1, 3.5631031310892, 2, 4.21971242404268), ncol = 2, dimnames = list(NULL, c("a", "b"))), matrix(c(3, 5.86563641722901, 5, 7.5631031310892), ncol = 2, dimnames = list(NULL, c("a", "b")))) ) expect_equal( quantile(dist, c(0.5, 0.9, 0.95)), list( matrix(c(1, 3.5631031310892, 4.28970725390294, 2, 4.21971242404268, 4.84897005289389), ncol = 2), matrix(c(3, 5.86563641722901, 6.67800452290057, 5, 7.5631031310892, 8.28970725390294), ncol = 2) ) ) expect_equal( quantile(dist_named, c(0.5, 0.9, 0.95)), list( matrix(c(1, 3.5631031310892, 4.28970725390294, 2, 4.21971242404268, 4.84897005289389), ncol = 2, dimnames = list(NULL, c("a","b"))), matrix(c(3, 5.86563641722901, 6.67800452290057, 5, 7.5631031310892, 8.28970725390294), ncol = 2, dimnames = list(NULL, c("a", "b"))) ) ) expect_equal( quantile(dist, list(single = 0.5, varied = c(0.8, 0.3))), new_data_frame( list(single = quantile(dist, 0.5), varied = rbind(quantile(dist[1], 0.8), quantile(dist[2], 0.3))) ) ) expect_equal( quantile(dist_named, list(single = 0.5, varied = c(0.8, 0.3))), new_data_frame( list(single = quantile(dist_named, 0.5), varied = rbind(quantile(dist_named[1], 0.8), quantile(dist_named[2], 0.3))) ) ) expect_equal( density(dist, cbind(2, 3)), c(0.046649277604197, 0.0215708514518913) ) expect_equal( density(dist_named, cbind(2, 3)), c(0.046649277604197, 0.0215708514518913) ) expect_equal( mean(dist), matrix(c(1,3,2,5), nrow = 2) ) expect_equal( mean(dist_named), matrix(c(1,3,2,5), nrow = 2, dimnames = list(NULL, c("a", "b"))) ) expect_equal( covariance(dist), list( matrix(c(4,2,2,3), nrow = 2), matrix(c(5,1,1,4), nrow = 2) ) ) expect_equal( covariance(dist_named), list( matrix(c(4,2,2,3), nrow = 2, dimnames = list(NULL, c("a", "b"))), matrix(c(5,1,1,4), nrow = 2, dimnames = list(NULL, c("a", "b"))) ) ) }) distributional/tests/testthat/test-distribution.R0000644000176200001440000000116714165413625022143 0ustar liggesuserstest_that("is_distribution", { expect_false(is_distribution(iris)) expect_true(is_distribution(dist_normal())) expect_false(is_distribution(NULL)) expect_false(is_distribution(0)) df <- data.frame(a = 1:10, b = dist_poisson(1:10), c = dist_normal(1:10)) expect_true(all(sapply(df, is_distribution) == c(FALSE, TRUE, TRUE))) }) test_that("variance() works correctly on vectors/matrices of different dimension", { x = 1:8 expect_equal(variance(x), 6) expect_equal(variance(matrix(x, nrow = 2)), rep(0.5, 4)) }) test_that("variance() throws an error on non-numeric objects", { expect_error(variance("foo")) }) distributional/tests/testthat/test-dist-gumbel.R0000644000176200001440000000146014151532232021623 0ustar liggesuserstest_that("Gumbel distribution", { dist <- dist_gumbel(1, 2) expect_equal(format(dist), "Gumbel(1, 2)") # Require package installed skip_if_not_installed("actuar", "2.0.0") # quantiles expect_equal(quantile(dist, 0.1), actuar::qgumbel(0.1, 1, 2)) expect_equal(quantile(dist, 0.5), actuar::qgumbel(0.5, 1, 2)) # pdf expect_equal(density(dist, 0), actuar::dgumbel(0, 1, 2)) expect_equal(density(dist, 3), actuar::dgumbel(3, 1, 2)) # cdf expect_equal(cdf(dist, 0), actuar::pgumbel(0, 1, 2)) expect_equal(cdf(dist, 3), actuar::pgumbel(3, 1, 2)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4)), 0.4, tolerance = 1e-3) # stats expect_equal(mean(dist), actuar::mgumbel(1, 1, 2)) expect_equal(variance(dist), actuar::mgumbel(2, 1, 2) - actuar::mgumbel(1, 1, 2)^2) }) distributional/tests/testthat/test-dist-geometric.R0000644000176200001440000000124413703764147022344 0ustar liggesuserstest_that("Geometric distribution", { dist <- dist_geometric(0.4) expect_equal(format(dist), "Geometric(0.4)") # quantiles expect_equal(quantile(dist, 0.6), stats::qgeom(0.6, 0.4)) expect_equal(quantile(dist, 0.9), stats::qgeom(0.9, 0.4)) # pdf expect_equal(density(dist, 0), stats::dgeom(0, 0.4)) expect_equal(density(dist, 5), stats::dgeom(5, 0.4)) # cdf expect_equal(cdf(dist, 0), stats::pgeom(0, 0.4)) expect_equal(cdf(dist, 10), stats::pgeom(10, 0.4)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.64)), 0.64, tolerance = 1e-3) # stats expect_equal(mean(dist), 1/0.4 - 1) expect_equal(variance(dist), 1/0.4^2 - 1/0.4) }) distributional/tests/testthat/test-dist-sample.R0000644000176200001440000000131414406341620021631 0ustar liggesuserstest_that("Emperical/sample distribution", { x <- generate(dist_normal(0, 1), 100) dist <- dist_sample(x) expect_equal(format(dist), "sample[100]") # quantiles expect_equal(quantile(dist, 0.6), unname(quantile(x[[1]], 0.6))) expect_equal(quantile(dist, 0.24), unname(quantile(x[[1]], 0.24))) # pdf # cdf # F(Finv(a)) ~= a # stats expect_equal(mean(dist), mean(x[[1]])) expect_equal(median(dist), median(x[[1]])) expect_equal(median(dist[[1]]), median(x[[1]])) expect_equal(variance(dist), var(x[[1]])) # transform expect_equal( dist, dist + 1 - 1 ) }) test_that("CDF of degenerate dist_sample() is correct", { expect_equal(cdf(dist_sample(list(2)), 2)[[1]], 1) }) distributional/tests/testthat/test-dist-burr.R0000644000176200001440000000143614151532232021325 0ustar liggesuserstest_that("Burr distribution", { dist <- dist_burr(2, 3) expect_equal(format(dist), "Burr12(2, 3, 1)") # Require package installed skip_if_not_installed("actuar", "2.0.0") # quantiles expect_equal(quantile(dist, 0.1), actuar::qburr(0.1, 2, 3)) expect_equal(quantile(dist, 0.5), actuar::qburr(0.5, 2, 3)) # pdf expect_equal(density(dist, 0), actuar::dburr(0, 2, 3)) expect_equal(density(dist, 3), actuar::dburr(3, 2, 3)) # cdf expect_equal(cdf(dist, 0), actuar::pburr(0, 2, 3)) expect_equal(cdf(dist, 3), actuar::pburr(3, 2, 3)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4)), 0.4, tolerance = 1e-3) # stats expect_equal(mean(dist), actuar::mburr(1, 2, 3)) expect_equal(variance(dist), actuar::mburr(2, 2, 3) - actuar::mburr(1, 2, 3)^2) }) distributional/tests/testthat/test-dist-negative-binomial.R0000644000176200001440000000134313703764147023760 0ustar liggesuserstest_that("Negative Binomial distribution", { dist <- dist_negative_binomial(10, 0.4) expect_equal(format(dist), "NB(10, 0.4)") # quantiles expect_equal(quantile(dist, 0.6), stats::qnbinom(0.6, 10, 0.4)) expect_equal(quantile(dist, 0.61), stats::qnbinom(0.61, 10, 0.4)) # pdf expect_equal(density(dist, 0), stats::dnbinom(0, 10, 0.4)) expect_equal(density(dist, 1), stats::dnbinom(1, 10, 0.4)) # cdf expect_equal(cdf(dist, 0), stats::pnbinom(0, 10, 0.4)) expect_equal(cdf(dist, 1), stats::pnbinom(1, 10, 0.4)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.6358)), 0.6358, tolerance = 1e-3) # stats expect_equal(mean(dist), 0.6*10/(1-0.6)) expect_equal(variance(dist), 0.6*10/(1-0.6)^2) }) distributional/tests/testthat/test-hilo.R0000644000176200001440000000112213703764147020353 0ustar liggesuserstest_that("hilo", { # defaults hl <- new_hilo() expect_length(hl, 0) # display expect_output(print(hl), "") expect_output(print(new_hilo(0,1,95)), "\\[0, 1\\]95") dist <- dist_normal() # hilo.distribution hl <- hilo(dist, 95) expect_length(hl, 1) expect_equal(hl, new_hilo(qnorm(0.025), qnorm(0.975), 95)) # vec_math.hilo expect_equal(is.na(hl), FALSE) expect_equal(is.nan(hl), FALSE) # vec_arith.hilo expect_equal( hl*3+1, new_hilo(qnorm(0.025)*3+1, qnorm(0.975)*3+1, 95) ) expect_equal(-hl, hl) expect_equal(-3*hl, hl/(1/3)) }) distributional/tests/testthat/test-dist-student-t.R0000644000176200001440000000550313703764147022317 0ustar liggesuserstest_that("Student T distribution", { dist <- dist_student_t(5) expect_equal(format(dist), "t(5, 0, 1)") # quantiles expect_equal(quantile(dist, 0.1), stats::qt(0.1, 5)) expect_equal(quantile(dist, 0.5), stats::qt(0.5, 5)) # pdf expect_equal(density(dist, 0), stats::dt(0, 5)) expect_equal(density(dist, 3), stats::dt(3, 5)) # cdf expect_equal(cdf(dist, 0), stats::pt(0, 5)) expect_equal(cdf(dist, 3), stats::pt(3, 5)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4246)), 0.4246, tolerance = 1e-3) # stats expect_equal(mean(dist), 0) expect_equal(variance(dist), 5 / (5-2)) }) test_that("Noncentral Student t distribution", { dist <- dist_student_t(8, ncp = 6) expect_equal(format(dist), "t(8, 0, 1, 6)") # quantiles expect_equal(quantile(dist, 0.1), stats::qt(0.1, 8, ncp = 6)) expect_equal(quantile(dist, 0.5), stats::qt(0.5, 8, ncp = 6)) # pdf expect_equal(density(dist, 0), stats::dt(0, 8, ncp = 6)) expect_equal(density(dist, 3), stats::dt(3, 8, ncp = 6)) # cdf expect_equal(cdf(dist, 0), stats::pt(0, 8, ncp = 6)) expect_equal(cdf(dist, 3), stats::pt(3, 8, ncp = 6)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4246)), 0.4246, tolerance = 1e-3) # stats expect_equal(mean(dist), 2 * gamma(7/2)) expect_equal(variance(dist), 148/3 - 4 * gamma(7/2)^2) }) test_that("Location-scale Student t distribution", { dist <- dist_student_t(5, 2, 3) expect_equal(format(dist), "t(5, 2, 3)") # quantiles expect_equal(quantile(dist, 0.1), stats::qt(0.1, 5)*3 + 2) expect_equal(quantile(dist, 0.5), stats::qt(0.5, 5)*3 + 2) # pdf expect_equal(density(dist, 0), stats::dt(-2/3, 5)/3) expect_equal(density(dist, 3), stats::dt((3-2)/3, 5)/3) # cdf expect_equal(cdf(dist, 0), stats::pt(-2/3, 5)) expect_equal(cdf(dist, 3), stats::pt((3-2)/3, 5)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4246)), 0.4246, tolerance = 1e-3) # stats expect_equal(mean(dist), 2) expect_equal(variance(dist), 5 / (5-2) * 3^2) }) test_that("Noncentral location-scale Student t distribution", { dist <- dist_student_t(5, 2, 3, ncp = 6) expect_equal(format(dist), "t(5, 2, 3, 6)") # quantiles expect_equal(quantile(dist, 0.1), stats::qt(0.1, 5, 6)*3 + 2) expect_equal(quantile(dist, 0.5), stats::qt(0.5, 5, 6)*3 + 2) # pdf expect_equal(density(dist, 0), stats::dt(-2/3, 5, 6)/3) expect_equal(density(dist, 3), stats::dt((3-2)/3, 5, 6)/3) # cdf expect_equal(cdf(dist, 0), stats::pt(-2/3, 5, 6)) expect_equal(cdf(dist, 3), stats::pt((3-2)/3, 5, 6)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4246)), 0.4246, tolerance = 1e-3) # stats expect_equal(mean(dist), 2 + 6 * sqrt(5/2) * gamma(2)/gamma(5/2) * 3) expect_equal(variance(dist), ((5*(1+6^2))/(5-2) - (6 * sqrt(5/2) * (gamma((5-1)/2)/gamma(5/2)))^2)*3^2) }) distributional/tests/testthat/test-dist-chisq.R0000644000176200001440000000117113703764147021474 0ustar liggesuserstest_that("Chisq distribution", { dist <- dist_chisq(9) expect_equal(format(dist), "x2(9)") # quantiles expect_equal(quantile(dist, 0.1), stats::qchisq(0.1, 9)) expect_equal(quantile(dist, 0.5), stats::qchisq(0.5, 9)) # pdf expect_equal(density(dist, 0), stats::dchisq(0, 9)) expect_equal(density(dist, 3), stats::dchisq(3, 9)) # cdf expect_equal(cdf(dist, 0), stats::pchisq(0, 9)) expect_equal(cdf(dist, 3), stats::pchisq(3, 9)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4246)), 0.4246, tolerance = 1e-3) # stats expect_equal(mean(dist), 9) expect_equal(variance(dist), 2*9) }) distributional/tests/testthat/test-dist-logarithmic.R0000644000176200001440000000156514151532232022660 0ustar liggesuserstest_that("Logarithmic distribution", { dist <- dist_logarithmic(0.66) expect_equal(format(dist), "Logarithmic(0.66)") # Require package installed skip_if_not_installed("actuar", "2.0.0") # quantiles expect_equal(quantile(dist, 0.5), actuar::qlogarithmic(0.5, 0.66)) expect_equal(quantile(dist, 0.99), actuar::qlogarithmic(0.99, 0.66)) # pdf expect_equal(density(dist, 1), actuar::dlogarithmic(1, 0.66)) expect_equal(density(dist, 9), actuar::dlogarithmic(9, 0.66)) # cdf expect_equal(cdf(dist, 3), actuar::plogarithmic(3, 0.66)) expect_equal(cdf(dist, 12), actuar::plogarithmic(12, 0.66)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.9963064)), 0.9963064, tolerance = 1e-3) # stats expect_equal(mean(dist), -1/log(1-0.66)*(0.66/(1-0.66))) expect_equal(variance(dist), -(0.66^2 + 0.66*log(1-0.66))/((1-0.66)^2*log(1-0.66)^2)) }) distributional/tests/testthat/setup-tests.R0000644000176200001440000000007713703764147020753 0ustar liggesuserscontext("Configure test options") options(cli.unicode = FALSE) distributional/tests/testthat/test-inflated.R0000644000176200001440000000255613703764147021222 0ustar liggesuserstest_that("Check zero inflation", { dist <- dist_inflated(dist_poisson(6), 0.33) expect_equal(format(dist), "0+Pois(6)") # quantiles expect_equal(quantile(dist, 0.1), 0) expect_equal(quantile(dist, 0.5), 4) # pdf expect_equal(density(dist, 0), 0.33 + 0.67*dpois(0, 6)) expect_equal(density(dist, 3), 0.67*dpois(3, 6)) # cdf expect_equal(cdf(dist, 0), 0.33 + 0.67*ppois(0, 6)) expect_equal(cdf(dist, 3), 0.33 + 0.67*ppois(3, 6)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.52)), 0.52, tolerance = 1e-3) # stats expect_equal(mean(dist), 0.67*6) expect_equal(variance(dist), 0.67*6 + (0.33/0.67)*(0.67*6)^2) }) test_that("Check non-zero inflation", { dist <- dist_inflated(dist_poisson(6), 0.33, 2) expect_equal(format(dist), "2+Pois(6)") # quantiles expect_equal(quantile(dist, 0), 0) expect_equal(quantile(dist, 0.1), 2) expect_equal(quantile(dist, 0.33), 2) expect_equal(quantile(dist, 0.5), 4) # pdf expect_equal(density(dist, 0), 0.67*dpois(0, 6)) expect_equal(density(dist, 2), 0.33 + 0.67*dpois(2, 6)) expect_equal(density(dist, 3), 0.67*dpois(3, 6)) # cdf expect_equal(cdf(dist, 0), 0.67*ppois(0, 6)) expect_equal(cdf(dist, 2), 0.33 + 0.67*ppois(2, 6)) expect_equal(cdf(dist, 3), 0.33 + 0.67*ppois(3, 6)) # stats expect_equal(mean(dist), 0.33*2 + 0.67*6) # expect_equal(variance(d), ???) }) distributional/tests/testthat/test-dist-percentile.R0000644000176200001440000000123313703764147022516 0ustar liggesuserstest_that("Negative Binomial distribution", { dist <- dist_normal(0, 1) percentiles <- seq(0.01, 0.99, by = 0.01) x <- vapply(percentiles, quantile, double(1L), x = dist) dist <- dist_percentile(list(x), list(percentiles*100)) expect_equal(format(dist), "percentile[99]") # quantiles expect_equal(quantile(dist, 0.6), stats::qnorm(0.6, 0, 1)) expect_equal(quantile(dist, 0.61), stats::qnorm(0.61, 0, 1)) # pdf # cdf expect_equal(cdf(dist, 0), stats::pnorm(0, 0, 1)) expect_equal(cdf(dist, 1), stats::pnorm(1, 0, 1), tolerance = 1e-3) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.6)), 0.6, tolerance = 1e-3) # stats }) distributional/tests/testthat/test-transformations.R0000644000176200001440000000736314164770357022670 0ustar liggesuserstest_that("hilo of transformed distributions", { expect_identical( hilo(exp(dist_poisson(3))), exp(hilo((dist_poisson(3)))) ) }) test_that("chains of transformations", { expect_identical( hilo(dist_student_t(5)), hilo(log(exp(dist_student_t(5)))) ) expect_output( print(exp(dist_student_t(5))-1), "t\\(t\\(5, 0, 1\\)\\)" ) }) test_that("handling of transformation arguments", { expect_identical( hilo(logb(dist_normal(5, 1), base = 10)), logb(hilo(dist_normal(5, 1)), base = 10) ) expect_identical( hilo(10^logb(dist_normal(5, 1), base = 10)), 10^logb(hilo(dist_normal(5, 1)), base = 10) ) }) test_that("LogNormal distributions", { dist <- dist_transformed(dist_normal(0, 0.5), exp, log) ln_dist <- dist_lognormal(0, 0.5) # Test exp() shortcut expect_identical( exp(dist_normal(0, 0.5)), ln_dist ) expect_identical( log(ln_dist), dist_normal(0, 0.5) ) # Test log() shortcut with different bases expect_equal(log(dist_lognormal(0, log(3)), base = 3), dist_normal(0, 1)) expect_equal(log2(dist_lognormal(0, log(2))), dist_normal(0, 1)) expect_equal(log10(dist_lognormal(0, log(10))), dist_normal(0, 1)) # format expect_equal(format(dist), sprintf("t(%s)", format(dist_normal(0, 0.5)))) # quantiles expect_equal( quantile(dist, c(0.1, 0.5)), quantile(ln_dist, c(0.1, 0.5)) ) # pdf expect_equal( density(dist, c(1, 20)), density(ln_dist, c(1, 20)) ) # cdf expect_equal( cdf(dist, c(4, 90)), cdf(ln_dist, c(4, 90)) ) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.372)), 0.372, tolerance = 1e-3) # stats (approximate due to bias adjustment method) expect_equal(mean(dist), exp(0.25/2), tolerance = 0.01) expect_equal(variance(dist), (exp(0.25) - 1)*exp(0.25), tolerance = 0.1) }) test_that("inverses are applied automatically", { dist <- dist_gamma(1,1) log2dist <- log(dist, base = 2) log2dist_t <- dist_transformed(dist, log2, function(x) 2 ^ x) expect_equal(density(log2dist, 0.5), density(log2dist_t, 0.5)) expect_equal(cdf(log2dist, 0.5), cdf(log2dist_t, 0.5)) expect_equal(quantile(log2dist, 0.5), quantile(log2dist_t, 0.5)) # test multiple transformations that get stacked together by dist_transformed explogdist <- exp(log(dist)) expect_equal(density(dist, 0.5), density(explogdist, 0.5)) expect_equal(cdf(dist, 0.5), cdf(explogdist, 0.5)) expect_equal(quantile(dist, 0.5), quantile(explogdist, 0.5)) # test multiple transformations created by operators (via Ops) explog2dist <- 2 ^ log2dist expect_equal(density(dist, 0.5), density(explog2dist, 0.5)) expect_equal(cdf(dist, 0.5), cdf(explog2dist, 0.5)) expect_equal(quantile(dist, 0.5), quantile(explog2dist, 0.5)) # basic set of inverses expect_equal(density(sqrt(dist^2), 0.5), density(dist, 0.5)) expect_equal(density(exp(log(dist)), 0.5), density(dist, 0.5)) expect_equal(density(10^(log10(dist)), 0.5), density(dist, 0.5)) expect_equal(density(expm1(log1p(dist)), 0.5), density(dist, 0.5)) expect_equal(density(cos(acos(dist)), 0.5), density(dist, 0.5)) expect_equal(density(sin(asin(dist)), 0.5), density(dist, 0.5)) expect_equal(density(tan(atan(dist)), 0.5), density(dist, 0.5)) expect_equal(density(cosh(acosh(dist + 1)) - 1, 0.5), density(dist, 0.5)) expect_equal(density(sinh(asinh(dist)), 0.5), density(dist, 0.5)) expect_equal(density(tanh(atanh(dist)), 0.5), density(dist, 0.5)) expect_equal(density(dist + 1 - 1, 0.5), density(dist, 0.5)) expect_equal(density(dist * 2 / 2, 0.5), density(dist, 0.5)) # inverting a gamma distribution expect_equal(density(1/dist_gamma(4, 3), 0.5), density(dist_inverse_gamma(4, 1/3), 0.5)) expect_equal(density(1/(1/dist_gamma(4, 3)), 0.5), density(dist_gamma(4, 3), 0.5)) }) distributional/tests/testthat/test-dist-bernoulli.R0000644000176200001440000000120414151532232022337 0ustar liggesuserstest_that("Bernoulli distribution", { dist <- dist_bernoulli(0.4) expect_equal(format(dist), "Bernoulli(0.4)") # quantiles expect_equal(quantile(dist, 0.6), FALSE) expect_equal(quantile(dist, 0.61), TRUE) # pdf expect_equal(density(dist, 0), stats::dbinom(0, 1, 0.4)) expect_equal(density(dist, 1), stats::dbinom(1, 1, 0.4)) # cdf expect_equal(cdf(dist, 0), stats::pbinom(0, 1, 0.4)) expect_equal(cdf(dist, 1), stats::pbinom(1, 1, 0.4)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.6)), 0.6, tolerance = 1e-3) # stats expect_equal(mean(dist), 0.4) expect_equal(variance(dist), 0.4*(1-0.4)) }) distributional/tests/testthat/test-dist-hypergeometric.R0000644000176200001440000000144713703764147023421 0ustar liggesuserstest_that("Hypergeometric distribution", { dist <- dist_hypergeometric(500, 50, 100) expect_equal(format(dist), "Hypergeometric(500, 50, 100)") # quantiles expect_equal(quantile(dist, 0.1), stats::qhyper(0.1, 500, 50, 100)) expect_equal(quantile(dist, 0.5), stats::qhyper(0.5, 500, 50, 100)) # pdf expect_equal(density(dist, 0), stats::dhyper(0, 500, 50, 100)) expect_equal(density(dist, 3), stats::dhyper(3, 500, 50, 100)) # cdf expect_equal(cdf(dist, 0), stats::phyper(0, 500, 50, 100)) expect_equal(cdf(dist, 3), stats::phyper(3, 500, 50, 100)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4246)), 0.4246, tolerance = 1e-3) # stats p <- 500/(500+50) expect_equal(mean(dist), 100*p) expect_equal(variance(dist), 100*p*(1-p)*(500+50-100)/(500+50-1)) }) distributional/tests/testthat/Rplots.pdf0000644000176200001440000001324614312200115020261 0ustar 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.2)) expect_equal(density(dist, 3), actuar::dinvgauss(3, 3, .2)) # cdf expect_equal(cdf(dist, 0), actuar::pinvgauss(0, 3, .2)) expect_equal(cdf(dist, 3), actuar::pinvgauss(3, 3, .2)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4)), 0.4, tolerance = 1e-3) # stats expect_equal(mean(dist), actuar::minvgauss(1, 3, .2)) expect_equal(variance(dist), actuar::minvgauss(2, 3, .2) - actuar::minvgauss(1, 3, .2)^2) }) distributional/tests/testthat/test-dist-pareto.R0000644000176200001440000000147314151532232021646 0ustar liggesuserstest_that("Pareto distribution", { dist <- dist_pareto(10, 1) expect_equal(format(dist), "Pareto(10, 1)") # Require package installed skip_if_not_installed("actuar", "2.0.0") # quantiles expect_equal(quantile(dist, 0.1), actuar::qpareto(0.1, 10, 1)) expect_equal(quantile(dist, 0.5), actuar::qpareto(0.5, 10, 1)) # pdf expect_equal(density(dist, 0), actuar::dpareto(0, 10, 1)) expect_equal(density(dist, 3), actuar::dpareto(3, 10, 1)) # cdf expect_equal(cdf(dist, 0), actuar::ppareto(0, 10, 1)) expect_equal(cdf(dist, 3), actuar::ppareto(3, 10, 1)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4)), 0.4, tolerance = 1e-3) # stats expect_equal(mean(dist), actuar::mpareto(1, 10, 1)) expect_equal(variance(dist), actuar::mpareto(2, 10, 1) - actuar::mpareto(1, 10, 1)^2) }) distributional/tests/testthat/test-dist_lognormal.R0000644000176200001440000000165514151532232022432 0ustar liggesuserstest_that("Log-normal distribution", { # defaults dist <- dist_lognormal() expect_equal(mean(dist), exp(1/2)) expect_equal(variance(dist), (exp(1)-1)*exp(1)) # display expect_s3_class(dist, "distribution") expect_output(print(dist), "lN\\(0, 1\\)") expect_output(print(dist_lognormal(numeric())), "") # error checking expect_error( dist_lognormal(0, -1), "non-negative" ) expect_silent( dist_lognormal(mu = 0, sigma = 1) ) # density expect_equal( density(dist, 0), dlnorm(0, mean = 0, sd = 1) ) # cdf expect_equal( cdf(dist, 5), plnorm(5, mean = 0, sd = 1) ) # quantile expect_equal( quantile(dist, 0.1), qlnorm(0.1, mean = 0, sd = 1) ) # generate expect_equal( { set.seed(0) generate(dist, 10) }, { set.seed(0) mapply(function(m, s) rlnorm(10, m, s), m = 0, s = 1, SIMPLIFY = FALSE) } ) }) distributional/tests/testthat/test-dist-inverse-exponential.R0000644000176200001440000000151314151532232024346 0ustar liggesuserstest_that("Inverse Exponential distribution", { dist <- dist_inverse_exponential(5) expect_equal(format(dist), "InvExp(5)") # Require package installed skip_if_not_installed("actuar", "2.0.0") # quantiles expect_equal(quantile(dist, 0.1), actuar::qinvexp(0.1, 5)) expect_equal(quantile(dist, 0.5), actuar::qinvexp(0.5, 5)) # pdf expect_equal(density(dist, 0), actuar::dinvexp(0, 5)) expect_equal(density(dist, 3), actuar::dinvexp(3, 5)) # cdf expect_equal(cdf(dist, 0), actuar::pinvexp(0, 5)) expect_equal(cdf(dist, 3), actuar::pinvexp(3, 5)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4)), 0.4, tolerance = 1e-3) # stats expect_equal(mean(dist), NA_real_) # dput(actuar::minvexp(1, 5)) expect_equal(variance(dist), NA_real_) # dput(actuar::minvexp(2, 5) - actuar::minvexp(1, 5)^2) }) distributional/tests/testthat/test-dist-weibull.R0000644000176200001440000000136313703764147022033 0ustar liggesuserstest_that("Weibull distribution", { dist <- dist_weibull(1.5, 1) expect_equal(format(dist), "Weibull(1.5, 1)") # quantiles expect_equal(quantile(dist, 0.1), stats::qweibull(0.1, 1.5, 1)) expect_equal(quantile(dist, 0.5), stats::qweibull(0.5, 1.5, 1)) # pdf expect_equal(density(dist, 0), stats::dweibull(0, 1.5, 1)) expect_equal(density(dist, 3), stats::dweibull(3, 1.5, 1)) # cdf expect_equal(cdf(dist, 0), stats::pweibull(0, 1.5, 1)) expect_equal(cdf(dist, 3), stats::pweibull(3, 1.5, 1)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4246)), 0.4246, tolerance = 1e-3) # stats expect_equal(mean(dist), 1 * gamma(1 + 1/1.5)) expect_equal(variance(dist), 1^2 * (gamma(1 + 2/1.5) - gamma(1 + 1/1.5)^2)) }) distributional/tests/testthat/test-dist-gamma.R0000644000176200001440000000125413703764147021451 0ustar liggesuserstest_that("Gamma distribution", { dist <- dist_gamma(7.5, 2) expect_equal(format(dist), "Gamma(7.5, 2)") # quantiles expect_equal(quantile(dist, 0.1), stats::qgamma(0.1, 7.5, 2)) expect_equal(quantile(dist, 0.5), stats::qgamma(0.5, 7.5, 2)) # pdf expect_equal(density(dist, 0), stats::dgamma(0, 7.5, 2)) expect_equal(density(dist, 3), stats::dgamma(3, 7.5, 2)) # cdf expect_equal(cdf(dist, 0), stats::pgamma(0, 7.5, 2)) expect_equal(cdf(dist, 3), stats::pgamma(3, 7.5, 2)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4246)), 0.4246, tolerance = 1e-3) # stats expect_equal(mean(dist), 7.5/2) expect_equal(variance(dist), 7.5/2^2) }) distributional/tests/testthat/test-dist-normal.R0000644000176200001440000000256314151532232021645 0ustar liggesuserstest_that("Normal distribution", { # defaults dist <- dist_normal() expect_equal(mean(dist), 0) expect_equal(variance(dist), 1) # display expect_s3_class(dist, "distribution") expect_output(print(dist), "N\\(0, 1\\)") expect_output(print(dist_normal(numeric())), "") # error checking expect_error( dist_normal(0, -1), "non-negative" ) expect_silent( dist_normal(mu = 0L, sigma = 1L) ) mu <- rnorm(10) sigma <- abs(rnorm(10)) dist <- dist_normal(mu, sigma) # summary statistics expect_equal(mean(dist), mu) expect_equal(median(dist), mu) expect_equal(median(dist[[1]]), mu[[1]]) expect_equal(variance(dist), sigma^2) # math expect_equal(mean(dist*3+1), mu*3+1) expect_equal(variance(dist*3+1), (sigma*3)^2) expect_equal(mean(dist + dist), mean(dist) + mean(dist)) expect_equal(variance(dist + dist), variance(dist) + variance(dist)) # density expect_equal( density(dist, 0), dnorm(0, mean = mu, sd = sigma) ) # cdf expect_equal( cdf(dist, 5), pnorm(5, mean = mu, sd = sigma) ) # quantile expect_equal( quantile(dist, 0.1), qnorm(0.1, mean = mu, sd = sigma) ) # generate expect_equal( { set.seed(0) generate(dist, 10) }, { set.seed(0) mapply(function(m, s) rnorm(10, m, s), m = mu, s = sigma, SIMPLIFY = FALSE) } ) }) distributional/tests/testthat/test-dist-cauchy.R0000644000176200001440000000126113703764147021641 0ustar liggesuserstest_that("Cauchy distribution", { dist <- dist_cauchy(-2, 1) expect_equal(format(dist), "Cauchy(-2, 1)") # quantiles expect_equal(quantile(dist, 0.1), stats::qcauchy(0.1, -2, 1)) expect_equal(quantile(dist, 0.5), stats::qcauchy(0.5, -2, 1)) # pdf expect_equal(density(dist, 0), stats::dcauchy(0, -2, 1)) expect_equal(density(dist, 3), stats::dcauchy(3, -2, 1)) # cdf expect_equal(cdf(dist, 0), stats::pcauchy(0, -2, 1)) expect_equal(cdf(dist, 3), stats::pcauchy(3, -2, 1)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4246)), 0.4246, tolerance = 1e-3) # stats expect_equal(mean(dist), NA_real_) expect_equal(variance(dist), NA_real_) }) distributional/tests/testthat/test-dist-inverse-gamma.R0000644000176200001440000000164214151532232023105 0ustar liggesuserstest_that("Inverse Gamma distribution", { dist <- dist_inverse_gamma(3, 2) expect_equal(format(dist), "InvGamma(3, 0.5)") # Require package installed skip_if_not_installed("actuar", "2.0.0") # quantiles expect_equal(quantile(dist, 0.1), actuar::qinvgamma(0.1, 3, 2)) expect_equal(quantile(dist, 0.5), actuar::qinvgamma(0.5, 3, 2)) # pdf expect_equal(density(dist, 0), actuar::dinvgamma(0, 3, 2)) expect_equal(density(dist, 3), actuar::dinvgamma(3, 3, 2)) # cdf expect_equal(cdf(dist, 0), actuar::pinvgamma(0, 3, 2)) expect_equal(cdf(dist, 3), actuar::pinvgamma(3, 3, 2)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4)), 0.4, tolerance = 1e-3) # stats expect_equal(mean(dist), (1/2) / (3 - 1)) expect_equal(median(dist), actuar::qinvgamma(0.5, 3, 2)) expect_equal(median(dist[[1]]), actuar::qinvgamma(0.5, 3, 2)) expect_equal(variance(dist), (1/2)^2/((3-1)^2*(3-2))) }) distributional/tests/testthat/test-dist-f.R0000644000176200001440000000136713703764147020621 0ustar liggesuserstest_that("F distribution", { dist <- dist_f(5, 2) expect_equal(format(dist), "F(5, 2)") # quantiles expect_equal(quantile(dist, 0.1), stats::qf(0.1, 5, 2)) expect_equal(quantile(dist, 0.5), stats::qf(0.5, 5, 2)) # pdf expect_equal(density(dist, 0), stats::df(0, 5, 2)) expect_equal(density(dist, 3), stats::df(3, 5, 2)) # cdf expect_equal(cdf(dist, 0), stats::pf(0, 5, 2)) expect_equal(cdf(dist, 3), stats::pf(3, 5, 2)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4246)), 0.4246, tolerance = 1e-3) # stats expect_equal(mean(dist), NA_real_) expect_equal(variance(dist), NA_real_) dist <- dist_f(5, 5) expect_equal(mean(dist), 5/(5-2)) expect_equal(variance(dist), 2*5^2*(5+5-2)/(5*(5-2)^2*(5-4))) }) distributional/tests/testthat/test-dist-exponential.R0000644000176200001440000000117613703764147022720 0ustar liggesuserstest_that("Exponential distribution", { dist <- dist_exponential(2) expect_equal(format(dist), "Exp(2)") # quantiles expect_equal(quantile(dist, 0.1), stats::qexp(0.1, 2)) expect_equal(quantile(dist, 0.5), stats::qexp(0.5, 2)) # pdf expect_equal(density(dist, 0), stats::dexp(0, 2)) expect_equal(density(dist, 3), stats::dexp(3, 2)) # cdf expect_equal(cdf(dist, 0), stats::pexp(0, 2)) expect_equal(cdf(dist, 3), stats::pexp(3, 2)) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 0.4246)), 0.4246, tolerance = 1e-3) # stats expect_equal(mean(dist), 1/2) expect_equal(variance(dist), 1/2^2) }) distributional/tests/testthat/test-dist-degenerate.R0000644000176200001440000000136413703764147022474 0ustar liggesuserstest_that("Degenerate distribution", { dist <- dist_degenerate(1) expect_equal( dist, vec_cast(1, new_dist()) ) expect_equal(format(dist), "1") # quantiles expect_equal(quantile(dist, 0), 1) expect_equal(quantile(dist, 0.5), 1) expect_equal(quantile(dist, 1), 1) # pdf expect_equal(density(dist, 1), 1) expect_equal(density(dist, 0.5), 0) expect_equal(density(dist, 0.99999), 0) # cdf expect_equal(cdf(dist, 0), 0) expect_equal(cdf(dist, 1), 1) expect_equal(cdf(dist, 0.9999), 0) # F(Finv(a)) ~= a expect_equal(cdf(dist, quantile(dist, 1)), 1, tolerance = 1e-3) expect_equal(cdf(dist, quantile(dist, 0)), 1, tolerance = 1e-3) # stats expect_equal(mean(dist), 1) expect_equal(variance(dist), 0) }) distributional/tests/testthat.R0000644000176200001440000000011013703764147016437 0ustar liggesuserslibrary(testthat) library(distributional) test_check("distributional") distributional/R/0000755000176200001440000000000014534005030013501 5ustar liggesusersdistributional/R/dist_beta.R0000644000176200001440000000416614304310567015602 0ustar liggesusers#' The Beta distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' @param shape1,shape2 The non-negative shape parameters of the Beta distribution. #' #' @seealso [stats::Beta] #' #' @examples #' dist <- dist_beta(shape1 = c(0.5, 5, 1, 2, 2), shape2 = c(0.5, 1, 3, 2, 5)) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_beta #' @export dist_beta <- function(shape1, shape2){ shape1 <- vec_cast(shape1, double()) shape2 <- vec_cast(shape2, double()) if(any((shape1 < 0) | shape2 < 0)){ abort("Shape parameters of a Beta distribution must be non-negative.") } new_dist(shape1 = shape1, shape2 = shape2, class = "dist_beta") } #' @export format.dist_beta <- function(x, digits = 2, ...){ sprintf( "Beta(%s, %s)", format(x[["shape1"]], digits = digits, ...), format(x[["shape2"]], digits = digits, ...) ) } #' @export density.dist_beta <- function(x, at, ...){ stats::dbeta(at, x[["shape1"]], x[["shape2"]]) } #' @export log_density.dist_beta <- function(x, at, ...){ stats::dbeta(at, x[["shape1"]], x[["shape2"]], log = TRUE) } #' @export quantile.dist_beta <- function(x, p, ...){ stats::qbeta(p, x[["shape1"]], x[["shape2"]]) } #' @export cdf.dist_beta <- function(x, q, ...){ stats::pbeta(q, x[["shape1"]], x[["shape2"]]) } #' @export generate.dist_beta <- function(x, times, ...){ stats::rbeta(times, x[["shape1"]], x[["shape2"]]) } #' @export mean.dist_beta <- function(x, ...){ x[["shape1"]]/(x[["shape1"]] + x[["shape2"]]) } #' @export covariance.dist_beta <- function(x, ...){ a <- x[["shape1"]] b <- x[["shape2"]] a*b/((a+b)^2*(a+b+1)) } #' @export skewness.dist_beta <- function(x, ...) { a <- x[["shape1"]] b <- x[["shape2"]] 2 * (b - a) * sqrt(a + b + 1) / (a + b + 2) * sqrt(a * b) } #' @export kurtosis.dist_beta <- function(x, ...) { a <- x[["shape1"]] b <- x[["shape2"]] num <- 6 * ((a - b)^2 * (a + b + 1) - (a * b) * (a + b + 2)) denom <- a * b * (a + b + 2) * (a + b + 3) num / denom } distributional/R/dist_gumbel.R0000644000176200001440000000662314304314100016125 0ustar liggesusers#' The Gumbel distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' The Gumbel distribution is a special case of the Generalized Extreme Value #' distribution, obtained when the GEV shape parameter \eqn{\xi} is equal to 0. #' It may be referred to as a type I extreme value distribution. #' #' @inheritParams actuar::dgumbel #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X} be a Gumbel random variable with location #' parameter `mu` = \eqn{\mu}, scale parameter `sigma` = \eqn{\sigma}. #' #' **Support**: \eqn{R}, the set of all real numbers. #' #' **Mean**: \eqn{\mu + \sigma\gamma}, where \eqn{\gamma} is Euler's #' constant, approximately equal to 0.57722. #' #' **Median**: \eqn{\mu - \sigma\ln(\ln 2)}{\mu - \sigma ln(ln 2)}. #' #' **Variance**: \eqn{\sigma^2 \pi^2 / 6}. #' #' **Probability density function (p.d.f)**: #' #' \deqn{f(x) = \sigma ^ {-1} \exp[-(x - \mu) / \sigma]% #' \exp\{-\exp[-(x - \mu) / \sigma] \}}{% #' f(x) = (1 / \sigma) exp[-(x - \mu) / \sigma]% #' exp{-exp[-(x - \mu) / \sigma]}} #' for \eqn{x} in \eqn{R}, the set of all real numbers. #' #' **Cumulative distribution function (c.d.f)**: #' #' In the \eqn{\xi = 0} (Gumbel) special case #' \deqn{F(x) = \exp\{-\exp[-(x - \mu) / \sigma] \}}{% #' F(x) = exp{ - exp[-(x - \mu) / \sigma]} } #' for \eqn{x} in \eqn{R}, the set of all real numbers. #' #' @seealso [actuar::Gumbel] #' #' @examples #' dist <- dist_gumbel(alpha = c(0.5, 1, 1.5, 3), scale = c(2, 2, 3, 4)) #' dist #' #' @examplesIf requireNamespace("actuar", quietly = TRUE) #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' support(dist) #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_gumbel #' @export dist_gumbel <- function(alpha, scale){ alpha <- vec_cast(alpha, double()) scale <- vec_cast(scale, double()) if(any(scale <= 0)){ abort("The scale parameter of a Gumbel distribution must be strictly positive.") } new_dist(a = alpha, s = scale, class = "dist_gumbel") } #' @export format.dist_gumbel <- function(x, digits = 2, ...){ sprintf( "Gumbel(%s, %s)", format(x[["a"]], digits = digits, ...), format(x[["s"]], digits = digits, ...) ) } #' @export density.dist_gumbel <- function(x, at, ...){ require_package("actuar") actuar::dgumbel(at, x[["a"]], x[["s"]]) } #' @export log_density.dist_gumbel <- function(x, at, ...){ require_package("actuar") actuar::dgumbel(at, x[["a"]], x[["s"]], log = TRUE) } #' @export quantile.dist_gumbel <- function(x, p, ...){ require_package("actuar") actuar::qgumbel(p, x[["a"]], x[["s"]]) } #' @export cdf.dist_gumbel <- function(x, q, ...){ require_package("actuar") actuar::pgumbel(q, x[["a"]], x[["s"]]) } #' @export generate.dist_gumbel <- function(x, times, ...){ require_package("actuar") actuar::rgumbel(times, x[["a"]], x[["s"]]) } #' @export mean.dist_gumbel <- function(x, ...){ actuar::mgumbel(1, x[["a"]], x[["s"]]) } #' @export covariance.dist_gumbel <- function(x, ...){ (pi*x[["s"]])^2/6 } #' @export skewness.dist_gumbel <- function(x, ...) { zeta3 <- 1.20205690315959401459612 (12 * sqrt(6) * zeta3) / pi^3 } #' @export kurtosis.dist_gumbel <- function(x, ...) 12/5 distributional/R/dist_cauchy.R0000644000176200001440000000574014304314376016144 0ustar liggesusers#' The Cauchy distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' The Cauchy distribution is the student's t distribution with one degree of #' freedom. The Cauchy distribution does not have a well defined mean or #' variance. Cauchy distributions often appear as priors in Bayesian contexts #' due to their heavy tails. #' #' @inheritParams stats::dcauchy #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X} be a Cauchy variable with mean #' `location =` \eqn{x_0} and `scale` = \eqn{\gamma}. #' #' **Support**: \eqn{R}, the set of all real numbers #' #' **Mean**: Undefined. #' #' **Variance**: Undefined. #' #' **Probability density function (p.d.f)**: #' #' \deqn{ #' f(x) = \frac{1}{\pi \gamma \left[1 + \left(\frac{x - x_0}{\gamma} \right)^2 \right]} #' }{ #' f(x) = 1 / (\pi \gamma (1 + ((x - x_0) / \gamma)^2) #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' \deqn{ #' F(t) = \frac{1}{\pi} \arctan \left( \frac{t - x_0}{\gamma} \right) + #' \frac{1}{2} #' }{ #' F(t) = arctan((t - x_0) / \gamma) / \pi + 1/2 #' } #' #' **Moment generating function (m.g.f)**: #' #' Does not exist. #' #' @seealso [stats::Cauchy] #' #' @examples #' dist <- dist_cauchy(location = c(0, 0, 0, -2), scale = c(0.5, 1, 2, 1)) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_cauchy #' @export dist_cauchy <- function(location, scale){ location <- vec_cast(location, double()) scale <- vec_cast(scale, double()) if(any(scale[!is.na(scale)] <= 0)){ abort("The scale parameter of a Cauchy distribution must strictly positive.") } new_dist(location = location, scale = scale, class = "dist_cauchy") } #' @export format.dist_cauchy <- function(x, digits = 2, ...){ sprintf( "Cauchy(%s, %s)", format(x[["location"]], digits = digits, ...), format(x[["scale"]], digits = digits, ...) ) } #' @export density.dist_cauchy <- function(x, at, ...){ stats::dcauchy(at, x[["location"]], x[["scale"]]) } #' @export log_density.dist_cauchy <- function(x, at, ...){ stats::dcauchy(at, x[["location"]], x[["scale"]], log = TRUE) } #' @export quantile.dist_cauchy <- function(x, p, ...){ stats::qcauchy(p, x[["location"]], x[["scale"]]) } #' @export cdf.dist_cauchy <- function(x, q, ...){ stats::pcauchy(q, x[["location"]], x[["scale"]]) } #' @export generate.dist_cauchy <- function(x, times, ...){ stats::rcauchy(times, x[["location"]], x[["scale"]]) } #' @export mean.dist_cauchy <- function(x, ...){ NA_real_ } #' @export covariance.dist_cauchy <- function(x, ...){ NA_real_ } #' @export skewness.dist_cauchy <- function(x, ...){ NA_real_ } #' @export kurtosis.dist_cauchy <- function(x, ...){ NA_real_ } distributional/R/dist_logistic.R0000644000176200001440000000553514304314125016477 0ustar liggesusers#' The Logistic distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' A continuous distribution on the real line. For binary outcomes #' the model given by \eqn{P(Y = 1 | X) = F(X \beta)} where #' \eqn{F} is the Logistic [cdf()] is called *logistic regression*. #' #' @inheritParams stats::dlogis #' #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X} be a Logistic random variable with #' `location` = \eqn{\mu} and `scale` = \eqn{s}. #' #' **Support**: \eqn{R}, the set of all real numbers #' #' **Mean**: \eqn{\mu} #' #' **Variance**: \eqn{s^2 \pi^2 / 3} #' #' **Probability density function (p.d.f)**: #' #' \deqn{ #' f(x) = \frac{e^{-(\frac{x - \mu}{s})}}{s [1 + \exp(-(\frac{x - \mu}{s})) ]^2} #' }{ #' f(x) = e^(-(t - \mu) / s) / (s (1 + e^(-(t - \mu) / s))^2) #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' \deqn{ #' F(t) = \frac{1}{1 + e^{-(\frac{t - \mu}{s})}} #' }{ #' F(t) = 1 / (1 + e^(-(t - \mu) / s)) #' } #' #' **Moment generating function (m.g.f)**: #' #' \deqn{ #' E(e^{tX}) = e^{\mu t} \beta(1 - st, 1 + st) #' }{ #' E(e^(tX)) = = e^(\mu t) \beta(1 - st, 1 + st) #' } #' #' where \eqn{\beta(x, y)} is the Beta function. #' #' @seealso [stats::Logistic] #' #' @examples #' dist <- dist_logistic(location = c(5,9,9,6,2), scale = c(2,3,4,2,1)) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_logistic #' @export dist_logistic <- function(location, scale){ location <- vec_cast(location, double()) scale <- vec_cast(scale, double()) new_dist(l = location, s = scale, class = "dist_logistic") } #' @export format.dist_logistic <- function(x, digits = 2, ...){ sprintf( "Logistic(%s, %s)", format(x[["l"]], digits = digits, ...), format(x[["s"]], digits = digits, ...) ) } #' @export density.dist_logistic <- function(x, at, ...){ stats::dlogis(at, x[["l"]], x[["s"]]) } #' @export log_density.dist_logistic <- function(x, at, ...){ stats::dlogis(at, x[["l"]], x[["s"]], log = TRUE) } #' @export quantile.dist_logistic <- function(x, p, ...){ stats::qlogis(p, x[["l"]], x[["s"]]) } #' @export cdf.dist_logistic <- function(x, q, ...){ stats::plogis(q, x[["l"]], x[["s"]]) } #' @export generate.dist_logistic <- function(x, times, ...){ stats::rlogis(times, x[["l"]], x[["s"]]) } #' @export mean.dist_logistic <- function(x, ...){ x[["l"]] } #' @export covariance.dist_logistic <- function(x, ...){ (x[["s"]]*pi)^2/3 } #' @export skewness.dist_logistic <- function(x, ...) 0 #' @export kurtosis.dist_logistic <- function(x, ...) 6 / 5 distributional/R/dist_missing.R0000644000176200001440000000272514304314517016336 0ustar liggesusers#' Missing distribution #' #' @description #' `r lifecycle::badge('maturing')` #' #' A placeholder distribution for handling missing values in a vector of #' distributions. #' #' @param length The number of missing distributions #' #' @name dist_missing #' #' @examples #' dist <- dist_missing(3L) #' #' dist #' mean(dist) #' variance(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @export dist_missing <- function(length = 1) { vctrs::vec_rep(NA_dist_, length) } NA_dist_ <- structure(list(NULL), class = c("distribution", "vctrs_vctr", "list")) #' @export format.dist_na <- function(x, ...) { "NA" } #' @export density.dist_na <- function(x, at, ...){ NA_real_ } #' @export log_density.dist_na <- density.dist_na #' @export quantile.dist_na <- function(x, p, ...){ NA_real_ } #' @export log_quantile.dist_na <- quantile.dist_na #' @export cdf.dist_na <- function(x, q, ...){ NA_real_ } #' @export log_cdf.dist_na <- cdf.dist_na #' @export generate.dist_na <- function(x, times, ...){ rep(NA_real_, times) } #' @export mean.dist_na <- function(x, ...) NA_real_ #' @export covariance.dist_na <- function(x, ...) NA_real_ #' @export skewness.dist_na <- function(x, ...) NA_real_ #' @export kurtosis.dist_na <- function(x, ...) NA_real_ #' @export Math.dist_na <- function(x, ...) { x } #' @export Ops.dist_na <- function(e1, e2) { dist_missing(max(length(e1), length(e2))) } distributional/R/utils.R0000644000176200001440000001062314304205073014772 0ustar liggesuserstranspose <- function(.l) { if(is_empty(.l)) return(.l) inner_names <- names(.l[[1L]]) result <- lapply(seq_along(.l[[1L]]), function(i) { lapply(.l, .subset2, i) }) set_names(result, inner_names) } transpose_c <- function(.l) { stopifnot(is_list_of(.l)) .ptype <- vec_init(attr(.l, "ptype"), 1L) if(is_empty(.l)) return(.l) inner_names <- names(.l[[1L]]) .l <- vec_recycle_common(!!!.l) result <- lapply(seq_along(.l[[1L]]), function(i) { unname(vec_c(!!!lapply(.l, vec_slice, i), .ptype = .ptype)) }) set_names(result, inner_names) } split_matrix_rows <- function(x) { lapply(seq_len(nrow(x)), function(i) x[i,,drop=FALSE]) } # Declare a function's argument as allowing list inputs for mapping values arg_listable <- function(x, .ptype) { if(is.list(x)) { x <- as_list_of(as.list(x), .ptype) if(is.matrix(attr(x, "ptype"))) { x <- lapply(x, split_matrix_rows) x <- as_list_of(x, .ptype) } if(is.null(names(x))) { names(x) <- vec_as_names(character(vec_size(x)), repair = "unique") } } else if(is.matrix(x)) { x <- split_matrix_rows(x) } else { vec_assert(x, .ptype) } # Declares list arguments to be unpacked for dist_apply() class(x) <- c("arg_listable", class(x)) x } validate_recycling <- function(x, arg) { if(is_list_of(arg)) return(lapply(arg, validate_recycling, x = x)) if(!any(vec_size(arg) == c(1, vec_size(x)))) { abort( sprintf("Cannot recycle input of size %i to match the distributions (size %i).", vec_size(arg), vec_size(x) ) ) } } dist_apply <- function(x, .f, ...){ dn <- dimnames(x) x <- vec_data(x) dist_is_na <- vapply(x, is.null, logical(1L)) x[dist_is_na] <- list(structure(list(), class = c("dist_na", "dist_default"))) args <- dots_list(...) is_arg_listable <- vapply(args, inherits, FUN.VALUE = logical(1L), "arg_listable") unpack_listable <- multi_arg <- FALSE if(any(is_arg_listable)) { if(sum(is_arg_listable) > 1) abort("Only distribution argument can be unpacked at a time.\nThis shouldn't happen, please report a bug at https://github.com/mitchelloharawild/distributional/issues/") arg_pos <- which(is_arg_listable) if(unpack_listable <- is_list_of(args[[arg_pos]])) { validate_recycling(x, args[[arg_pos]]) .unpack_names <- names(args[[arg_pos]]) args[[arg_pos]] <- transpose_c(args[[arg_pos]]) } else if (multi_arg <- (length(args[[arg_pos]]) > 1)){ args[[arg_pos]] <- list(unclass(args[[arg_pos]])) } } out <- do.call(mapply, c(.f, list(x), args, SIMPLIFY = FALSE, USE.NAMES = FALSE)) # out <- mapply(.f, x, ..., SIMPLIFY = FALSE, USE.NAMES = FALSE) if(unpack_listable) { # TODO - update and repair multivariate distribution i/o with unpacking out <- as_list_of(out) if (rbind_mat <- is.matrix(attr(out, "ptype"))) { out <- as_list_of(lapply(out, split_matrix_rows)) } out <- transpose_c(out) if(rbind_mat) { out <- lapply(out, function(x) `colnames<-`(do.call(rbind, x), dn)) } names(out) <- .unpack_names out <- new_data_frame(out, n = vec_size(x)) # } else if(length(out[[1]]) > 1) { # out <- suppressMessages(vctrs::vec_rbind(!!!out)) } else if(multi_arg) { if(length(dn) > 1) out <- lapply(out, `colnames<-`, dn) } else { out <- vec_c(!!!out) out <- if(vec_is_list(out)) lapply(out, set_matrix_dimnames, dn = dn) else set_matrix_dimnames(out, dn) } out } set_matrix_dimnames <- function(x, dn) { if((is.matrix(x) || is.data.frame(x)) && !is.null(dn)){ # Set dimension names colnames(x) <- dn } x } # inlined from https://github.com/r-lib/cli/blob/master/R/utf8.R is_utf8_output <- function() { opt <- getOption("cli.unicode", NULL) if (!is_null(opt)) { isTRUE(opt) } else { l10n_info()$`UTF-8` && !is_latex_output() } } is_latex_output <- function() { if (!("knitr" %in% loadedNamespaces())) { return(FALSE) } get("is_latex_output", asNamespace("knitr"))() } require_package <- function(pkg){ if(!requireNamespace(pkg, quietly = TRUE)){ abort( sprintf('The `%s` package must be installed to use this functionality. It can be installed with install.packages("%s")', pkg, pkg) ) } } restore_rng <- function(expr, seed = NULL) { old_seed <- .GlobalEnv$.Random.seed # Set new temporary seed set.seed(seed) # Restore previous seed on.exit(.GlobalEnv$.Random.seed <- old_seed) expr } distributional/R/dist_inverse_exponential.R0000644000176200001440000000336014304314107020735 0ustar liggesusers#' The Inverse Exponential distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' @inheritParams actuar::dinvexp #' #' @seealso [actuar::InverseExponential] #' #' @examples #' dist <- dist_inverse_exponential(rate = 1:5) #' dist #' #' @examplesIf requireNamespace("actuar", quietly = TRUE) #' mean(dist) #' variance(dist) #' support(dist) #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_inverse_exponential #' @export dist_inverse_exponential <- function(rate){ rate <- vec_cast(rate, double()) if(any(rate <= 0)){ abort("The rate parameter of a Inverse Exponential distribution must be strictly positive.") } new_dist(r = rate, class = "dist_inverse_exponential") } #' @export format.dist_inverse_exponential <- function(x, digits = 2, ...){ sprintf( "InvExp(%s)", format(x[["r"]], digits = digits, ...) ) } #' @export density.dist_inverse_exponential <- function(x, at, ...){ require_package("actuar") actuar::dinvexp(at, x[["r"]]) } #' @export log_density.dist_inverse_exponential <- function(x, at, ...){ require_package("actuar") actuar::dinvexp(at, x[["r"]], log = TRUE) } #' @export quantile.dist_inverse_exponential <- function(x, p, ...){ require_package("actuar") actuar::qinvexp(p, x[["r"]]) } #' @export cdf.dist_inverse_exponential <- function(x, q, ...){ require_package("actuar") actuar::pinvexp(q, x[["r"]]) } #' @export generate.dist_inverse_exponential <- function(x, times, ...){ require_package("actuar") actuar::rinvexp(times, x[["r"]]) } #' @export mean.dist_inverse_exponential <- function(x, ...){ NA_real_ } #' @export covariance.dist_inverse_exponential <- function(x, ...){ NA_real_ } distributional/R/truncated.R0000644000176200001440000000531414304316310015621 0ustar liggesusers#' Truncate a distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' Note that the samples are generated using inverse transform sampling, and the #' means and variances are estimated from samples. #' #' @param dist The distribution(s) to truncate. #' @param lower,upper The range of values to keep from a distribution. #' #' @name dist_truncated #' #' @examples #' dist <- dist_truncated(dist_normal(2,1), lower = 0) #' #' dist #' mean(dist) #' variance(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' if(requireNamespace("ggdist")) { #' library(ggplot2) #' ggplot() + #' ggdist::stat_dist_halfeye( #' aes(y = c("Normal", "Truncated"), #' dist = c(dist_normal(2,1), dist_truncated(dist_normal(2,1), lower = 0))) #' ) #' } #' #' @export dist_truncated <- function(dist, lower = -Inf, upper = Inf){ vec_is(dist, new_dist()) vec_is(lower, numeric()) vec_is(upper, numeric()) if(any(lower >= upper)){ abort("The `lower` truncation bound must be lower than the `upper` bound.") } new_dist(dist = dist, lower = lower, upper = upper, dimnames = dimnames(dist), class = "dist_truncated") } #' @export format.dist_truncated <- function(x, ...){ sprintf( "%s[%s,%s]", format(x[["dist"]]), x[["lower"]], x[["upper"]] ) } #' @export density.dist_truncated <- function(x, at, ...){ in_lim <- at >= x[["lower"]] & at <= x[["upper"]] cdf_upr <- cdf(x[["dist"]], x[["upper"]]) cdf_lwr <- cdf(x[["dist"]], x[["lower"]]) out <- numeric(length(at)) out[in_lim] <- density(x[["dist"]], at = at[in_lim], ...)/(cdf_upr - cdf_lwr) out } #' @export quantile.dist_truncated <- function(x, p, ...){ F_lwr <- cdf(x[["dist"]], x[["lower"]]) F_upr <- cdf(x[["dist"]], x[["upper"]]) qt <- quantile(x[["dist"]], F_lwr + p * (F_upr - F_lwr), ...) pmin(pmax(x[["lower"]], qt), x[["upper"]]) } #' @export cdf.dist_truncated <- function(x, q, ...){ cdf_upr <- cdf(x[["dist"]], x[["upper"]]) cdf_lwr <- cdf(x[["dist"]], x[["lower"]]) out <- numeric(length(q)) q_lwr <- q < x[["lower"]] # out[q_lwr <- q < x[["lower"]]] <- 0 out[q_upr <- q > x[["upper"]]] <- 1 q_mid <- !(q_lwr|q_upr) out[q_mid] <- (cdf(x[["dist"]], q = q[q_mid], ...) - cdf_lwr)/(cdf_upr - cdf_lwr) out } #' @export mean.dist_truncated <- function(x, ...) { if(inherits(x$dist, "dist_sample")) { y <- x$dist[[1]] mean(y[y >= x$lower & y <= x$upper]) } else if(inherits(x$dist, "dist_normal")) { mu <- x$dist$mu s <- x$dist$sigma a <- (x$lower - mu) / s b <- (x$upper - mu) / s mu + (stats::dnorm(a) - stats::dnorm(b))/(stats::pnorm(b) - stats::pnorm(a))*s } else { NextMethod() } } distributional/R/dist_exponential.R0000644000176200001440000000311214304314056017200 0ustar liggesusers#' The Exponential Distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' @inheritParams stats::dexp #' #' @seealso [stats::Exponential] #' #' @examples #' dist <- dist_exponential(rate = c(2, 1, 2/3)) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_exponential #' @export dist_exponential <- function(rate){ rate <- vec_cast(rate, double()) if(any(rate < 0)){ abort("The rate parameter of an Exponential distribution must be non-negative.") } new_dist(rate = rate, class = "dist_exponential") } #' @export format.dist_exponential <- function(x, digits = 2, ...){ sprintf( "Exp(%s)", format(x[["rate"]], digits = digits, ...) ) } #' @export density.dist_exponential <- function(x, at, ...){ stats::dexp(at, x[["rate"]]) } #' @export log_density.dist_exponential <- function(x, at, ...){ stats::dexp(at, x[["rate"]], log = TRUE) } #' @export quantile.dist_exponential <- function(x, p, ...){ stats::qexp(p, x[["rate"]]) } #' @export cdf.dist_exponential <- function(x, q, ...){ stats::pexp(q, x[["rate"]]) } #' @export generate.dist_exponential <- function(x, times, ...){ stats::rexp(times, x[["rate"]]) } #' @export mean.dist_exponential <- function(x, ...){ 1/x[["rate"]] } #' @export covariance.dist_exponential <- function(x, ...){ 1/x[["rate"]]^2 } #' @export skewness.dist_exponential <- function(x, ...) 2 #' @export kurtosis.dist_exponential <- function(x, ...) 6 distributional/R/dist_bernoulli.R0000644000176200001440000000647014304314027016655 0ustar liggesusers#' The Bernoulli distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' Bernoulli distributions are used to represent events like coin flips #' when there is single trial that is either successful or unsuccessful. #' The Bernoulli distribution is a special case of the [Binomial()] #' distribution with `n = 1`. #' #' @inheritParams dist_binomial #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X} be a Bernoulli random variable with parameter #' `p` = \eqn{p}. Some textbooks also define \eqn{q = 1 - p}, or use #' \eqn{\pi} instead of \eqn{p}. #' #' The Bernoulli probability distribution is widely used to model #' binary variables, such as 'failure' and 'success'. The most #' typical example is the flip of a coin, when \eqn{p} is thought as the #' probability of flipping a head, and \eqn{q = 1 - p} is the #' probability of flipping a tail. #' #' **Support**: \eqn{\{0, 1\}}{{0, 1}} #' #' **Mean**: \eqn{p} #' #' **Variance**: \eqn{p \cdot (1 - p) = p \cdot q}{p (1 - p)} #' #' **Probability mass function (p.m.f)**: #' #' \deqn{ #' P(X = x) = p^x (1 - p)^{1-x} = p^x q^{1-x} #' }{ #' P(X = x) = p^x (1 - p)^(1-x) #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' \deqn{ #' P(X \le x) = #' \left \{ #' \begin{array}{ll} #' 0 & x < 0 \\ #' 1 - p & 0 \leq x < 1 \\ #' 1 & x \geq 1 #' \end{array} #' \right. #' }{ #' P(X \le x) = (1 - p) 1_{[0, 1)}(x) + 1_{1}(x) #' } #' #' **Moment generating function (m.g.f)**: #' #' \deqn{ #' E(e^{tX}) = (1 - p) + p e^t #' }{ #' E(e^(tX)) = (1 - p) + p e^t #' } #' #' @examples #' dist <- dist_bernoulli(prob = c(0.05, 0.5, 0.3, 0.9, 0.1)) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @export dist_bernoulli <- function(prob){ prob <- vec_cast(prob, double()) if(any((prob < 0) | (prob > 1))){ abort("The probability of success must be between 0 and 1.") } new_dist(p = prob, class = "dist_bernoulli") } #' @export format.dist_bernoulli <- function(x, digits = 2, ...){ sprintf( "Bernoulli(%s)", format(x[["p"]], digits = digits, ...) ) } #' @export density.dist_bernoulli <- function(x, at, ...){ stats::dbinom(at, 1, x[["p"]]) } #' @export log_density.dist_bernoulli <- function(x, at, ...){ stats::dbinom(at, 1, x[["p"]], log = TRUE) } #' @export quantile.dist_bernoulli <- function(x, p, ...){ as.logical(stats::qbinom(p, 1, x[["p"]])) } #' @export cdf.dist_bernoulli <- function(x, q, ...){ stats::pbinom(q, 1, x[["p"]]) } #' @export generate.dist_bernoulli <- function(x, times, ...){ as.logical(stats::rbinom(times, 1, x[["p"]])) } #' @export mean.dist_bernoulli <- function(x, ...){ x[["p"]] } #' @export covariance.dist_bernoulli <- function(x, ...){ x[["p"]]*(1-x[["p"]]) } #' @export skewness.dist_bernoulli <- function(x, ...) { p <- x[["p"]] q <- 1 - x[["p"]] (1 - (2 * p)) / sqrt(p * q) } #' @export kurtosis.dist_bernoulli <- function(x, ...) { p <- x[["p"]] q <- 1 - x[["p"]] (1 - (6 * p * q)) / (p * q) } distributional/R/dist_multivariate_normal.R0000644000176200001440000000510214304314511020725 0ustar liggesusers#' The multivariate normal distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' @param mu A list of numeric vectors for the distribution's mean. #' @param sigma A list of matrices for the distribution's variance-covariance matrix. #' #' @seealso [mvtnorm::dmvnorm], [mvtnorm::qmvnorm] #' #' @examples #' dist <- dist_multivariate_normal(mu = list(c(1,2)), sigma = list(matrix(c(4,2,2,3), ncol=2))) #' dist #' #' @examplesIf requireNamespace("mvtnorm", quietly = TRUE) #' mean(dist) #' variance(dist) #' support(dist) #' generate(dist, 10) #' #' density(dist, c(2, 1)) #' density(dist, c(2, 1), log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @export dist_multivariate_normal <- function(mu = 0, sigma = diag(1)){ new_dist(mu = mu, sigma = sigma, dimnames = colnames(sigma[[1]]), class = "dist_mvnorm") } #' @export format.dist_mvnorm <- function(x, digits = 2, ...){ sprintf( "MVN[%i]", length(x[["mu"]]) ) } #' @export density.dist_mvnorm <- function(x, at, ..., na.rm = FALSE){ require_package("mvtnorm") if(is.list(at)) return(vapply(at, density, numeric(1L), x = x, ...)) mvtnorm::dmvnorm(at, x[["mu"]], x[["sigma"]]) } #' @export log_density.dist_mvnorm <- function(x, at, ..., na.rm = FALSE){ require_package("mvtnorm") if(is.list(at)) return(vapply(at, log_density, numeric(1L), x = x, ...)) mvtnorm::dmvnorm(at, x[["mu"]], x[["sigma"]], log = TRUE) } #' @export quantile.dist_mvnorm <- function(x, p, type = c("univariate", "equicoordinate"), ..., na.rm = FALSE){ type <- match.arg(type) if (type == "univariate") { matrix( stats::qnorm(p, mean = rep(x[["mu"]], each = length(p)), sd = rep(diag(sqrt(x[["sigma"]])), each = length(p)), ...), nrow = length(p) ) } else { require_package("mvtnorm") mvtnorm::qmvnorm(p, mean = x[["mu"]], sigma = x[["sigma"]], ...)$quantile } } #' @export cdf.dist_mvnorm <- function(x, q, ..., na.rm = FALSE){ if(is.list(q)) return(vapply(q, cdf, numeric(1L), x = x, ...)) require_package("mvtnorm") mvtnorm::pmvnorm(as.numeric(q), mean = x[["mu"]], sigma = x[["sigma"]], ...)[1] } #' @export generate.dist_mvnorm <- function(x, times, ..., na.rm = FALSE){ require_package("mvtnorm") mvtnorm::rmvnorm(times, x[["mu"]], x[["sigma"]], ...) } #' @export mean.dist_mvnorm <- function(x, ...){ matrix(x[["mu"]], nrow = 1) } #' @export covariance.dist_mvnorm <- function(x, ...){ # Wrap in list to preserve matrix structure list(x[["sigma"]]) } #' @export dim.dist_mvnorm <- function(x){ length(x[["mu"]]) } distributional/R/dist_poisson_inverse_gaussian.R0000644000176200001440000000432614304314155022001 0ustar liggesusers#' The Poisson-Inverse Gaussian distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' @inheritParams actuar::dpoisinvgauss #' #' @seealso [actuar::PoissonInverseGaussian] #' #' @examples #' dist <- dist_poisson_inverse_gaussian(mean = rep(0.1, 3), shape = c(0.4, 0.8, 1)) #' dist #' #' @examplesIf requireNamespace("actuar", quietly = TRUE) #' mean(dist) #' variance(dist) #' support(dist) #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_poisson_inverse_gaussian #' @export dist_poisson_inverse_gaussian <- function(mean, shape){ mean <- vec_cast(mean, double()) shape <- vec_cast(shape, double()) if(any(mean[!is.na(mean)] <= 0)){ abort("The mean parameter of a Poisson-Inverse Gaussian distribution must be strictly positive.") } if(any(shape[!is.na(shape)] <= 0)){ abort("The shape parameter of a Poisson-Inverse Gaussian distribution must be strictly positive.") } new_dist(m = mean, s = shape, class = "dist_poisson_inverse_gaussian") } #' @export format.dist_poisson_inverse_gaussian <- function(x, digits = 2, ...){ sprintf( "PIG(%s, %s)", format(x[["m"]], digits = digits, ...), format(x[["s"]], digits = digits, ...) ) } #' @export density.dist_poisson_inverse_gaussian <- function(x, at, ...){ require_package("actuar") actuar::dpoisinvgauss(at, x[["m"]], x[["s"]]) } #' @export log_density.dist_poisson_inverse_gaussian <- function(x, at, ...){ require_package("actuar") actuar::dpoisinvgauss(at, x[["m"]], x[["s"]], log = TRUE) } #' @export quantile.dist_poisson_inverse_gaussian <- function(x, p, ...){ require_package("actuar") actuar::qpoisinvgauss(p, x[["m"]], x[["s"]]) } #' @export cdf.dist_poisson_inverse_gaussian <- function(x, q, ...){ require_package("actuar") actuar::ppoisinvgauss(q, x[["m"]], x[["s"]]) } #' @export generate.dist_poisson_inverse_gaussian <- function(x, times, ...){ require_package("actuar") actuar::rpoisinvgauss(times, x[["m"]], x[["s"]]) } #' @export mean.dist_poisson_inverse_gaussian <- function(x, ...){ x[["m"]] } #' @export covariance.dist_poisson_inverse_gaussian <- function(x, ...){ x[["m"]]/x[["s"]] * (x[["m"]]^2 + x[["s"]]) } distributional/R/dist_wrap.R0000644000176200001440000000706514304314661015640 0ustar liggesusers#' Create a distribution from p/d/q/r style functions #' #' @description #' `r lifecycle::badge('maturing')` #' #' If a distribution is not yet supported, you can vectorise p/d/q/r functions #' using this function. `dist_wrap()` stores the distributions parameters, and #' provides wrappers which call the appropriate p/d/q/r functions. #' #' Using this function to wrap a distribution should only be done if the #' distribution is not yet available in this package. If you need a distribution #' which isn't in the package yet, consider making a request at #' https://github.com/mitchelloharawild/distributional/issues. #' #' @param dist The name of the distribution used in the functions (name that is #' prefixed by p/d/q/r) #' @param ... Named arguments used to parameterise the distribution. #' @param package The package from which the distribution is provided. If NULL, #' the calling environment's search path is used to find the distribution #' functions. Alternatively, an arbitrary environment can also be provided here. # #' @param p,d,q,r The functions used to compute the p/d/q/r # #' (pdf/cdf/quantile/generate) #' #' @examples #' dist <- dist_wrap("norm", mean = 1:3, sd = c(3, 9, 2)) #' #' density(dist, 1) # dnorm() #' cdf(dist, 4) # pnorm() #' quantile(dist, 0.975) # qnorm() #' generate(dist, 10) # rnorm() #' #' library(actuar) #' dist <- dist_wrap("invparalogis", package = "actuar", shape = 2, rate = 2) #' density(dist, 1) # actuar::dinvparalogis() #' cdf(dist, 4) # actuar::pinvparalogis() #' quantile(dist, 0.975) # actuar::qinvparalogis() #' generate(dist, 10) # actuar::rinvparalogis() #' #' @export dist_wrap <- function(dist, ..., package = NULL){ vec_assert(dist, character(), 1L) if(is.null(package)) { env <- rlang::caller_env() } else if (is.character(package)) { env <- rlang::pkg_env(package) } else { env <- as.environment(package) } par <- vec_recycle_common(dist = dist, env = list(env), ...) new_dist(!!!par, class = "dist_wrap") } #' @export format.dist_wrap <- function(x, ...){ sprintf( "%s(%s)", x[["dist"]], paste0(x[-(1:2)], collapse = ", ") ) } #' @export density.dist_wrap <- function(x, at, ...){ fn <- get(paste0("d", x[["dist"]][[1]]), envir = x$env, mode = "function") # Remove distribution name and environment from parameters par <- x[-(1:2)] do.call(fn, c(list(at), par)) } #' @export log_density.dist_wrap <- function(x, at, ...){ fn <- get(paste0("d", x[["dist"]][[1]]), envir = x$env, mode = "function") # Remove distribution name and environment from parameters par <- x[-(1:2)] # Use density(log = TRUE) if supported if(is.null(formals(fn)$log)){ log(do.call(fn, c(list(at), par))) } else { do.call(fn, c(list(at), par, log = TRUE)) } } #' @export cdf.dist_wrap <- function(x, q, ...){ fn <- get(paste0("p", x[["dist"]][[1]]), envir = x$env, mode = "function") # Remove distribution name and environment from parameters par <- x[-(1:2)] do.call(fn, c(list(q), par)) } #' @export quantile.dist_wrap <- function(x, p, ...){ fn <- get(paste0("q", x[["dist"]][[1]]), envir = x$env, mode = "function") # Remove distribution name and environment from parameters par <- x[-(1:2)] do.call(fn, c(list(p), par)) } #' @export generate.dist_wrap <- function(x, times, ...){ fn <- get(paste0("r", x[["dist"]][[1]]), envir = x$env, mode = "function") # Remove distribution name and environment from parameters par <- x[-(1:2)] do.call(fn, c(list(times), par)) } #' @export parameters.dist_wrap <- function(x, ...) { # All parameters except distribution environment x[-2L] } distributional/R/distribution.R0000644000176200001440000003612414406341746016370 0ustar liggesusers#' Create a new distribution #' #' @description #' `r lifecycle::badge('maturing')` #' #' Allows extension package developers to define a new distribution class #' compatible with the distributional package. #' #' @param ... Parameters of the distribution (named). #' @param class The class of the distribution for S3 dispatch. #' @param dimnames The names of the variables in the distribution (optional). #' #' @export new_dist <- function(..., class = NULL, dimnames = NULL){ args <- transpose(vctrs::vec_recycle_common(...)) wrap_dist( lapply(args, enclass_dist, class = class), dimnames = dimnames ) } enclass_dist <- function(x, class) { structure(x, class = c(class, "dist_default")) } wrap_dist <- function(x, dimnames = NULL){ vctrs::new_vctr(x, vars = dimnames, class = "distribution") } #' @export vec_ptype_abbr.distribution <- function(x, ...){ "dist" } #' @export format.distribution <- function(x, ...){ x <- vec_data(x) out <- vapply(x, format, character(1L), ...) out[vapply(x, is.null, logical(1L))] <- "NA" out } #' @export `dimnames<-.distribution` <- function(x, value){ attr(x, "vars") <- value x } #' @export dimnames.distribution <- function(x){ attr(x, "vars") } #' @export `[[.distribution` <- `[` #' The probability density/mass function #' #' @description #' `r lifecycle::badge('stable')` #' #' Computes the probability density function for a continuous distribution, or #' the probability mass function for a discrete distribution. #' #' @param x The distribution(s). #' @param at The point at which to compute the density/mass. #' @param ... Additional arguments passed to methods. #' @param log If `TRUE`, probabilities will be given as log probabilities. #' #' @importFrom stats density #' @export density.distribution <- function(x, at, ..., log = FALSE){ if(log) return(log_density(x, at, ...)) at <- arg_listable(at, .ptype = NULL) dist_apply(x, density, at = at, ...) } log_density <- function(x, at, ...) { UseMethod("log_density") } #' @export log_density.distribution <- function(x, at, ...){ at <- arg_listable(at, .ptype = NULL) dist_apply(x, log_density, at = at, ...) } #' Distribution Quantiles #' #' @description #' `r lifecycle::badge('stable')` #' #' Computes the quantiles of a distribution. #' #' @inheritParams density.distribution #' @param p The probability of the quantile. #' @param ... Additional arguments passed to methods. #' #' @importFrom stats quantile #' @export quantile.distribution <- function(x, p, ..., log = FALSE){ if(log) return(log_quantile(x, p, ...)) p <- arg_listable(p, .ptype = double()) dist_apply(x, quantile, p = p, ...) } log_quantile <- function(x, p, ...) { UseMethod("log_quantile") } #' @export log_quantile.distribution <- function(x, p, ...){ vec_assert(q, double(), 1L) p <- arg_listable(p, .ptype = double()) dist_apply(x, log_quantile, p = p, ...) } #' The cumulative distribution function #' #' @description #' `r lifecycle::badge('stable')` #' #' @inheritParams density.distribution #' @param q The quantile at which the cdf is calculated. #' #' @name cdf #' @export cdf <- function (x, q, ..., log = FALSE){ if(log) return(log_cdf(x, q, ...)) UseMethod("cdf") } #' @rdname cdf #' @export cdf.distribution <- function(x, q, ...){ q <- arg_listable(q, .ptype = NULL) dist_apply(x, cdf, q = q, ...) } log_cdf <- function(x, q, ...) { UseMethod("log_cdf") } #' @export log_cdf.distribution <- function(x, q, ...){ q <- arg_listable(q, .ptype = NULL) dist_apply(x, log_cdf, q = q, ...) } #' Randomly sample values from a distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' Generate random samples from probability distributions. #' #' @param x The distribution(s). #' @param times The number of samples. #' @param ... Additional arguments used by methods. #' #' @export generate.distribution <- function(x, times, ...){ times <- vec_cast(times, integer()) times <- vec_recycle(times, size = length(x)) x <- vec_data(x) dist_is_na <- vapply(x, is.null, logical(1L)) x[dist_is_na] <- list(structure(list(), class = c("dist_na", "dist_default"))) mapply(generate, x, times = times, ..., SIMPLIFY = FALSE) # dist_apply(x, generate, times = times, ...) # Needs work to structure MV appropriately. } #' The (log) likelihood of a sample matching a distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' @param x The distribution(s). #' @param ... Additional arguments used by methods. #' #' @name likelihood #' @export likelihood <- function (x, ...){ UseMethod("likelihood") } #' @rdname likelihood #' @param sample A list of sampled values to compare to distribution(s). #' @param log If `TRUE`, the log-likelihood will be computed. #' @export likelihood.distribution <- function(x, sample, ..., log = FALSE){ if(vec_is(sample, numeric())) { warn("The `sample` argument of `likelihood()` should contain a list of numbers. The same sample will be used for each distribution, i.e. `sample = list(sample)`.") sample <- list(sample) } if(log){ dist_apply(x, log_likelihood, sample = sample, ...) } else { dist_apply(x, likelihood, sample = sample, ...) } } #' @rdname likelihood #' @export log_likelihood <- function(x, ...) { UseMethod("log_likelihood") } #' @export log_likelihood.distribution <- function(x, sample, ...){ dist_apply(x, log_likelihood, sample = sample, ...) } #' Extract the parameters of a distribution #' #' @description #' `r lifecycle::badge('experimental')` #' #' @param x The distribution(s). #' @param ... Additional arguments used by methods. #' #' @name parameters #' @examples #' dist <- c( #' dist_normal(1:2), #' dist_poisson(3), #' dist_multinomial(size = c(4, 3), #' prob = list(c(0.3, 0.5, 0.2), c(0.1, 0.5, 0.4))) #' ) #' parameters(dist) #' @export parameters <- function(x, ...) { UseMethod("parameters") } #' @rdname parameters #' @export parameters.distribution <- function(x, ...) { x <- lapply(vec_data(x), parameters) x <- lapply(x, function(z) data_frame(!!!z, .name_repair = "minimal")) vec_rbind(!!!x) } #' Extract the name of the distribution family #' #' @description #' `r lifecycle::badge('experimental')` #' #' @param object The distribution(s). #' @param ... Additional arguments used by methods. #' #' @examples #' dist <- c( #' dist_normal(1:2), #' dist_poisson(3), #' dist_multinomial(size = c(4, 3), #' prob = list(c(0.3, 0.5, 0.2), c(0.1, 0.5, 0.4))) #' ) #' family(dist) #' #' @importFrom stats family #' @export family.distribution <- function(object, ...) { vapply(vec_data(object), family, character(1L)) } #' Region of support of a distribution #' #' @description #' `r lifecycle::badge('experimental')` #' #' @param x The distribution(s). #' @param ... Additional arguments used by methods. #' #' @name support #' @export support <- function(x, ...) { UseMethod("support") } #' @rdname support #' @export support.distribution <- function(x, ...) { dist_apply(x, support, ...) } #' Mean of a probability distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' Returns the empirical mean of the probability distribution. If the method #' does not exist, the mean of a random sample will be returned. #' #' @param x The distribution(s). #' @param ... Additional arguments used by methods. #' #' @export mean.distribution <- function(x, ...){ dist_apply(x, mean, ...) } #' Variance #' #' @description #' `r lifecycle::badge('stable')` #' #' A generic function for computing the variance of an object. #' #' @param x An object. #' @param ... Additional arguments used by methods. #' #' @details #' #' The implementation of `variance()` for numeric variables coerces the input to #' a vector then uses [`stats::var()`] to compute the variance. This means that, #' unlike [`stats::var()`], if `variance()` is passed a matrix or a 2-dimensional #' array, it will still return the variance ([`stats::var()`] returns the #' covariance matrix in that case). #' #' @seealso [`variance.distribution()`], [`covariance()`] #' #' @export variance <- function(x, ...){ UseMethod("variance") } #' @export variance.default <- function(x, ...){ stop( "The variance() method is not supported for objects of type ", paste(deparse(class(x)), collapse = "") ) } #' @rdname variance #' @export variance.numeric <- function(x, ...){ stats::var(as.vector(x), ...) } #' @rdname variance #' @export variance.matrix <- function(x, ...){ diag(stats::cov(x, ...)) } #' Variance of a probability distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' Returns the empirical variance of the probability distribution. If the method #' does not exist, the variance of a random sample will be returned. #' #' @param x The distribution(s). #' @param ... Additional arguments used by methods. #' #' @export variance.distribution <- function(x, ...){ dist_apply(x, variance, ...) } #' Covariance #' #' @description #' `r lifecycle::badge('stable')` #' #' A generic function for computing the covariance of an object. #' #' @param x An object. #' @param ... Additional arguments used by methods. #' #' @seealso [`covariance.distribution()`], [`variance()`] #' #' @export covariance <- function(x, ...){ UseMethod("covariance") } #' @export covariance.default <- function(x, ...){ stop( "The covariance() method is not supported for objects of type ", paste(deparse(class(x)), collapse = "") ) } #' @rdname variance #' @export covariance.numeric <- function(x, ...){ stats::cov(x, ...) } #' Covariance of a probability distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' Returns the empirical covariance of the probability distribution. If the #' method does not exist, the covariance of a random sample will be returned. #' #' @param x The distribution(s). #' @param ... Additional arguments used by methods. #' #' @export covariance.distribution <- function(x, ...){ dist_apply(x, covariance, ...) } #' Skewness of a probability distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' @param x The distribution(s). #' @param ... Additional arguments used by methods. #' #' @export skewness <- function(x, ...) { UseMethod("skewness") } #' @rdname skewness #' @export skewness.distribution <- function(x, ...){ dist_apply(x, skewness, ...) } #' Kurtosis of a probability distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' @param x The distribution(s). #' @param ... Additional arguments used by methods. #' #' @export kurtosis <- function(x, ...) { UseMethod("kurtosis") } #' @rdname kurtosis #' @export kurtosis.distribution <- function(x, ...){ dist_apply(x, kurtosis, ...) } #' Median of a probability distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' Returns the median (50th percentile) of a probability distribution. This is #' equivalent to `quantile(x, p=0.5)`. #' #' @param x The distribution(s). #' @param na.rm Unused, included for consistency with the generic function. #' @param ... Additional arguments used by methods. #' #' @importFrom stats median #' @export median.distribution <- function(x, na.rm = FALSE, ...){ dist_apply(x, median, na.rm = na.rm, ...) } #' Probability intervals of a probability distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' Returns a `hilo` central probability interval with probability coverage of #' `size`. By default, the distribution's [`quantile()`] will be used to compute #' the lower and upper bound for a centered interval #' #' @param x The distribution(s). #' @param size The size of the interval (between 0 and 100). #' @param ... Additional arguments used by methods. #' #' @seealso [`hdr.distribution()`] #' #' @importFrom stats median #' @export hilo.distribution <- function(x, size = 95, ...){ size <- arg_listable(size, .ptype = double()) dist_apply(x, hilo, size = size, ...) } #' Highest density regions of probability distributions #' #' @description #' `r lifecycle::badge('maturing')` #' #' This function is highly experimental and will change in the future. In #' particular, improved functionality for object classes and visualisation tools #' will be added in a future release. #' #' Computes minimally sized probability intervals highest density regions. #' #' @param x The distribution(s). #' @param size The size of the interval (between 0 and 100). #' @param n The resolution used to estimate the distribution's density. #' @param ... Additional arguments used by methods. #' #' @export hdr.distribution <- function(x, size = 95, n = 512, ...){ size <- arg_listable(size, .ptype = double()) dist_apply(x, hdr, size = size, n = n, ...) } #' @export sum.distribution <- function(x, ...){ vec_restore(list(Reduce("+", x)), x) } #' @method vec_arith distribution #' @export vec_arith.distribution <- function(op, x, y, ...){ UseMethod("vec_arith.distribution", y) } #' @method vec_arith.distribution default #' @export vec_arith.distribution.default <- function(op, x, y, ...){ dist_is_na <- vapply(x, is.null, logical(1L)) x[dist_is_na] <- list(structure(list(), class = c("dist_na", "dist_default"))) if(is_empty(y)){ out <- lapply(vec_data(x), get(op)) } else { x <- vec_recycle_common(x = x, y = y) y <- x[["y"]] if(is_distribution(y)) y <- vec_data(y) x <- x[["x"]] out <- mapply(get(op), x = vec_data(x), y = y, SIMPLIFY = FALSE) } vec_restore(out, x) } #' @method vec_arith.numeric distribution #' @export vec_arith.numeric.distribution <- function(op, x, y, ...){ x <- vec_recycle_common(x = x, y = y) y <- x[["y"]] x <- x[["x"]] out <- mapply(get(op), x = x, y = vec_data(y), SIMPLIFY = FALSE) vec_restore(out, y) } #' @method vec_math distribution #' @export vec_math.distribution <- function(.fn, .x, ...) { if(.fn %in% c("is.nan", "is.infinite")) return(rep_len(FALSE, length(.x))) if(.fn == "is.finite") return(rep_len(TRUE, length(.x))) out <- lapply(vec_data(.x), get(.fn), ...) vec_restore(out, .x) } #' @export vec_ptype2.distribution.distribution <- function(x, y, ...){ if(!identical(dimnames(x), dimnames(y))){ abort("Distributions must have the same `dimnames` to be combined.") } x } #' @export vec_ptype2.double.distribution <- function(x, y, ...) new_dist() #' @export vec_ptype2.distribution.double <- function(x, y, ...) new_dist() #' @export vec_ptype2.integer.distribution <- function(x, y, ...) new_dist() #' @export vec_ptype2.distribution.integer <- function(x, y, ...) new_dist() #' @export vec_cast.distribution.distribution <- function(x, to, ...){ dimnames(x) <- dimnames(to) x } #' @export vec_cast.distribution.double <- function(x, to, ...){ x <- dist_degenerate(x) dimnames(x) <- dimnames(to) x } #' @export vec_cast.distribution.integer <- vec_cast.distribution.double #' @export vec_cast.character.distribution <- function(x, to, ...){ format(x) } #' Test if the object is a distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' This function returns `TRUE` for distributions and `FALSE` for all other objects. #' #' @param x An object. #' #' @return TRUE if the object inherits from the distribution class. #' @rdname is-distribution #' @examples #' dist <- dist_normal() #' is_distribution(dist) #' is_distribution("distributional") #' @export is_distribution <- function(x) { inherits(x, "distribution") } distributional/R/dist_burr.R0000644000176200001440000000444614304314037015636 0ustar liggesusers#' The Burr distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' @inheritParams actuar::dburr #' #' @seealso [actuar::Burr] #' #' @examples #' dist <- dist_burr(shape1 = c(1,1,1,2,3,0.5), shape2 = c(1,2,3,1,1,2)) #' dist #' #' @examplesIf requireNamespace("actuar", quietly = TRUE) #' mean(dist) #' variance(dist) #' support(dist) #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_burr #' @export dist_burr <- function(shape1, shape2, rate = 1, scale = 1/rate){ shape1 <- vec_cast(shape1, double()) shape2 <- vec_cast(shape2, double()) if(any(shape1 <= 0)){ abort("The shape1 parameter of a Burr distribution must be strictly positive.") } if(any(shape2 <= 0)){ abort("The shape2 parameter of a Burr distribution must be strictly positive.") } if(any(rate <= 0)){ abort("The rate parameter of a Burr distribution must be strictly positive.") } new_dist(s1 = shape1, s2 = shape2, r = 1/scale, class = "dist_burr") } #' @export format.dist_burr <- function(x, digits = 2, ...){ sprintf( "Burr12(%s, %s, %s)", format(x[["s1"]], digits = digits, ...), format(x[["s2"]], x[["r"]], digits = digits, ...), format(x[["r"]], digits = digits, ...) ) } #' @export density.dist_burr <- function(x, at, ...){ require_package("actuar") actuar::dburr(at, x[["s1"]], x[["s2"]], x[["r"]]) } #' @export log_density.dist_burr <- function(x, at, ...){ require_package("actuar") actuar::dburr(at, x[["s1"]], x[["s2"]], x[["r"]], log = TRUE) } #' @export quantile.dist_burr <- function(x, p, ...){ require_package("actuar") actuar::qburr(p, x[["s1"]], x[["s2"]], x[["r"]]) } #' @export cdf.dist_burr <- function(x, q, ...){ require_package("actuar") actuar::pburr(q, x[["s1"]], x[["s2"]], x[["r"]]) } #' @export generate.dist_burr <- function(x, times, ...){ require_package("actuar") actuar::rburr(times, x[["s1"]], x[["s2"]], x[["r"]]) } #' @export mean.dist_burr <- function(x, ...){ require_package("actuar") actuar::mburr(1, x[["s1"]], x[["s2"]], x[["r"]]) } #' @export covariance.dist_burr <- function(x, ...){ require_package("actuar") m1 <- actuar::mburr(1, x[["s1"]], x[["s2"]], x[["r"]]) m2 <- actuar::mburr(2, x[["s1"]], x[["s2"]], x[["r"]]) -m1^2 + m2 } distributional/R/dist_inverse_gaussian.R0000644000176200001440000000405514304314117020224 0ustar liggesusers#' The Inverse Gaussian distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' @inheritParams actuar::dinvgauss #' #' @seealso [actuar::InverseGaussian] #' #' @examples #' dist <- dist_inverse_gaussian(mean = c(1,1,1,3,3), shape = c(0.2, 1, 3, 0.2, 1)) #' dist #' #' @examplesIf requireNamespace("actuar", quietly = TRUE) #' mean(dist) #' variance(dist) #' support(dist) #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_inverse_gaussian #' @export dist_inverse_gaussian <- function(mean, shape){ mean <- vec_cast(mean, double()) shape <- vec_cast(shape, double()) if(any(mean[!is.na(mean)] <= 0)){ abort("The mean parameter of a Inverse Gaussian distribution must be strictly positive.") } if(any(shape[!is.na(shape)] <= 0)){ abort("The shape parameter of a Inverse Gaussian distribution must be strictly positive.") } new_dist(m = mean, s = shape, class = "dist_inverse_gaussian") } #' @export format.dist_inverse_gaussian <- function(x, digits = 2, ...){ sprintf( "IG(%s, %s)", format(x[["m"]], digits = digits, ...), format(x[["s"]], digits = digits, ...) ) } #' @export density.dist_inverse_gaussian <- function(x, at, ...){ require_package("actuar") actuar::dinvgauss(at, x[["m"]], x[["s"]]) } #' @export log_density.dist_inverse_gaussian <- function(x, at, ...){ require_package("actuar") actuar::dinvgauss(at, x[["m"]], x[["s"]], log = TRUE) } #' @export quantile.dist_inverse_gaussian <- function(x, p, ...){ require_package("actuar") actuar::qinvgauss(p, x[["m"]], x[["s"]]) } #' @export cdf.dist_inverse_gaussian <- function(x, q, ...){ require_package("actuar") actuar::pinvgauss(q, x[["m"]], x[["s"]]) } #' @export generate.dist_inverse_gaussian <- function(x, times, ...){ require_package("actuar") actuar::rinvgauss(times, x[["m"]], x[["s"]]) } #' @export mean.dist_inverse_gaussian <- function(x, ...){ x[["m"]] } #' @export covariance.dist_inverse_gaussian <- function(x, ...){ x[["m"]]^3/x[["s"]] } distributional/R/mixture.R0000644000176200001440000000477114406341620015340 0ustar liggesusers#' Create a mixture of distributions #' #' @description #' `r lifecycle::badge('maturing')` #' #' @param ... Distributions to be used in the mixture. #' @param weights The weight of each distribution passed to `...`. #' #' @examples #' dist_mixture(dist_normal(0, 1), dist_normal(5, 2), weights = c(0.3, 0.7)) #' #' @export dist_mixture <- function(..., weights = numeric()){ dist <- dots_list(...) dn <- unique(lapply(dist, dimnames)) dn <- if(length(dn) == 1) dn[[1]] else NULL vec_is(weights, numeric(), length(dist)) if(sum(weights) != 1){ abort("Weights of a mixture model must sum to 1.") } if(any(weights < 0)){ abort("All weights in a mixtue model must be non-negative.") } new_dist(dist = transpose(dist), w = list(weights), class = "dist_mixture", dimnames = dn) } #' @export format.dist_mixture <- function(x, ...){ sprintf( "mixture(n=%i)", length(x[["dist"]]) ) } #' @export density.dist_mixture <- function(x, at, ...){ if(length(at) > 1) return(vapply(at, density, numeric(1L), x = x, ...)) sum(x[["w"]]*vapply(x[["dist"]], density, numeric(1L), at = at, ...)) } #' @export quantile.dist_mixture <- function(x, p, ...){ if(length(p) > 1) return(vapply(p, quantile, numeric(1L), x = x, ...)) # Find bounds for optimisation based on range of each quantile dist_q <- vapply(x[["dist"]], quantile, numeric(1L), p, ..., USE.NAMES = FALSE) if(vctrs::vec_unique_count(dist_q) == 1) return(dist_q[1]) if(p == 0) return(min(dist_q)) if(p == 1) return(max(dist_q)) # Search the cdf() for appropriate quantile stats::uniroot( function(pos) p - cdf(x, pos, ...), interval = c(min(dist_q), max(dist_q)), extendInt = "yes" )$root } #' @export cdf.dist_mixture <- function(x, q, ...){ if(length(q) > 1) return(vapply(q, cdf, numeric(1L), x = x, ...)) sum(x[["w"]]*vapply(x[["dist"]], cdf, numeric(1L), q = q, ...)) } #' @export generate.dist_mixture <- function(x, times, ...){ dist_idx <- .bincode(stats::runif(times), breaks = c(0, cumsum(x[["w"]]))) r <- numeric(times) for(i in seq_along(x[["dist"]])){ r_pos <- dist_idx == i r[r_pos] <- generate(x[["dist"]][[i]], sum(r_pos), ...) } r } #' @export mean.dist_mixture <- function(x, ...){ sum(x[["w"]]*vapply(x[["dist"]], mean, numeric(1L), ...)) } #' @export covariance.dist_mixture <- function(x, ...){ m <- vapply(x[["dist"]], mean, numeric(1L), ...) v <- vapply(x[["dist"]], variance, numeric(1L), ...) m1 <- sum(x[["w"]]*m) m2 <- sum(x[["w"]]*(m^2 + v)) m2 - m1^2 } distributional/R/dist_negative_binomial.R0000644000176200001440000000571414304314134020335 0ustar liggesusers#' The Negative Binomial distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' A generalization of the geometric distribution. It is the number #' of failures in a sequence of i.i.d. Bernoulli trials before #' a specified number of successes (`size`) occur. The probability of success in #' each trial is given by `prob`. #' #' @inheritParams stats::NegBinomial #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X} be a Negative Binomial random variable with #' success probability `prob` = \eqn{p} and the number of successes `size` = #' \eqn{r}. #' #' #' **Support**: \eqn{\{0, 1, 2, 3, ...\}} #' #' **Mean**: \eqn{\frac{p r}{1-p}} #' #' **Variance**: \eqn{\frac{pr}{(1-p)^2}} #' #' **Probability mass function (p.m.f)**: #' #' \deqn{ #' f(k) = {k + r - 1 \choose k} \cdot (1-p)^r p^k #' }{ #' f(k) = (k+r-1)!/(k!(r-1)!) (1-p)^r p^k #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' Too nasty, omitted. #' #' **Moment generating function (m.g.f)**: #' #' \deqn{ #' \left(\frac{1-p}{1-pe^t}\right)^r, t < -\log p #' }{ #' \frac{(1-p)^r}{(1-pe^t)^r}, t < -\log p #' } #' #' @seealso [stats::NegBinomial] #' #' @examples #' dist <- dist_negative_binomial(size = 10, prob = 0.5) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' support(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @export dist_negative_binomial <- function(size, prob){ size <- vec_cast(size, double()) prob <- vec_cast(prob, double()) if(any(prob < 0 | prob > 1)){ abort("Probability of success must be between 0 and 1.") } new_dist(n = size, p = prob, class = "dist_negbin") } #' @export format.dist_negbin <- function(x, digits = 2, ...){ sprintf( "NB(%s, %s)", format(x[["n"]], digits = digits, ...), format(x[["p"]], digits = digits, ...) ) } #' @export density.dist_negbin <- function(x, at, ...){ stats::dnbinom(at, x[["n"]], x[["p"]]) } #' @export log_density.dist_negbin <- function(x, at, ...){ stats::dnbinom(at, x[["n"]], x[["p"]], log = TRUE) } #' @export quantile.dist_negbin <- function(x, p, ...){ stats::qnbinom(p, x[["n"]], x[["p"]]) } #' @export cdf.dist_negbin <- function(x, q, ...){ stats::pnbinom(q, x[["n"]], x[["p"]]) } #' @export generate.dist_negbin <- function(x, times, ...){ stats::rnbinom(times, x[["n"]], x[["p"]]) } #' @export mean.dist_negbin <- function(x, ...){ x[["n"]] * (1 - x[["p"]]) / x[["p"]] } #' @export covariance.dist_negbin <- function(x, ...){ x[["n"]] * (1 - x[["p"]]) / x[["p"]]^2 } #' @export skewness.dist_negbin <- function(x, ...) { (1 + x[["p"]]) / sqrt(x[["p"]] * x[["n"]]) } #' @export kurtosis.dist_negbin <- function(x, ...) { 6 / x[["n"]] + (1 - x[["p"]])^2 / x[["n"]] * x[["p"]] } distributional/R/dist_hypergeometric.R0000644000176200001440000000704314304314104017701 0ustar liggesusers#' The Hypergeometric distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' To understand the HyperGeometric distribution, consider a set of #' \eqn{r} objects, of which \eqn{m} are of the type I and #' \eqn{n} are of the type II. A sample with size \eqn{k} (\eqn{k, where the math #' will render nicely. #' #' In the following, let \eqn{X} be a HyperGeometric random variable with #' success probability `p` = \eqn{p = m/(m+n)}. #' #' **Support**: \eqn{x \in { \{\max{(0, k-n)}, \dots, \min{(k,m)}}\}} #' #' **Mean**: \eqn{\frac{km}{n+m} = kp} #' #' **Variance**: \eqn{\frac{km(n)(n+m-k)}{(n+m)^2 (n+m-1)} = #' kp(1-p)(1 - \frac{k-1}{m+n-1})} #' #' **Probability mass function (p.m.f)**: #' #' \deqn{ #' P(X = x) = \frac{{m \choose x}{n \choose k-x}}{{m+n \choose k}} #' }{ #' P(X = x) = \frac{{m \choose x}{n \choose k-x}}{{m+n \choose k}} #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' \deqn{ #' P(X \le k) \approx \Phi\Big(\frac{x - kp}{\sqrt{kp(1-p)}}\Big) #' } #' #' @seealso [stats::Hypergeometric] #' #' @examples #' dist <- dist_hypergeometric(m = rep(500, 3), n = c(50, 60, 70), k = c(100, 200, 300)) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_hypergeometric #' @export dist_hypergeometric <- function(m, n, k){ m <- vec_cast(m, integer()) n <- vec_cast(n, integer()) k <- vec_cast(k, integer()) new_dist(m = m, n = n, k = k, class = "dist_hypergeometric") } #' @export format.dist_hypergeometric <- function(x, digits = 2, ...){ sprintf( "Hypergeometric(%s, %s, %s)", format(x[["m"]], digits = digits, ...), format(x[["n"]], digits = digits, ...), format(x[["k"]], digits = digits, ...) ) } #' @export density.dist_hypergeometric <- function(x, at, ...){ stats::dhyper(at, x[["m"]], x[["n"]], x[["k"]]) } #' @export log_density.dist_hypergeometric <- function(x, at, ...){ stats::dhyper(at, x[["m"]], x[["n"]], x[["k"]], log = TRUE) } #' @export quantile.dist_hypergeometric <- function(x, p, ...){ stats::qhyper(p, x[["m"]], x[["n"]], x[["k"]]) } #' @export cdf.dist_hypergeometric <- function(x, q, ...){ stats::phyper(q, x[["m"]], x[["n"]], x[["k"]]) } #' @export generate.dist_hypergeometric <- function(x, times, ...){ stats::rhyper(times, x[["m"]], x[["n"]], x[["k"]]) } #' @export mean.dist_hypergeometric <- function(x, ...){ p <- x[["m"]]/(x[["m"]] + x[["n"]]) x[["k"]] * p } #' @export covariance.dist_hypergeometric <- function(x, ...){ m <- x[["m"]] n <- x[["n"]] k <- x[["k"]] p <- m/(m + n) k * p * (1 - p) * ((m + n - k) / (m + n - 1)) } #' @export skewness.dist_hypergeometric <- function(x, ...) { N <- x[["n"]] + x[["m"]] K <- x[["m"]] n <- x[["k"]] a <- (N - 2 * K) * (N - 1)^0.5 * (N - 2 * n) b <- (n * K * (N - K) * (N - n))^0.5 * (N - 2) a / b } #' @export kurtosis.dist_hypergeometric <- function(x, ...) { N <- x[["n"]] + x[["m"]] K <- x[["m"]] n <- x[["k"]] 1 / (n * K * (N - K) * (N - n) * (N - 2) * (N - 3)) } distributional/R/distributional-package.R0000644000176200001440000000061014304310432020246 0ustar liggesusers#' @keywords internal "_PACKAGE" # The following block is used by usethis to automatically manage # roxygen namespace tags. Modify with care! ## usethis namespace: start #' @importFrom lifecycle deprecate_soft #' @importFrom lifecycle deprecated ## usethis namespace: end #' @import vctrs #' @import rlang NULL # Used for generating transformation function expressions globalVariables("x") distributional/R/dist_uniform.R0000644000176200001440000000572014304314175016342 0ustar liggesusers#' The Uniform distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' A distribution with constant density on an interval. #' #' @inheritParams stats::dunif #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X} be a Poisson random variable with parameter #' `lambda` = \eqn{\lambda}. #' #' **Support**: \eqn{[a,b]}{[a,b]} #' #' **Mean**: \eqn{\frac{1}{2}(a+b)} #' #' **Variance**: \eqn{\frac{1}{12}(b-a)^2} #' #' **Probability mass function (p.m.f)**: #' #' \deqn{ #' f(x) = \frac{1}{b-a} for x \in [a,b] #' }{ #' f(x) = \frac{1}{b-a} for x in [a,b] #' } #' \deqn{ #' f(x) = 0 otherwise #' }{ #' f(x) = 0 otherwise #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' \deqn{ #' F(x) = 0 for x < a #' }{ #' F(x) = 0 for x < a #' } #' \deqn{ #' F(x) = \frac{x - a}{b-a} for x \in [a,b] #' }{ #' F(x) = \frac{x - a}{b-a} for x in [a,b] #' } #' \deqn{ #' F(x) = 1 for x > b #' }{ #' F(x) = 1 for x > b #' } #' #' **Moment generating function (m.g.f)**: #' #' \deqn{ #' E(e^{tX}) = \frac{e^{tb} - e^{ta}}{t(b-a)} for t \neq 0 #' }{ #' E(e^(tX)) = \frac{e^{tb} - e^{ta}}{t(b-a)} for t \neq 0 #' } #' \deqn{ #' E(e^{tX}) = 1 for t = 0 #' }{ #' E(e^(tX)) = 1 for t = 0 #' } #' #' @seealso [stats::Uniform] #' #' @examples #' dist <- dist_uniform(min = c(3, -2), max = c(5, 4)) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_uniform #' @export dist_uniform <- function(min, max){ min <- vec_cast(min, double()) max <- vec_cast(max, double()) if(any(min > max)){ abort("The min of a Uniform distribution must be less than max.") } new_dist(l = min, u = max, class = "dist_uniform") } #' @export format.dist_uniform <- function(x, digits = 2, ...){ sprintf( "U(%s, %s)", format(x[["l"]], digits = digits, ...), format(x[["u"]], digits = digits, ...) ) } #' @export density.dist_uniform <- function(x, at, ...){ stats::dunif(at, x[["l"]], x[["u"]]) } #' @export log_density.dist_uniform <- function(x, at, ...){ stats::dunif(at, x[["l"]], x[["u"]], log = TRUE) } #' @export quantile.dist_uniform <- function(x, p, ...){ stats::qunif(p, x[["l"]], x[["u"]]) } #' @export cdf.dist_uniform <- function(x, q, ...){ stats::punif(q, x[["l"]], x[["u"]]) } #' @export generate.dist_uniform <- function(x, times, ...){ stats::runif(times, x[["l"]], x[["u"]]) } #' @export mean.dist_uniform <- function(x, ...){ (x[["u"]]+x[["l"]])/2 } #' @export covariance.dist_uniform <- function(x, ...){ (x[["u"]]-x[["l"]])^2/12 } #' @export skewness.dist_uniform <- function(x, ...) 0 #' @export kurtosis.dist_uniform <- function(x, ...) -6/5 distributional/R/dist_percentile.R0000644000176200001440000000235214476623220017017 0ustar liggesusers#' Percentile distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' @param x A list of values #' @param percentile A list of percentiles #' #' @examples #' dist <- dist_normal() #' percentiles <- seq(0.01, 0.99, by = 0.01) #' x <- vapply(percentiles, quantile, double(1L), x = dist) #' dist_percentile(list(x), list(percentiles*100)) #' #' @export dist_percentile <- function(x, percentile){ x <- as_list_of(x, .ptype = double()) percentile <- as_list_of(percentile, .ptype = double()) new_dist(x = x, percentile = percentile, class = "dist_percentile") } #' @export format.dist_percentile <- function(x, ...){ sprintf( "percentile[%s]", length(x[["x"]]) ) } # #' @export # density.dist_percentile <- function(x, at, ...){ # } # #' @export quantile.dist_percentile <- function(x, p, ...){ out <- x[["x"]][match(p, x[["percentile"]])] out[is.na(out)] <- stats::approx(x = x[["percentile"]]/100, y = x[["x"]], xout = p[is.na(out)])$y out } #' @export cdf.dist_percentile <- function(x, q, ...){ stats::approx(x = x[["x"]], y = x[["percentile"]]/100, xout = q)$y } #' @export generate.dist_percentile <- function(x, times, ...){ stats::approx(x[["percentile"]]/100, x[["x"]], xout=stats::runif(times,0,1))$y } distributional/R/dist_f.R0000644000176200001440000001047214304314062015103 0ustar liggesusers#' The F Distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' @inheritParams stats::df #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X} be a Gamma random variable #' with parameters #' `shape` = \eqn{\alpha} and #' `rate` = \eqn{\beta}. #' #' **Support**: \eqn{x \in (0, \infty)} #' #' **Mean**: \eqn{\frac{\alpha}{\beta}} #' #' **Variance**: \eqn{\frac{\alpha}{\beta^2}} #' #' **Probability density function (p.m.f)**: #' #' \deqn{ #' f(x) = \frac{\beta^{\alpha}}{\Gamma(\alpha)} x^{\alpha - 1} e^{-\beta x} #' }{ #' f(x) = \frac{\beta^{\alpha}}{\Gamma(\alpha)} x^{\alpha - 1} e^{-\beta x} #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' \deqn{ #' f(x) = \frac{\Gamma(\alpha, \beta x)}{\Gamma{\alpha}} #' }{ #' f(x) = \frac{\Gamma(\alpha, \beta x)}{\Gamma{\alpha}} #' } #' #' **Moment generating function (m.g.f)**: #' #' \deqn{ #' E(e^{tX}) = \Big(\frac{\beta}{ \beta - t}\Big)^{\alpha}, \thinspace t < \beta #' }{ #' E(e^(tX)) = \Big(\frac{\beta}{ \beta - t}\Big)^{\alpha}, \thinspace t < \beta #' } #' #' @seealso [stats::FDist] #' #' @examples #' dist <- dist_f(df1 = c(1,2,5,10,100), df2 = c(1,1,2,1,100)) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_f #' @export dist_f <- function(df1, df2, ncp = NULL){ df1 <- vec_cast(df1, double()) df2 <- vec_cast(df2, double()) ncp <- vec_cast(ncp, double()) if(any((df1 < 0) | (df2 < 0))){ abort("The degrees of freedom parameters of the F distribution must be non-negative.") } if(is.null(ncp)){ new_dist(df1 = df1, df2 = df2, class = "dist_f") } else { new_dist(df1 = df1, df2 = df2, ncp = ncp, class = "dist_f") } } #' @export format.dist_f <- function(x, digits = 2, ...){ sprintf( "F(%s, %s)", format(x[["df1"]], digits = digits, ...), format(x[["df2"]], digits = digits, ...) ) } #' @export density.dist_f <- function(x, at, ...){ if(is.null(x[["ncp"]])) { stats::df(at, x[["df1"]], x[["df2"]]) } else { stats::df(at, x[["df1"]], x[["df2"]], x[["ncp"]]) } } #' @export log_density.dist_f <- function(x, at, ...){ if(is.null(x[["ncp"]])) { stats::df(at, x[["df1"]], x[["df2"]], log = TRUE) } else { stats::df(at, x[["df1"]], x[["df2"]], x[["ncp"]], log = TRUE) } } #' @export quantile.dist_f <- function(x, p, ...){ if(is.null(x[["ncp"]])) { stats::qf(p, x[["df1"]], x[["df2"]]) } else { stats::qf(p, x[["df1"]], x[["df2"]], x[["ncp"]]) } } #' @export cdf.dist_f <- function(x, q, ...){ if(is.null(x[["ncp"]])) { stats::pf(q, x[["df1"]], x[["df2"]]) } else { stats::pf(q, x[["df1"]], x[["df2"]], x[["ncp"]]) } } #' @export generate.dist_f <- function(x, times, ...){ if(is.null(x[["ncp"]])) { stats::rf(times, x[["df1"]], x[["df2"]]) } else { stats::rf(times, x[["df1"]], x[["df2"]], x[["ncp"]]) } } #' @export mean.dist_f <- function(x, ...){ df1 <- x[["df1"]] df2 <- x[["df2"]] if(df2 > 2) { if(is.null(x[["ncp"]])){ df2 / (df2 - 2) } else { (df2 * (df1 + x[["ncp"]])) / (df1 * (df2 - 2)) } } else { NA_real_ } } #' @export covariance.dist_f <- function(x, ...){ df1 <- x[["df1"]] df2 <- x[["df2"]] if(df2 > 4) { if(is.null(x[["ncp"]])){ (2 * df2^2 * (df1 + df2 - 2))/(df1*(df2-2)^2*(df2-4)) } else { 2*((df1 + x[["ncp"]])^2 + (df1 + 2*x[["ncp"]])*(df2 - 2))/((df2-2)^2*(df2-4)) * (df2^2/df1^2) } } else { NA_real_ } } #' @export skewness.dist_f <- function(x, ...) { df1 <- x[["df1"]] df2 <- x[["df2"]] if(!is.null(x[["ncp"]])) return(NA_real_) if (df2 > 6) { a <- (2 * df1 + df2 - 2) * sqrt(8 * (df2 - 4)) b <- (df2 - 6) * sqrt(df1 * (df1 + df2 - 2)) a / b } else { NA_real_ } } #' @export kurtosis.dist_f <- function(x, ...) { df1 <- x[["df1"]] df2 <- x[["df2"]] if(!is.null(x[["ncp"]])) return(NA_real_) if (df2 > 8) { a <- df1 * (5 * df2 - 22) * (df1 + df2 - 2) + (df2 - 4) * (df2 - 2)^2 b <- df1 * (df2 - 6) * (df2 - 8) * (df1 + df2 - 2) 12 * a / b } else { NA_real_ } } distributional/R/dist_logarithmic.R0000644000176200001440000000340414304314122017152 0ustar liggesusers#' The Logarithmic distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' @inheritParams actuar::dlogarithmic #' #' @seealso [actuar::Logarithmic] #' #' @examples #' dist <- dist_logarithmic(prob = c(0.33, 0.66, 0.99)) #' dist #' #' @examplesIf requireNamespace("actuar", quietly = TRUE) #' mean(dist) #' variance(dist) #' support(dist) #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' @name dist_logarithmic #' @export dist_logarithmic <- function(prob){ prob <- vec_cast(prob, double()) if(any((prob < 0) | (prob > 1))){ abort("The prob parameter of a Logarithmic distribution must be between 0 and 1.") } new_dist(p = prob, class = "dist_logarithmic") } #' @export format.dist_logarithmic <- function(x, digits = 2, ...){ sprintf( "Logarithmic(%s)", format(x[["p"]], digits = digits, ...) ) } #' @export density.dist_logarithmic <- function(x, at, ...){ require_package("actuar") actuar::dlogarithmic(at, x[["p"]]) } #' @export log_density.dist_logarithmic <- function(x, at, ...){ require_package("actuar") actuar::dlogarithmic(at, x[["p"]], log = TRUE) } #' @export quantile.dist_logarithmic <- function(x, p, ...){ require_package("actuar") actuar::qlogarithmic(p, x[["p"]]) } #' @export cdf.dist_logarithmic <- function(x, q, ...){ require_package("actuar") actuar::plogarithmic(q, x[["p"]]) } #' @export generate.dist_logarithmic <- function(x, times, ...){ require_package("actuar") actuar::rlogarithmic(times, x[["p"]]) } #' @export mean.dist_logarithmic <- function(x, ...){ p <- x[["p"]] (-1/(log(1-p)))*(p/(1-p)) } #' @export covariance.dist_logarithmic <- function(x, ...){ p <- x[["p"]] -(p^2 + p*log(1-p))/((1-p)*log(1-p))^2 } distributional/R/dist_student_t.R0000644000176200001440000001010214304314164016660 0ustar liggesusers#' The (non-central) location-scale Student t Distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' The Student's T distribution is closely related to the [Normal()] #' distribution, but has heavier tails. As \eqn{\nu} increases to \eqn{\infty}, #' the Student's T converges to a Normal. The T distribution appears #' repeatedly throughout classic frequentist hypothesis testing when #' comparing group means. #' #' @inheritParams stats::dt #' @param mu The location parameter of the distribution. #' If `ncp == 0` (or `NULL`), this is the median. #' @param sigma The scale parameter of the distribution. #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X} be a **central** Students T random variable #' with `df` = \eqn{\nu}. #' #' **Support**: \eqn{R}, the set of all real numbers #' #' **Mean**: Undefined unless \eqn{\nu \ge 2}, in which case the mean is #' zero. #' #' **Variance**: #' #' \deqn{ #' \frac{\nu}{\nu - 2} #' }{ #' \nu / (\nu - 2) #' } #' #' Undefined if \eqn{\nu < 1}, infinite when \eqn{1 < \nu \le 2}. #' #' **Probability density function (p.d.f)**: #' #' \deqn{ #' f(x) = \frac{\Gamma(\frac{\nu + 1}{2})}{\sqrt{\nu \pi} \Gamma(\frac{\nu}{2})} (1 + \frac{x^2}{\nu} )^{- \frac{\nu + 1}{2}} #' }{ #' f(x) = \Gamma((\nu + 1) / 2) / (\sqrt(\nu \pi) \Gamma(\nu / 2)) (1 + x^2 / \nu)^(- (\nu + 1) / 2) #' } #' #' @seealso [stats::TDist] #' #' @examples #' dist <- dist_student_t(df = c(1,2,5), mu = c(0,1,2), sigma = c(1,2,3)) #' #' dist #' mean(dist) #' variance(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_student_t #' @export dist_student_t <- function(df, mu = 0, sigma = 1, ncp = NULL){ df <- vec_cast(df, numeric()) if(any(df <= 0)){ abort("The degrees of freedom parameter of a Student t distribution must be strictly positive.") } mu <- vec_cast(mu, double()) sigma <- vec_cast(sigma, double()) if(any(sigma[!is.na(sigma)] <= 0)){ abort("The scale (sigma) parameter of a Student t distribution must be strictly positive.") } new_dist(df = df, mu = mu, sigma = sigma, ncp = ncp, class = "dist_student_t") } #' @export format.dist_student_t <- function(x, digits = 2, ...){ out <- sprintf( "t(%s, %s, %s%s)", format(x[["df"]], digits = digits, ...), format(x[["mu"]], digits = digits, ...), format(x[["sigma"]], digits = digits, ...), if(is.null(x[["ncp"]])) "" else paste(",", format(x[["ncp"]], digits = digits, ...)) ) } #' @export density.dist_student_t <- function(x, at, ...){ ncp <- x[["ncp"]] %||% missing_arg() sigma <- x[["sigma"]] stats::dt((at - x[["mu"]])/sigma, x[["df"]], ncp) / sigma } #' @export log_density.dist_student_t <- function(x, at, ...){ ncp <- x[["ncp"]] %||% missing_arg() sigma <- x[["sigma"]] stats::dt((at - x[["mu"]])/sigma, x[["df"]], ncp, log = TRUE) - log(sigma) } #' @export quantile.dist_student_t <- function(x, p, ...){ ncp <- x[["ncp"]] %||% missing_arg() stats::qt(p, x[["df"]], ncp) * x[["sigma"]] + x[["mu"]] } #' @export cdf.dist_student_t <- function(x, q, ...){ ncp <- x[["ncp"]] %||% missing_arg() stats::pt((q - x[["mu"]])/x[["sigma"]], x[["df"]], ncp) } #' @export generate.dist_student_t <- function(x, times, ...){ ncp <- x[["ncp"]] %||% missing_arg() stats::rt(times, x[["df"]], ncp) * x[["sigma"]] + x[["mu"]] } #' @export mean.dist_student_t <- function(x, ...){ df <- x[["df"]] if(df <= 1) return(NA_real_) if(is.null(x[["ncp"]])){ x[["mu"]] } else { x[["mu"]] + x[["ncp"]] * sqrt(df/2) * (gamma((df-1)/2)/gamma(df/2)) * x[["sigma"]] } } #' @export covariance.dist_student_t <- function(x, ...){ df <- x[["df"]] ncp <- x[["ncp"]] if(df <= 1) return(NA_real_) if(df <= 2) return(Inf) if(is.null(ncp)){ df / (df - 2) * x[["sigma"]]^2 } else { ((df*(1+ncp^2))/(df-2) - (ncp * sqrt(df/2) * (gamma((df-1)/2)/gamma(df/2)))^2) * x[["sigma"]]^2 } } distributional/R/transformed.R0000755000176200001440000000777314304316273016202 0ustar liggesusers#' Modify a distribution with a transformation #' #' @description #' `r lifecycle::badge('maturing')` #' #' The [`density()`], [`mean()`], and [`variance()`] methods are approximate as #' they are based on numerical derivatives. #' #' @param dist A univariate distribution vector. #' @param transform A function used to transform the distribution. This #' transformation should be monotonic over appropriate domain. #' @param inverse The inverse of the `transform` function. #' #' @examples #' # Create a log normal distribution #' dist <- dist_transformed(dist_normal(0, 0.5), exp, log) #' density(dist, 1) # dlnorm(1, 0, 0.5) #' cdf(dist, 4) # plnorm(4, 0, 0.5) #' quantile(dist, 0.1) # qlnorm(0.1, 0, 0.5) #' generate(dist, 10) # rlnorm(10, 0, 0.5) #' #' @export dist_transformed <- function(dist, transform, inverse){ vec_is(dist, new_dist()) if(is.function(transform)) transform <- list(transform) if(is.function(inverse)) inverse <- list(inverse) new_dist(dist = vec_data(dist), transform = transform, inverse = inverse, dimnames = dimnames(dist), class = "dist_transformed") } #' @export format.dist_transformed <- function(x, ...){ sprintf( "t(%s)", format(x[["dist"]]) ) } #' @export density.dist_transformed <- function(x, at, ...){ density(x[["dist"]], x[["inverse"]](at))*abs(vapply(at, numDeriv::jacobian, numeric(1L), func = x[["inverse"]])) } #' @export cdf.dist_transformed <- function(x, q, ...){ cdf(x[["dist"]], x[["inverse"]](q), ...) } #' @export quantile.dist_transformed <- function(x, p, ...){ x[["transform"]](quantile(x[["dist"]], p, ...)) } #' @export generate.dist_transformed <- function(x, ...){ x[["transform"]](generate(x[["dist"]], ...)) } #' @export mean.dist_transformed <- function(x, ...){ mu <- mean(x[["dist"]]) sigma2 <- variance(x[["dist"]]) if(is.na(sigma2)){ # warning("Could not compute the transformed distribution's mean as the base distribution's variance is unknown. The transformed distribution's median has been returned instead.") return(x[["transform"]](mu)) } drop( x[["transform"]](mu) + numDeriv::hessian(x[["transform"]], mu, method.args=list(d = 0.01))/2*sigma2 ) } #' @export covariance.dist_transformed <- function(x, ...){ mu <- mean(x[["dist"]]) sigma2 <- variance(x[["dist"]]) if(is.na(sigma2)) return(NA_real_) drop( numDeriv::jacobian(x[["transform"]], mu)^2*sigma2 + (numDeriv::hessian(x[["transform"]], mu, method.args=list(d = 0.01))*sigma2)^2/2 ) } #' @method Math dist_transformed #' @export Math.dist_transformed <- function(x, ...) { trans <- new_function(exprs(x = ), body = expr((!!sym(.Generic))((!!x$transform)(x), !!!dots_list(...)))) inverse_fun <- get_unary_inverse(.Generic) inverse <- new_function(exprs(x = ), body = expr((!!x$inverse)((!!inverse_fun)(x, !!!dots_list(...))))) vec_data(dist_transformed(wrap_dist(list(x[["dist"]])), trans, inverse))[[1]] } #' @method Ops dist_transformed #' @export Ops.dist_transformed <- function(e1, e2) { is_dist <- c(inherits(e1, "dist_default"), inherits(e2, "dist_default")) trans <- if(all(is_dist)) { if(identical(e1$dist, e2$dist)){ new_function(exprs(x = ), expr((!!sym(.Generic))((!!e1$transform)(x), (!!e2$transform)(x)))) } else { stop(sprintf("The %s operation is not supported for <%s> and <%s>", .Generic, class(e1)[1], class(e2)[1])) } } else if(is_dist[1]){ new_function(exprs(x = ), body = expr((!!sym(.Generic))((!!e1$transform)(x), !!e2))) } else { new_function(exprs(x = ), body = expr((!!sym(.Generic))(!!e1, (!!e2$transform)(x)))) } inverse <- if(all(is_dist)) { invert_fail } else if(is_dist[1]){ inverse_fun <- get_binary_inverse_1(.Generic, e2) new_function(exprs(x = ), body = expr((!!e1$inverse)((!!inverse_fun)(x)))) } else { inverse_fun <- get_binary_inverse_2(.Generic, e1) new_function(exprs(x = ), body = expr((!!e2$inverse)((!!inverse_fun)(x)))) } vec_data(dist_transformed(wrap_dist(list(list(e1,e2)[[which(is_dist)[1]]][["dist"]])), trans, inverse))[[1]] } distributional/R/dist_binomial.R0000644000176200001440000001041414304314034016443 0ustar liggesusers#' The Binomial distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' Binomial distributions are used to represent situations can that can #' be thought as the result of \eqn{n} Bernoulli experiments (here the #' \eqn{n} is defined as the `size` of the experiment). The classical #' example is \eqn{n} independent coin flips, where each coin flip has #' probability `p` of success. In this case, the individual probability of #' flipping heads or tails is given by the Bernoulli(p) distribution, #' and the probability of having \eqn{x} equal results (\eqn{x} heads, #' for example), in \eqn{n} trials is given by the Binomial(n, p) distribution. #' The equation of the Binomial distribution is directly derived from #' the equation of the Bernoulli distribution. #' #' @param size The number of trials. Must be an integer greater than or equal #' to one. When `size = 1L`, the Binomial distribution reduces to the #' Bernoulli distribution. Often called `n` in textbooks. #' @param prob The probability of success on each trial, `prob` can be any #' value in `[0, 1]`. #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' The Binomial distribution comes up when you are interested in the portion #' of people who do a thing. The Binomial distribution #' also comes up in the sign test, sometimes called the Binomial test #' (see [stats::binom.test()]), where you may need the Binomial C.D.F. to #' compute p-values. #' #' In the following, let \eqn{X} be a Binomial random variable with parameter #' `size` = \eqn{n} and `p` = \eqn{p}. Some textbooks define \eqn{q = 1 - p}, #' or called \eqn{\pi} instead of \eqn{p}. #' #' **Support**: \eqn{\{0, 1, 2, ..., n\}}{{0, 1, 2, ..., n}} #' #' **Mean**: \eqn{np} #' #' **Variance**: \eqn{np \cdot (1 - p) = np \cdot q}{np (1 - p)} #' #' **Probability mass function (p.m.f)**: #' #' \deqn{ #' P(X = k) = {n \choose k} p^k (1 - p)^{n-k} #' }{ #' P(X = k) = choose(n, k) p^k (1 - p)^(n - k) #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' \deqn{ #' P(X \le k) = \sum_{i=0}^{\lfloor k \rfloor} {n \choose i} p^i (1 - p)^{n-i} #' }{ #' P(X \le k) = \sum_{i=0}^k choose(n, i) p^i (1 - p)^(n-i) #' } #' #' **Moment generating function (m.g.f)**: #' #' \deqn{ #' E(e^{tX}) = (1 - p + p e^t)^n #' }{ #' E(e^(tX)) = (1 - p + p e^t)^n #' } #' #' @examples #' dist <- dist_binomial(size = 1:5, prob = c(0.05, 0.5, 0.3, 0.9, 0.1)) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_binomial #' @export dist_binomial <- function(size, prob){ size <- vec_cast(size, integer()) prob <- vec_cast(prob, double()) if(any(size < 0)){ abort("The number of observations cannot be negative.") } if(any((prob < 0) | (prob > 1))){ abort("The probability of success must be between 0 and 1.") } new_dist(n = size, p = prob, class = "dist_binomial") } #' @export format.dist_binomial <- function(x, digits = 2, ...){ sprintf( "B(%s, %s)", format(x[["n"]], digits = digits, ...), format(x[["p"]], digits = digits, ...) ) } #' @export density.dist_binomial <- function(x, at, ...){ stats::dbinom(at, x[["n"]], x[["p"]]) } #' @export log_density.dist_binomial <- function(x, at, ...){ stats::dbinom(at, x[["n"]], x[["p"]], log = TRUE) } #' @export quantile.dist_binomial <- function(x, p, ...){ as.integer(stats::qbinom(p, x[["n"]], x[["p"]])) } #' @export cdf.dist_binomial <- function(x, q, ...){ stats::pbinom(q, x[["n"]], x[["p"]]) } #' @export generate.dist_binomial <- function(x, times, ...){ as.integer(stats::rbinom(times, x[["n"]], x[["p"]])) } #' @export mean.dist_binomial <- function(x, ...){ x[["n"]]*x[["p"]] } #' @export covariance.dist_binomial <- function(x, ...){ x[["n"]]*x[["p"]]*(1-x[["p"]]) } #' @export skewness.dist_binomial <- function(x, ...) { n <- x[["n"]] p <- x[["p"]] q <- 1 - p (1 - (2 * p)) / sqrt(n * p * q) } #' @export kurtosis.dist_binomial <- function(x, ...) { n <- x[["n"]] p <- x[["p"]] q <- 1 - p (1 - (6 * p * q)) / (n * p * q) } distributional/R/dist_studentized_range.R0000644000176200001440000000303214304314167020374 0ustar liggesusers#' The Studentized Range distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' Tukey's studentized range distribution, used for Tukey's #' honestly significant differences test in ANOVA. #' #' @inheritParams stats::qtukey #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' **Support**: \eqn{R^+}, the set of positive real numbers. #' #' Other properties of Tukey's Studentized Range Distribution #' are omitted, largely because the distribution is not fun #' to work with. #' #' @seealso [stats::Tukey] #' #' @examples #' dist <- dist_studentized_range(nmeans = c(6, 2), df = c(5, 4), nranges = c(1, 1)) #' #' dist #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_studentized_range #' @export dist_studentized_range <- function(nmeans, df, nranges){ nmeans <- vec_cast(nmeans, double()) df <- vec_cast(df, double()) new_dist(nm = nmeans, df = df, nr = nranges, class = "dist_studentized_range") } #' @export format.dist_studentized_range <- function(x, digits = 2, ...){ sprintf( "StudentizedRange(%s, %s, %s)", format(x[["nm"]], digits = digits, ...), format(x[["df"]], digits = digits, ...), format(x[["nr"]], digits = digits, ...) ) } #' @export quantile.dist_studentized_range <- function(x, p, ...){ stats::qtukey(p, x[["nm"]], x[["df"]], x[["nr"]]) } #' @export cdf.dist_studentized_range <- function(x, q, ...){ stats::ptukey(q, x[["nm"]], x[["df"]], x[["nr"]]) } distributional/R/dist_chisq.R0000644000176200001440000000651014304314046015765 0ustar liggesusers#' The (non-central) Chi-Squared Distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' Chi-square distributions show up often in frequentist settings #' as the sampling distribution of test statistics, especially #' in maximum likelihood estimation settings. #' #' @inheritParams stats::dchisq #' #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X} be a \eqn{\chi^2} random variable with #' `df` = \eqn{k}. #' #' **Support**: \eqn{R^+}, the set of positive real numbers #' #' **Mean**: \eqn{k} #' #' **Variance**: \eqn{2k} #' #' **Probability density function (p.d.f)**: #' #' \deqn{ #' f(x) = \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-(x - \mu)^2 / 2 \sigma^2} #' }{ #' f(x) = 1 / (2 \pi \sigma^2) exp(-(x - \mu)^2 / (2 \sigma^2)) #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' The cumulative distribution function has the form #' #' \deqn{ #' F(t) = \int_{-\infty}^t \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-(x - \mu)^2 / 2 \sigma^2} dx #' }{ #' F(t) = integral_{-\infty}^t 1 / (2 \pi \sigma^2) exp(-(x - \mu)^2 / (2 \sigma^2)) dx #' } #' #' but this integral does not have a closed form solution and must be #' approximated numerically. The c.d.f. of a standard normal is sometimes #' called the "error function". The notation \eqn{\Phi(t)} also stands #' for the c.d.f. of a standard normal evaluated at \eqn{t}. Z-tables #' list the value of \eqn{\Phi(t)} for various \eqn{t}. #' #' **Moment generating function (m.g.f)**: #' #' \deqn{ #' E(e^{tX}) = e^{\mu t + \sigma^2 t^2 / 2} #' }{ #' E(e^(tX)) = e^(\mu t + \sigma^2 t^2 / 2) #' } #' #' #' @seealso [stats::Chisquare] #' #' @examples #' dist <- dist_chisq(df = c(1,2,3,4,6,9)) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_chisq #' @export dist_chisq <- function(df, ncp = 0){ df <- vec_cast(df, double()) ncp <- vec_cast(ncp, double()) if(any(df < 0)){ abort("The degrees of freedom parameter of a Chi-Squared distribution must be non-negative.") } new_dist(df = df, ncp = ncp, class = "dist_chisq") } #' @export format.dist_chisq <- function(x, digits = 2, ...){ sprintf( if (is_utf8_output()) "\u1d6a\u00b2(%s)" else "x2(%s)", format(x[["df"]], digits = digits, ...) ) } #' @export density.dist_chisq <- function(x, at, ...){ stats::dchisq(at, x[["df"]], x[["ncp"]]) } #' @export log_density.dist_chisq <- function(x, at, ...){ stats::dchisq(at, x[["df"]], x[["ncp"]], log = TRUE) } #' @export quantile.dist_chisq <- function(x, p, ...){ stats::qchisq(p, x[["df"]], x[["ncp"]]) } #' @export cdf.dist_chisq <- function(x, q, ...){ stats::pchisq(q, x[["df"]], x[["ncp"]]) } #' @export generate.dist_chisq <- function(x, times, ...){ stats::rchisq(times, x[["df"]], x[["ncp"]]) } #' @export mean.dist_chisq <- function(x, ...){ x[["df"]] + x[["ncp"]] } #' @export covariance.dist_chisq <- function(x, ...){ 2*(x[["df"]] + 2*x[["ncp"]]) } #' @export skewness.dist_chisq <- function(x, ...) sqrt(8 / x[["df"]]) #' @export kurtosis.dist_chisq <- function(x, ...) 12 / x[["df"]] distributional/R/dist_degenerate.R0000644000176200001440000000425414304314052016761 0ustar liggesusers#' The degenerate distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' The degenerate distribution takes a single value which is certain to be #' observed. It takes a single parameter, which is the value that is observed #' by the distribution. #' #' @param x The value of the distribution. #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X} be a degenerate random variable with value #' `x` = \eqn{k_0}. #' #' **Support**: \eqn{R}, the set of all real numbers #' #' **Mean**: \eqn{k_0} #' #' **Variance**: \eqn{0} #' #' **Probability density function (p.d.f)**: #' #' \deqn{ #' f(x) = 1 for x = k_0 #' }{ #' f(x) = 1 for x = k_0 #' } #' \deqn{ #' f(x) = 0 for x \neq k_0 #' }{ #' f(x) = 0 for x \neq k_0 #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' The cumulative distribution function has the form #' #' \deqn{ #' F(x) = 0 for x < k_0 #' }{ #' F(x) = 0 for x < k_0 #' } #' \deqn{ #' F(x) = 1 for x \ge k_0 #' }{ #' F(x) = 1 for x \ge k_0 #' } #' #' **Moment generating function (m.g.f)**: #' #' \deqn{ #' E(e^{tX}) = e^{k_0 t} #' }{ #' E(e^(tX)) = e^(k_0 t) #' } #' #' @examples #' dist_degenerate(x = 1:5) #' #' @export dist_degenerate <- function(x){ vec_is(x, numeric()) new_dist(x = x, class = "dist_degenerate") } #' @export format.dist_degenerate <- function(x, ...){ format(x[["x"]], ...) } #' @export density.dist_degenerate <- function(x, at, ...){ ifelse(at == x[["x"]], 1, 0) } #' @export quantile.dist_degenerate <- function(x, p, ...){ ifelse(p < 0 | p > 1, NaN, x[["x"]]) } #' @export cdf.dist_degenerate <- function(x, q, ...){ ifelse(q >= x[["x"]], 1, 0) } #' @export generate.dist_degenerate <- function(x, times, ...){ rep(x[["x"]], times) } #' @export mean.dist_degenerate <- function(x, ...){ x[["x"]] } #' @export covariance.dist_degenerate <- function(x, ...){ 0 } #' @export skewness.dist_degenerate <- function(x, ...) NA_real_ #' @export kurtosis.dist_degenerate <- function(x, ...) NA_real_ distributional/R/dist_multinomial.R0000644000176200001440000000706314304314507017216 0ustar liggesusers#' The Multinomial distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' The multinomial distribution is a generalization of the binomial #' distribution to multiple categories. It is perhaps easiest to think #' that we first extend a [dist_bernoulli()] distribution to include more #' than two categories, resulting in a [dist_categorical()] distribution. #' We then extend repeat the Categorical experiment several (\eqn{n}) #' times. #' #' @param size The number of draws from the Categorical distribution. #' @param prob The probability of an event occurring from each draw. #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X = (X_1, ..., X_k)} be a Multinomial #' random variable with success probability `p` = \eqn{p}. Note that #' \eqn{p} is vector with \eqn{k} elements that sum to one. Assume #' that we repeat the Categorical experiment `size` = \eqn{n} times. #' #' **Support**: Each \eqn{X_i} is in \eqn{{0, 1, 2, ..., n}}. #' #' **Mean**: The mean of \eqn{X_i} is \eqn{n p_i}. #' #' **Variance**: The variance of \eqn{X_i} is \eqn{n p_i (1 - p_i)}. #' For \eqn{i \neq j}, the covariance of \eqn{X_i} and \eqn{X_j} #' is \eqn{-n p_i p_j}. #' #' **Probability mass function (p.m.f)**: #' #' \deqn{ #' P(X_1 = x_1, ..., X_k = x_k) = \frac{n!}{x_1! x_2! ... x_k!} p_1^{x_1} \cdot p_2^{x_2} \cdot ... \cdot p_k^{x_k} #' }{ #' P(X_1 = x_1, ..., X_k = x_k) = n! / (x_1! x_2! ... x_k!) p_1^x_1 p_2^x_2 ... p_k^x_k #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' Omitted for multivariate random variables for the time being. #' #' **Moment generating function (m.g.f)**: #' #' \deqn{ #' E(e^{tX}) = \left(\sum_{i=1}^k p_i e^{t_i}\right)^n #' }{ #' E(e^(tX)) = (p_1 e^t_1 + p_2 e^t_2 + ... + p_k e^t_k)^n #' } #' #' @seealso [stats::Multinomial] #' #' @examples #' dist <- dist_multinomial(size = c(4, 3), prob = list(c(0.3, 0.5, 0.2), c(0.1, 0.5, 0.4))) #' #' dist #' mean(dist) #' variance(dist) #' #' generate(dist, 10) #' #' # TODO: Needs fixing to support multiple inputs #' # density(dist, 2) #' # density(dist, 2, log = TRUE) #' #' @name dist_multinomial #' @export dist_multinomial <- function(size, prob){ size <- vec_cast(size, double()) prob <- lapply(prob, function(x) x/sum(x)) prob <- as_list_of(prob, .ptype = double()) new_dist(s = size, p = prob, class = "dist_multinomial") } #' @export format.dist_multinomial <- function(x, digits = 2, ...){ sprintf( "Multinomial(%s)[%s]", format(x[["s"]], digits = digits, ...), format(length(x[["p"]]), digits = digits, ...) ) } #' @export density.dist_multinomial <- function(x, at, ...){ if(is.list(at)) return(vapply(at, density, numeric(1L), x = x, ...)) stats::dmultinom(at, x[["s"]], x[["p"]]) } #' @export log_density.dist_multinomial <- function(x, at, ...){ stats::dmultinom(at, x[["s"]], x[["p"]], log = TRUE) } #' @export generate.dist_multinomial <- function(x, times, ...){ t(stats::rmultinom(times, x[["s"]], x[["p"]])) } #' @export mean.dist_multinomial <- function(x, ...){ matrix(x[["s"]]*x[["p"]], nrow = 1) } #' @export covariance.dist_multinomial <- function(x, ...){ s <- x[["s"]] p <- x[["p"]] v <- numeric(length(p)^2) for(i in seq_along(p)){ for(j in seq_along(p)){ v[(i-1)*length(p) + j] <- if(i == j) s*p[i]*(1-p[j]) else -s*p[i]*p[j] } } list(matrix(v, nrow = length(p))) } #' @export dim.dist_multinomial <- function(x){ length(x[["p"]]) } distributional/R/support.R0000644000176200001440000000223214252317402015345 0ustar liggesusers#' Create a new support region vector #' #' @param x A list of prototype vectors defining the distribution type. #' @param limits A list of value limits for the distribution. #' new_support_region <- function(x, limits = NULL) { vctrs::new_rcrd(list(x = x, lim = limits), class = "support_region") } #' @export format.support_region <- function(x, ...) { type <- vapply(field(x, "x"), function(z) { out <- if(is.integer(z)) "Z" else if(is.numeric(z)) "R" else if(is.complex(z)) "C" else vec_ptype_abbr(z) if(is.matrix(z)) { if(ncol(z) > 1) { out <- paste(out, ncol(z), sep = "^") } } out }, FUN.VALUE = character(1L)) mapply(function(type, z) { if(any(is.na(z)) || all(is.infinite(z))) type else if (type == "Z" && identical(z[2], Inf)) { if(z[1] == 0L) "N0" else if (z[2] == 1L) "N+" else paste0("[", z[1], ",", z[1]+1L, ",...,", z[2], "]") } else if (type == "R") paste0("[", z[1], ",", z[2], "]") else if (type == "Z") paste0("[", z[1], ",", z[1]+1L, ",...,", z[2], "]") else type }, type, field(x, "lim")) } #' @export vec_ptype_abbr.support_region <- function(x, ...){ "support" } distributional/R/dist_weibull.R0000644000176200001440000000636514304314202016323 0ustar liggesusers#' The Weibull distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' Generalization of the gamma distribution. Often used in survival and #' time-to-event analyses. #' #' @inheritParams stats::dweibull #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X} be a Weibull random variable with #' success probability `p` = \eqn{p}. #' #' **Support**: \eqn{R^+} and zero. #' #' **Mean**: \eqn{\lambda \Gamma(1+1/k)}, where \eqn{\Gamma} is #' the gamma function. #' #' **Variance**: \eqn{\lambda [ \Gamma (1 + \frac{2}{k} ) - (\Gamma(1+ \frac{1}{k}))^2 ]} #' #' **Probability density function (p.d.f)**: #' #' \deqn{ #' f(x) = \frac{k}{\lambda}(\frac{x}{\lambda})^{k-1}e^{-(x/\lambda)^k}, x \ge 0 #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' \deqn{F(x) = 1 - e^{-(x/\lambda)^k}, x \ge 0} #' #' **Moment generating function (m.g.f)**: #' #' \deqn{\sum_{n=0}^\infty \frac{t^n\lambda^n}{n!} \Gamma(1+n/k), k \ge 1} #' #' @seealso [stats::Weibull] #' #' @examples #' dist <- dist_weibull(shape = c(0.5, 1, 1.5, 5), scale = rep(1, 4)) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_weibull #' @export dist_weibull <- function(shape, scale){ shape <- vec_cast(shape, double()) scale <- vec_cast(scale, double()) if(any(shape[!is.na(shape)] < 0)){ abort("The shape parameter of a Weibull distribution must be non-negative.") } if(any(scale[!is.na(scale)] <= 0)){ abort("The scale parameter of a Weibull distribution must be strictly positive.") } new_dist(shape = shape, scale = scale, class = "dist_weibull") } #' @export format.dist_weibull <- function(x, digits = 2, ...){ sprintf( "Weibull(%s, %s)", format(x[["shape"]], digits = digits, ...), format(x[["scale"]], digits = digits, ...) ) } #' @export density.dist_weibull <- function(x, at, ...){ stats::dweibull(at, x[["shape"]], x[["scale"]]) } #' @export log_density.dist_weibull <- function(x, at, ...){ stats::dweibull(at, x[["shape"]], x[["scale"]], log = TRUE) } #' @export quantile.dist_weibull <- function(x, p, ...){ stats::qweibull(p, x[["shape"]], x[["scale"]]) } #' @export cdf.dist_weibull <- function(x, q, ...){ stats::pweibull(q, x[["shape"]], x[["scale"]]) } #' @export generate.dist_weibull <- function(x, times, ...){ stats::rweibull(times, x[["shape"]], x[["scale"]]) } #' @export mean.dist_weibull <- function(x, ...){ x[["scale"]] * gamma(1 + 1/x[["shape"]]) } #' @export covariance.dist_weibull <- function(x, ...){ x[["scale"]]^2 * (gamma(1 + 2/x[["shape"]]) - gamma(1 + 1/x[["shape"]])^2) } #' @export skewness.dist_weibull <- function(x, ...) { mu <- mean(x) sigma <- sqrt(variance(x)) r <- mu / sigma gamma(1 + 3/x[["shape"]]) * (x[["scale"]]/sigma)^3 - 3*r - 3^r } #' @export kurtosis.dist_weibull <- function(x, ...) { mu <- mean(x) sigma <- sqrt(variance(x)) gamma <- skewness(x) r <- mu / sigma (x[["scale"]]/sigma)^4 * gamma(1 + 4/x[["shape"]]) - 4*gamma*r -6*r^2 - r^4 - 3 } distributional/R/dist_lognormal.R0000644000176200001440000001052414304314131016643 0ustar liggesusers#' The log-normal distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' The log-normal distribution is a commonly used transformation of the Normal #' distribution. If \eqn{X} follows a log-normal distribution, then \eqn{\ln{X}} #' would be characteristed by a Normal distribution. #' #' @param mu The mean (location parameter) of the distribution, which is the #' mean of the associated Normal distribution. Can be any real number. #' @param sigma The standard deviation (scale parameter) of the distribution. #' Can be any positive number. #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{Y} be a Normal random variable with mean #' `mu` = \eqn{\mu} and standard deviation `sigma` = \eqn{\sigma}. The #' log-normal distribution \eqn{X = exp(Y)} is characterised by: #' #' **Support**: \eqn{R+}, the set of all real numbers greater than or equal to 0. #' #' **Mean**: \eqn{e^(\mu + \sigma^2/2} #' #' **Variance**: \eqn{(e^(\sigma^2)-1) e^(2\mu + \sigma^2} #' #' **Probability density function (p.d.f)**: #' #' \deqn{ #' f(x) = \frac{1}{x\sqrt{2 \pi \sigma^2}} e^{-(\ln{x} - \mu)^2 / 2 \sigma^2} #' }{ #' f(x) = 1 / (x * sqrt(2 \pi \sigma^2)) exp(-(log(x) - \mu)^2 / (2 \sigma^2)) #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' The cumulative distribution function has the form #' #' \deqn{ #' F(x) = \Phi((\ln{x} - \mu)/\sigma) #' }{ #' F(x) = Phi((log(x) - \mu)/\sigma) #' } #' #' Where \eqn{Phi}{Phi} is the CDF of a standard Normal distribution, N(0,1). #' #' @seealso [stats::Lognormal] #' #' @examples #' dist <- dist_lognormal(mu = 1:5, sigma = 0.1) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' # A log-normal distribution X is exp(Y), where Y is a Normal distribution of #' # the same parameters. So log(X) will produce the Normal distribution Y. #' log(dist) #' @export dist_lognormal <- function(mu = 0, sigma = 1){ mu <- vec_cast(mu, double()) sigma <- vec_cast(sigma, double()) if(any(sigma[!is.na(sigma)] < 0)){ abort("Standard deviation of a log-normal distribution must be non-negative") } new_dist(mu = mu, sigma = sigma, class = "dist_lognormal") } #' @export format.dist_lognormal <- function(x, digits = 2, ...){ sprintf( "lN(%s, %s)", format(x[["mu"]], digits = digits, ...), format(x[["sigma"]]^2, digits = digits, ...) ) } #' @export density.dist_lognormal <- function(x, at, ...){ stats::dlnorm(at, x[["mu"]], x[["sigma"]]) } #' @export log_density.dist_lognormal <- function(x, at, ...){ stats::dlnorm(at, x[["mu"]], x[["sigma"]], log = TRUE) } #' @export quantile.dist_lognormal <- function(x, p, ...){ stats::qlnorm(p, x[["mu"]], x[["sigma"]]) } #' @export log_quantile.dist_lognormal <- function(x, p, ...){ stats::qlnorm(p, x[["mu"]], x[["sigma"]], log.p = TRUE) } #' @export cdf.dist_lognormal <- function(x, q, ...){ stats::plnorm(q, x[["mu"]], x[["sigma"]]) } #' @export log_cdf.dist_lognormal <- function(x, q, ...){ stats::plnorm(q, x[["mu"]], x[["sigma"]], log.p = TRUE) } #' @export generate.dist_lognormal <- function(x, times, ...){ stats::rlnorm(times, x[["mu"]], x[["sigma"]]) } #' @export mean.dist_lognormal <- function(x, ...){ exp(x[["mu"]] + x[["sigma"]]^2/2) } #' @export covariance.dist_lognormal <- function(x, ...){ s2 <- x[["sigma"]]^2 (exp(s2)-1)*exp(2*x[["mu"]] + s2) } #' @export skewness.dist_lognormal <- function(x, ...) { es2 <- exp(x[["sigma"]]^2) (es2+2)*sqrt(es2-1) } #' @export kurtosis.dist_lognormal <- function(x, ...) { s2 <- x[["sigma"]]^2 exp(4*s2) + 2*exp(3*s2) + 3*exp(2*s2) - 6 } # make a normal distribution from a lognormal distribution using the # specified base normal_dist_with_base <- function(x, base = exp(1)) { vec_data(dist_normal(x[["mu"]], x[["sigma"]]) / log(base))[[1]] } #' @method Math dist_lognormal #' @export Math.dist_lognormal <- function(x, ...) { switch(.Generic, # Shortcuts to get Normal distribution from log-normal. log = normal_dist_with_base(x, ...), log2 = normal_dist_with_base(x, 2), log10 = normal_dist_with_base(x, 10), NextMethod() ) } distributional/R/hilo.R0000644000176200001440000001065514534004563014600 0ustar liggesusers#' Construct hilo intervals #' #' @description #' `r lifecycle::badge('stable')` #' #' Class constructor function to help with manually creating hilo interval #' objects. #' #' @param lower,upper A numeric vector of values for lower and upper limits. #' @param size Size of the interval between \[0, 100\]. #' #' @return A "hilo" vector #' #' @author Earo Wang & Mitchell O'Hara-Wild #' #' @examples #' new_hilo(lower = rnorm(10), upper = rnorm(10) + 5, size = 95) #' #' @export new_hilo <- function(lower = double(), upper = double(), size = double()) { vec_assert(size, double()) if (any(size < 0 | size > 100, na.rm = TRUE)) abort("'size' must be between [0, 100].") out <- vec_recycle_common(lower = lower, upper = upper) if(vec_is(lower, double()) && vec_is(upper, double())) { if (any(out[["upper"]] < out[["lower"]], na.rm = TRUE)) { abort("`upper` can't be lower than `lower`.") } } len <- vec_size(out[[1]]) out[["level"]] <- vctrs::vec_recycle(size, len) vctrs::new_rcrd(out, class = "hilo") } #' Compute intervals #' #' @description #' `r lifecycle::badge('stable')` #' #' Used to extract a specified prediction interval at a particular confidence #' level from a distribution. #' #' The numeric lower and upper bounds can be extracted from the interval using #' `$lower` and `$upper` as shown in the examples below. #' #' @param x Object to create hilo from. #' @param ... Additional arguments used by methods. #' #' @examples #' # 95% interval from a standard normal distribution #' interval <- hilo(dist_normal(0, 1), 95) #' interval #' #' # Extract the individual quantities with `$lower`, `$upper`, and `$level` #' interval$lower #' interval$upper #' interval$level #' @export hilo <- function(x, ...){ UseMethod("hilo") } #' @export hilo.default <- function(x, ...){ abort(sprintf( "Objects of type `%s` are not supported by `hilo()`, you can create a custom `hilo` with `new_hilo()`", class(x) )) } #' Is the object a hilo #' #' @param x An object. #' #' @export is_hilo <- function(x) { inherits(x, "hilo") } #' @export format.hilo <- function(x, justify = "right", ...) { lwr <- field(x, "lower") upr <- field(x, "upper") if(is.matrix(lwr)) { lwr <- if(ncol(lwr) > 1) vctrs::vec_ptype_abbr(lwr) else drop(lwr) } if(is.matrix(upr)) { upr <- if(ncol(upr) > 1) vctrs::vec_ptype_abbr(upr) else drop(upr) } limit <- paste( format(lwr, justify = justify, ...), format(upr, justify = justify, ...), sep = ", " ) paste0("[", limit, "]", field(x, "level")) } #' @export is.na.hilo <- function(x) { # both lower and upper are NA's x <- vec_data(x) is.na(x$lower) & is.na(x$upper) } #' @export vec_ptype2.hilo.hilo <- function(x, y, ...){ x } #' @export vec_cast.character.hilo <- function(x, to, ...){ sprintf( "[%s, %s]%s", as.character(x$lower), as.character(x$upper), as.character(x$level) ) } #' @method vec_math hilo #' @export vec_math.hilo <- function(.fn, .x, ...){ out <- vec_data(.x) if(.fn == "mean") abort("Cannot compute the mean of hilo intervals.") out[["lower"]] <- get(.fn)(out[["lower"]], ...) out[["upper"]] <- get(.fn)(out[["upper"]], ...) if(.fn %in% c("is.nan", "is.finite", "is.infinite")) return(out[["lower"]] | out[["upper"]]) vec_restore(out, .x) } #' @method vec_arith hilo #' @export vec_arith.hilo <- function(op, x, y, ...){ out <- dt_x <- vec_data(x) if(is_hilo(y)){ abort("Intervals should not be added to other intervals, the sum of intervals is not the interval from a sum of distributions.") } else if(is_empty(y)){ if(op == "-"){ out[["upper"]] <- get(op)(dt_x[["lower"]]) out[["lower"]] <- get(op)(dt_x[["upper"]]) } } else{ out[["lower"]] <- get(op)(dt_x[["lower"]], y) out[["upper"]] <- get(op)(dt_x[["upper"]], y) } vec_restore(out, x) } #' @method vec_arith.numeric hilo #' @export vec_arith.numeric.hilo <- function(op, x, y, ...){ out <- hl <- vec_data(y) out[["lower"]] <- get(op)(x, hl[["lower"]]) out[["upper"]] <- get(op)(x, hl[["upper"]]) if(x < 0 && op %in% c("*", "/")){ out[c("lower", "upper")] <- out[c("upper", "lower")] } vec_restore(out, y) } #' @importFrom utils .DollarNames #' @export .DollarNames.hilo <- function(x, pattern){ utils::.DollarNames(vec_data(x), pattern) } #' @export `$.hilo` <- function(x, name){ field(x, name) } #' @export `names<-.hilo` <- function(x, value) { # abort("A object cannot be named.") x } distributional/R/dist_normal.R0000644000176200001440000001364414304314143016152 0ustar liggesusers#' The Normal distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' The Normal distribution is ubiquitous in statistics, partially because #' of the central limit theorem, which states that sums of i.i.d. random #' variables eventually become Normal. Linear transformations of Normal #' random variables result in new random variables that are also Normal. If #' you are taking an intro stats course, you'll likely use the Normal #' distribution for Z-tests and in simple linear regression. Under #' regularity conditions, maximum likelihood estimators are #' asymptotically Normal. The Normal distribution is also called the #' gaussian distribution. #' #' @param mu,mean The mean (location parameter) of the distribution, which is also #' the mean of the distribution. Can be any real number. #' @param sigma,sd The standard deviation (scale parameter) of the distribution. #' Can be any positive number. If you would like a Normal distribution with #' **variance** \eqn{\sigma^2}, be sure to take the square root, as this is a #' common source of errors. #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X} be a Normal random variable with mean #' `mu` = \eqn{\mu} and standard deviation `sigma` = \eqn{\sigma}. #' #' **Support**: \eqn{R}, the set of all real numbers #' #' **Mean**: \eqn{\mu} #' #' **Variance**: \eqn{\sigma^2} #' #' **Probability density function (p.d.f)**: #' #' \deqn{ #' f(x) = \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-(x - \mu)^2 / 2 \sigma^2} #' }{ #' f(x) = 1 / sqrt(2 \pi \sigma^2) exp(-(x - \mu)^2 / (2 \sigma^2)) #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' The cumulative distribution function has the form #' #' \deqn{ #' F(t) = \int_{-\infty}^t \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-(x - \mu)^2 / 2 \sigma^2} dx #' }{ #' F(t) = integral_{-\infty}^t 1 / sqrt(2 \pi \sigma^2) exp(-(x - \mu)^2 / (2 \sigma^2)) dx #' } #' #' but this integral does not have a closed form solution and must be #' approximated numerically. The c.d.f. of a standard Normal is sometimes #' called the "error function". The notation \eqn{\Phi(t)} also stands #' for the c.d.f. of a standard Normal evaluated at \eqn{t}. Z-tables #' list the value of \eqn{\Phi(t)} for various \eqn{t}. #' #' **Moment generating function (m.g.f)**: #' #' \deqn{ #' E(e^{tX}) = e^{\mu t + \sigma^2 t^2 / 2} #' }{ #' E(e^(tX)) = e^(\mu t + \sigma^2 t^2 / 2) #' } #' #' @seealso [stats::Normal] #' #' @examples #' dist <- dist_normal(mu = 1:5, sigma = 3) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @export dist_normal <- function(mu = 0, sigma = 1, mean = mu, sd = sigma){ mean <- vec_cast(mean, double()) sd <- vec_cast(sd, double()) if(any(sd[!is.na(sd)] < 0)){ abort("Standard deviation of a normal distribution must be non-negative") } new_dist(mu = mean, sigma = sd, class = "dist_normal") } #' @export format.dist_normal <- function(x, digits = 2, ...){ sprintf( "N(%s, %s)", format(x[["mu"]], digits = digits, ...), format(x[["sigma"]]^2, digits = digits, ...) ) } #' @export density.dist_normal <- function(x, at, ...){ stats::dnorm(at, x[["mu"]], x[["sigma"]]) } #' @export log_density.dist_normal <- function(x, at, ...){ stats::dnorm(at, x[["mu"]], x[["sigma"]], log = TRUE) } #' @export quantile.dist_normal <- function(x, p, ...){ stats::qnorm(p, x[["mu"]], x[["sigma"]]) } #' @export log_quantile.dist_normal <- function(x, p, ...){ stats::qnorm(p, x[["mu"]], x[["sigma"]], log.p = TRUE) } #' @export cdf.dist_normal <- function(x, q, ...){ stats::pnorm(q, x[["mu"]], x[["sigma"]]) } #' @export log_cdf.dist_normal <- function(x, q, ...){ stats::pnorm(q, x[["mu"]], x[["sigma"]], log.p = TRUE) } #' @export generate.dist_normal <- function(x, times, ...){ stats::rnorm(times, x[["mu"]], x[["sigma"]]) } #' @export mean.dist_normal <- function(x, ...){ x[["mu"]] } #' @export covariance.dist_normal <- function(x, ...){ x[["sigma"]]^2 } #' @export skewness.dist_normal <- function(x, ...) 0 #' @export kurtosis.dist_normal <- function(x, ...) 0 #' @export Ops.dist_normal <- function(e1, e2){ ok <- switch(.Generic, `+` = , `-` = , `*` = , `/` = TRUE, FALSE) if (!ok) { return(NextMethod()) } if(.Generic == "/" && inherits(e2, "dist_normal")){ abort(sprintf("Cannot divide by a normal distribution")) } if(.Generic %in% c("-", "+") && missing(e2)){ e2 <- e1 e1 <- if(.Generic == "+") 1 else -1 .Generic <- "*" } if(.Generic == "-"){ .Generic <- "+" e2 <- -e2 } else if(.Generic == "/"){ .Generic <- "*" e2 <- 1/e2 } # Ops between two normals if(inherits(e1, "dist_normal") && inherits(e2, "dist_normal")){ if(.Generic == "*"){ abort(sprintf("Multiplying two normal distributions is not supported.")) } e1$mu <- e1$mu + e2$mu e1$sigma <- sqrt(e1$sigma^2 + e2$sigma^2) return(e1) } # Ops between a normal and scalar if(inherits(e1, "dist_normal")){ dist <- e1 scalar <- e2 } else { dist <- e2 scalar <- e1 } if(!is.numeric(scalar)){ abort(sprintf("Cannot %s a `%s` with a normal distribution", switch(.Generic, `+` = "add", `-` = "subtract", `*` = "multiply", `/` = "divide"), class(scalar))) } if(.Generic == "+"){ dist$mu <- dist$mu + scalar } else if(.Generic == "*"){ dist$mu <- dist$mu * scalar dist$sigma <- dist$sigma * abs(scalar) } dist } #' @method Math dist_normal #' @export Math.dist_normal <- function(x, ...) { # Shortcut to get log-normal distribution from Normal. if(.Generic == "exp") return(vec_data(dist_lognormal(x[["mu"]], x[["sigma"]]))[[1]]) NextMethod() } distributional/R/dist_sample.R0000644000176200001440000000734514406341620016147 0ustar liggesusers#' Sampling distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' @param x A list of sampled values. #' #' @examples #' # Univariate numeric samples #' dist <- dist_sample(x = list(rnorm(100), rnorm(100, 10))) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' generate(dist, 10) #' #' density(dist, 1) #' #' # Multivariate numeric samples #' dist <- dist_sample(x = list(cbind(rnorm(100), rnorm(100, 10)))) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' generate(dist, 10) #' #' density(dist, 1) #' #' @export dist_sample <- function(x){ vec_assert(x, list()) x <- as_list_of(x, .ptype = vec_ptype(x[[1]])) new_dist(x = x, class = "dist_sample") } #' @export format.dist_sample <- function(x, ...){ sprintf( "sample[%s]", vapply(x, vec_size, integer(1L)) ) } #' @export density.dist_sample <- function(x, at, ..., na.rm = TRUE){ # Apply independently over sample variates if(is.matrix(x$x)) { return( apply(x$x, 2, function(x, ...) density.dist_sample(list(x=x), ...), at = at, ..., na.rm = TRUE ) ) } # Shortcut if only one point in density is needed if(vec_size(at) == 1){ return(density(x[["x"]], from = at, to = at, n = 1)$y) } d <- density(x[["x"]], from = min(at), to = max(at), ..., na.rm=na.rm) stats::approx(d$x, d$y, xout = at)$y } #' @export quantile.dist_sample <- function(x, p, ..., na.rm = TRUE){ # Apply independently over sample variates if(is.matrix(x$x)) { return( apply(x$x, 2, function(x, ...) quantile.dist_sample(list(x=x), ...), p = p, ..., na.rm = TRUE ) ) } quantile(x$x, probs = p, ..., na.rm = na.rm, names = FALSE) } #' @export cdf.dist_sample <- function(x, q, ..., na.rm = TRUE){ # Apply independently over sample variates if(is.matrix(x$x)) { return( apply(x$x, 2, function(x, ...) cdf.dist_sample(list(x=x), ...), q = q, ..., na.rm = TRUE ) ) } if(length(q) > 1) return(vapply(q, cdf, numeric(1L), x = x, ...)) vapply(x, function(x, q) mean(x <= q, ..., na.rm = na.rm), numeric(1L), q = q) } #' @export generate.dist_sample <- function(x, times, ...){ i <- sample.int(vec_size(x[["x"]]), size = times, replace = TRUE) if(is.matrix(x$x)) x$x[i,,drop = FALSE] else x$x[i] } #' @export mean.dist_sample <- function(x, ...){ if(is.matrix(x$x)) apply(x$x, 2, mean, ...) else mean(x$x, ...) } #' @export median.dist_sample <- function(x, na.rm = FALSE, ...){ if(is.matrix(x$x)) apply(x$x, 2, median, na.rm = na.rm, ...) else median(x$x, na.rm = na.rm, ...) } #' @export covariance.dist_sample <- function(x, ...){ if(is.matrix(x$x)) stats::cov(x$x, ...) else stats::var(x$x, ...) } #' @export skewness.dist_sample <- function(x, ..., na.rm = FALSE) { if(is.matrix(x)) {abort("Multivariate sample skewness is not yet implemented.")} n <- lengths(x, use.names = FALSE) x <- lapply(x, function(.) . - mean(., na.rm = na.rm)) sum_x2 <- vapply(x, function(.) sum(.^2, na.rm = na.rm), numeric(1L), USE.NAMES = FALSE) sum_x3 <- vapply(x, function(.) sum(.^3, na.rm = na.rm), numeric(1L), USE.NAMES = FALSE) y <- sqrt(n) * sum_x3/(sum_x2^(3/2)) y * ((1 - 1/n))^(3/2) } #' @method Math dist_sample #' @export Math.dist_sample <- function(x, ...) { x <- mapply(.Generic, parameters(x)$x, ..., SIMPLIFY = FALSE) names(x) <- "x" enclass_dist(x, "dist_sample") } #' @method Ops dist_sample #' @export Ops.dist_sample <- function(e1, e2) { is_dist <- c(inherits(e1, "dist_sample"), inherits(e2, "dist_sample")) if(is_dist[1]) { e1 <- parameters(e1)$x } if(is_dist[2]) { e2 <- parameters(e2)$x } x <- mapply(.Generic, e1, e2, SIMPLIFY = FALSE) names(x) <- "x" enclass_dist(x, "dist_sample") } distributional/R/dist_poisson.R0000644000176200001440000000510414304314151016343 0ustar liggesusers#' The Poisson Distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' Poisson distributions are frequently used to model counts. #' #' @inheritParams stats::dpois #' #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X} be a Poisson random variable with parameter #' `lambda` = \eqn{\lambda}. #' #' **Support**: \eqn{\{0, 1, 2, 3, ...\}}{{0, 1, 2, 3, ...}} #' #' **Mean**: \eqn{\lambda} #' #' **Variance**: \eqn{\lambda} #' #' **Probability mass function (p.m.f)**: #' #' \deqn{ #' P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!} #' }{ #' P(X = k) = \lambda^k e^(-\lambda) / k! #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' \deqn{ #' P(X \le k) = e^{-\lambda} #' \sum_{i = 0}^{\lfloor k \rfloor} \frac{\lambda^i}{i!} #' }{ #' P(X \le k) = e^(-\lambda) #' \sum_{i = 0}^k \lambda^i / i! #' } #' #' **Moment generating function (m.g.f)**: #' #' \deqn{ #' E(e^{tX}) = e^{\lambda (e^t - 1)} #' }{ #' E(e^(tX)) = e^(\lambda (e^t - 1)) #' } #' @seealso [stats::Poisson] #' #' @examples #' dist <- dist_poisson(lambda = c(1, 4, 10)) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_poisson #' @export dist_poisson <- function(lambda){ lambda <- vec_cast(lambda, double()) if(any(lambda < 0)){ abort("The lambda parameter of an Poisson distribution must be non-negative.") } new_dist(l = lambda, class = "dist_poisson") } #' @export format.dist_poisson <- function(x, digits = 2, ...){ sprintf( "Pois(%s)", format(x[["l"]], digits = digits, ...) ) } #' @export density.dist_poisson <- function(x, at, ...){ stats::dpois(at, x[["l"]]) } #' @export log_density.dist_poisson <- function(x, at, ...){ stats::dpois(at, x[["l"]], log = TRUE) } #' @export quantile.dist_poisson <- function(x, p, ...){ stats::qpois(p, x[["l"]]) } #' @export cdf.dist_poisson <- function(x, q, ...){ stats::ppois(q, x[["l"]]) } #' @export generate.dist_poisson <- function(x, times, ...){ as.integer(stats::rpois(times, x[["l"]])) } #' @export mean.dist_poisson <- function(x, ...){ x[["l"]] } #' @export covariance.dist_poisson <- function(x, ...){ x[["l"]] } #' @export skewness.dist_poisson <- function(x, ...) 1 / sqrt(x[["l"]]) #' @export kurtosis.dist_poisson <- function(x, ...) 1 / x[["l"]] distributional/R/reexports.R0000644000176200001440000000007713711726207015677 0ustar liggesusers#' @importFrom generics generate #' @export generics::generate distributional/R/dist_categorical.R0000644000176200001440000000712314406341620017135 0ustar liggesusers#' The Categorical distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' Categorical distributions are used to represent events with multiple #' outcomes, such as what number appears on the roll of a dice. This is also #' referred to as the 'generalised Bernoulli' or 'multinoulli' distribution. #' The Cateogorical distribution is a special case of the [Multinomial()] #' distribution with `n = 1`. #' #' @param prob A list of probabilities of observing each outcome category. #' @param outcomes The values used to represent each outcome. #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X} be a Categorical random variable with #' probability parameters `p` = \eqn{\{p_1, p_2, \ldots, p_k\}}. #' #' The Categorical probability distribution is widely used to model the #' occurance of multiple events. A simple example is the roll of a dice, where #' \eqn{p = \{1/6, 1/6, 1/6, 1/6, 1/6, 1/6\}} giving equal chance of observing #' each number on a 6 sided dice. #' #' **Support**: \eqn{\{1, \ldots, k\}}{{1, ..., k}} #' #' **Mean**: \eqn{p} #' #' **Variance**: \eqn{p \cdot (1 - p) = p \cdot q}{p (1 - p)} #' #' **Probability mass function (p.m.f)**: #' #' \deqn{ #' P(X = i) = p_i #' }{ #' P(X = i) = p_i #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' The cdf() of a categorical distribution is undefined as the outcome categories aren't ordered. #' #' @examples #' dist <- dist_categorical(prob = list(c(0.05, 0.5, 0.15, 0.2, 0.1), c(0.3, 0.1, 0.6))) #' #' dist #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' # The outcomes aren't ordered, so many statistics are not applicable. #' cdf(dist, 4) #' quantile(dist, 0.7) #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' dist <- dist_categorical( #' prob = list(c(0.05, 0.5, 0.15, 0.2, 0.1), c(0.3, 0.1, 0.6)), #' outcomes = list(letters[1:5], letters[24:26]) #' ) #' #' generate(dist, 10) #' #' density(dist, "a") #' density(dist, "z", log = TRUE) #' #' @export dist_categorical <- function(prob, outcomes = NULL){ prob <- lapply(prob, function(x) x/sum(x)) prob <- as_list_of(prob, .ptype = double()) if(is.null(outcomes)) { new_dist(p = prob, class = "dist_categorical") } else { new_dist(p = prob, x = outcomes, class = "dist_categorical") } } #' @export format.dist_categorical <- function(x, digits = 2, ...){ sprintf( "Categorical[%s]", format(length(x[["p"]]), digits = digits, ...) ) } #' @export density.dist_categorical <- function(x, at, ...){ if(!is.null(x[["x"]])) at <- match(at, x[["x"]]) at[at <= 0] <- NA x[["p"]][at] } #' @export quantile.dist_categorical <- function(x, p, ...){ NA_real_ } #' @export cdf.dist_categorical <- function(x, q, ...){ NA_real_ } #' @export generate.dist_categorical <- function(x, times, ...){ z <- sample( x = seq_along(x[["p"]]), size = times, prob = x[["p"]], replace = TRUE ) if(is.null(x[["x"]])) return(z) x[["x"]][z] } #' @export support.dist_categorical <- function(x, ...) { region <- if(is.null(x[["p"]])) seq_along(x[["p"]]) else x[["x"]] new_support_region( list(vctrs::vec_init(region, n = 0L)), list(region) ) } #' @export mean.dist_categorical <- function(x, ...){ NA_real_ } #' @export covariance.dist_categorical <- function(x, ...){ NA_real_ } #' @export skewness.dist_categorical <- function(x, ...) { NA_real_ } #' @export kurtosis.dist_categorical <- function(x, ...) { NA_real_ } distributional/R/dist_inverse_gamma.R0000644000176200001440000000414514304314114017471 0ustar liggesusers#' The Inverse Gamma distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' @inheritParams actuar::dinvgamma #' #' @seealso [actuar::InverseGamma] #' #' @examples #' dist <- dist_inverse_gamma(shape = c(1,2,3,3), rate = c(1,1,1,2)) #' dist #' #' @examplesIf requireNamespace("actuar", quietly = TRUE) #' mean(dist) #' variance(dist) #' support(dist) #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_inverse_gamma #' @export dist_inverse_gamma <- function(shape, rate = 1/scale, scale){ shape <- vec_cast(shape, double()) rate <- vec_cast(rate, double()) if(any(shape <= 0)){ abort("The shape parameter of a Inverse Gamma distribution must be strictly positive.") } if(any(rate <= 0)){ abort("The rate/scale parameter of a Inverse Gamma distribution must be strictly positive.") } new_dist(s = shape, r = rate, class = "dist_inverse_gamma") } #' @export format.dist_inverse_gamma <- function(x, digits = 2, ...){ sprintf( "InvGamma(%s, %s)", format(x[["s"]], digits = digits, ...), format(1/x[["r"]], digits = digits, ...) ) } #' @export density.dist_inverse_gamma <- function(x, at, ...){ require_package("actuar") actuar::dinvgamma(at, x[["s"]], x[["r"]]) } #' @export log_density.dist_inverse_gamma <- function(x, at, ...){ require_package("actuar") actuar::dinvgamma(at, x[["s"]], x[["r"]], log = TRUE) } #' @export quantile.dist_inverse_gamma <- function(x, p, ...){ require_package("actuar") actuar::qinvgamma(p, x[["s"]], x[["r"]]) } #' @export cdf.dist_inverse_gamma <- function(x, q, ...){ require_package("actuar") actuar::pinvgamma(q, x[["s"]], x[["r"]]) } #' @export generate.dist_inverse_gamma <- function(x, times, ...){ require_package("actuar") actuar::rinvgamma(times, x[["s"]], x[["r"]]) } #' @export mean.dist_inverse_gamma <- function(x, ...){ if(x[["s"]] <= 1) return(NA_real_) 1/(x[["r"]]*(x[["s"]]-1)) } #' @export covariance.dist_inverse_gamma <- function(x, ...){ if(x[["s"]] <= 2) return(NA_real_) 1/(x[["r"]]^2*(x[["s"]]-1)^2*(x[["s"]]-2)) } distributional/R/dist_gamma.R0000644000176200001440000000747014304314065015747 0ustar liggesusers#' The Gamma distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' Several important distributions are special cases of the Gamma #' distribution. When the shape parameter is `1`, the Gamma is an #' exponential distribution with parameter \eqn{1/\beta}. When the #' \eqn{shape = n/2} and \eqn{rate = 1/2}, the Gamma is a equivalent to #' a chi squared distribution with n degrees of freedom. Moreover, if #' we have \eqn{X_1} is \eqn{Gamma(\alpha_1, \beta)} and #' \eqn{X_2} is \eqn{Gamma(\alpha_2, \beta)}, a function of these two variables #' of the form \eqn{\frac{X_1}{X_1 + X_2}} \eqn{Beta(\alpha_1, \alpha_2)}. #' This last property frequently appears in another distributions, and it #' has extensively been used in multivariate methods. More about the Gamma #' distribution will be added soon. #' #' @inheritParams stats::dgamma #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X} be a Gamma random variable #' with parameters #' `shape` = \eqn{\alpha} and #' `rate` = \eqn{\beta}. #' #' **Support**: \eqn{x \in (0, \infty)} #' #' **Mean**: \eqn{\frac{\alpha}{\beta}} #' #' **Variance**: \eqn{\frac{\alpha}{\beta^2}} #' #' **Probability density function (p.m.f)**: #' #' \deqn{ #' f(x) = \frac{\beta^{\alpha}}{\Gamma(\alpha)} x^{\alpha - 1} e^{-\beta x} #' }{ #' f(x) = \frac{\beta^{\alpha}}{\Gamma(\alpha)} x^{\alpha - 1} e^{-\beta x} #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' \deqn{ #' f(x) = \frac{\Gamma(\alpha, \beta x)}{\Gamma{\alpha}} #' }{ #' f(x) = \frac{\Gamma(\alpha, \beta x)}{\Gamma{\alpha}} #' } #' #' **Moment generating function (m.g.f)**: #' #' \deqn{ #' E(e^{tX}) = \Big(\frac{\beta}{ \beta - t}\Big)^{\alpha}, \thinspace t < \beta #' }{ #' E(e^(tX)) = \Big(\frac{\beta}{ \beta - t}\Big)^{\alpha}, \thinspace t < \beta #' } #' #' @seealso [stats::GammaDist] #' #' @examples #' dist <- dist_gamma(shape = c(1,2,3,5,9,7.5,0.5), rate = c(0.5,0.5,0.5,1,2,1,1)) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_gamma #' @export dist_gamma <- function(shape, rate, scale = 1/rate){ shape <- vec_cast(shape, double()) rate <- vec_cast(rate, double()) if(any(shape[!is.na(shape)] < 0)){ abort("The shape parameter of a Gamma distribution must be non-negative.") } if(any(rate[!is.na(rate)] <= 0)){ abort("The rate parameter of a Gamma distribution must be strictly positive.") } new_dist(shape = shape, rate = 1/scale, class = "dist_gamma") } #' @export format.dist_gamma <- function(x, digits = 2, ...){ sprintf( if (is_utf8_output()) "\u0393(%s, %s)" else "Gamma(%s, %s)", format(x[["shape"]], digits = digits, ...), format(x[["rate"]], digits = digits, ...) ) } #' @export density.dist_gamma <- function(x, at, ...){ stats::dgamma(at, x[["shape"]], x[["rate"]]) } #' @export log_density.dist_gamma <- function(x, at, ...){ stats::dgamma(at, x[["shape"]], x[["rate"]], log = TRUE) } #' @export quantile.dist_gamma <- function(x, p, ...){ stats::qgamma(p, x[["shape"]], x[["rate"]]) } #' @export cdf.dist_gamma <- function(x, q, ...){ stats::pgamma(q, x[["shape"]], x[["rate"]]) } #' @export generate.dist_gamma <- function(x, times, ...){ stats::rgamma(times, x[["shape"]], x[["rate"]]) } #' @export mean.dist_gamma <- function(x, ...){ x[["shape"]] / x[["rate"]] } #' @export covariance.dist_gamma <- function(x, ...){ x[["shape"]] / x[["rate"]]^2 } #' @export skewness.dist_gamma <- function(x, ...) 2 / sqrt(x[["shape"]]) #' @export kurtosis.dist_gamma <- function(x, ...) 6 / x[["shape"]] distributional/R/default.R0000755000176200001440000001755014250542636015300 0ustar liggesusers#' @export density.dist_default <- function(x, ...){ abort( sprintf("The distribution class `%s` does not support `density()`", class(x)[1]) ) } #' @export log_density.dist_default <- function(x, ...){ log(density(x, ...)) } #' @export quantile.dist_default <- function(x, p, ...){ # abort( # sprintf("The distribution class `%s` does not support `quantile()`", # class(x)[1]) # ) stats::optim(0, function(pos){ (p - cdf(x, pos, ...))^2 })$par } #' @export log_quantile.dist_default <- function(x, p, ...){ quantile(x, exp(p), ...) } #' @export cdf.dist_default <- function(x, ...){ abort( sprintf("The distribution class `%s` does not support `cdf()`", class(x)[1]) ) } #' @export log_cdf.dist_default <- function(x, q, ...){ log(cdf(x, q, ...)) } #' @export generate.dist_default <- function(x, times, ...){ vapply(stats::runif(times,0,1), quantile, numeric(1L), x = x, ...) } #' @export likelihood.dist_default <- function(x, sample, ...){ prod(vapply(sample, density, numeric(1L), x = x)) } #' @export log_likelihood.dist_default <- function(x, sample, ...){ sum(vapply(sample, log_density, numeric(1L), x = x)) } #' @export parameters.dist_default <- function(x, ...) { # Reduce parameter structures to length 1 list if needed. lapply(unclass(x), function(z) { if(inherits(z, "dist_default")) wrap_dist(list(z)) else if (tryCatch(vec_size(z), error = function(e) Inf) > 1) list(z) else z }) } #' @export family.dist_default <- function(object, ...) { substring(class(object)[1], first = 6) } #' @export support.dist_default <- function(x, ...) { new_support_region( list(vctrs::vec_init(generate(x, 1), n = 0L)), list(quantile(x, c(0, 1))) ) } #' @export mean.dist_default <- function(x, ...){ x_sup <- support(x) dist_type <- field(x_sup, "x")[[1]] if (!is.numeric(dist_type)) return(NA_real_) if (is.double(dist_type)) { limits <- field(x_sup, "lim")[[1]] tryCatch( stats::integrate(function(at) density(x, at) * at, limits[1], limits[2])$value, error = function(e) NA_real_ ) } else { mean(quantile(x, stats::ppoints(1000)), na.rm = TRUE) } } #' @export variance.dist_default <- function(x, ...){ x <- covariance(x, ...) if(is.matrix(x[[1]]) && ncol(x[[1]]) > 1){ matrix(diag(x[[1]]), nrow = 1) } else x } #' @export covariance.dist_default <- function(x, ...){ x_sup <- support(x) dist_type <- field(x_sup, "x")[[1]] if (!is.numeric(dist_type)) return(NA_real_) else if (is.matrix(dist_type)) stats::cov(generate(x, times = 1000)) else if (is.double(dist_type)) { limits <- field(x_sup, "lim")[[1]] tryCatch( stats::integrate(function(at) density(x, at) * at^2, limits[1], limits[2])$value, error = function(e) NA_real_ ) - mean(x)^2 } else { stats::var(quantile(x, stats::ppoints(1000)), na.rm = TRUE) } } #' @export median.dist_default <- function(x, na.rm = FALSE, ...){ quantile(x, p = 0.5, ...) } #' @export hilo.dist_default <- function(x, size = 95, ...){ lower <- quantile(x, 0.5-size/200, ...) upper <- quantile(x, 0.5+size/200, ...) if(is.matrix(lower) && is.matrix(upper)) { return( vctrs::new_data_frame(split( new_hilo(drop(lower), drop(upper), size = rep_len(size, length(lower))), seq_along(lower))) ) } new_hilo(lower, upper, size) } #' @export hdr.dist_default <- function(x, size = 95, n = 512, ...){ dist_x <- quantile(x, seq(0.5/n, 1 - 0.5/n, length.out = n)) # Remove duplicate values of dist_x from less continuous distributions dist_x <- unique(dist_x) dist_y <- density(x, dist_x) alpha <- quantile(dist_y, probs = 1-size/100) crossing_alpha <- function(alpha, x, y){ it <- seq_len(length(y) - 1) dd <- y - alpha dd <- dd[it + 1] * dd[it] index <- it[dd <= 0] # unique() removes possible duplicates if sequential dd has same value. # More robust approach is required. out <- unique( vapply( index, function(.x) stats::approx(y[.x + c(0,1)], x[.x + c(0,1)], xout = alpha)$y, numeric(1L) ) ) # Add boundary values which may exceed the crossing point. c(x[1][y[1]>alpha], out, x[length(x)][y[length(y)]>alpha]) } # purrr::map(alpha, crossing_alpha, dist_x, dist_y) hdr <- crossing_alpha(alpha, dist_x, dist_y) lower_hdr <- seq_along(hdr)%%2==1 new_hdr(lower = list(hdr[lower_hdr]), upper = list(hdr[!lower_hdr]), size = size) } #' @export format.dist_default <- function(x, ...){ "?" } #' @export print.dist_default <- function(x, ...){ cat(format(x, ...)) } #' @export dim.dist_default <- function(x){ 1 } invert_fail <- function(...) stop("Inverting transformations for distributions is not yet supported.") #' Attempt to get the inverse of f(x) by name. Returns invert_fail #' (a function that raises an error if called) if there is no known inverse. #' @param f string. Name of a function. #' @noRd get_unary_inverse <- function(f) { switch(f, sqrt = function(x) x^2, exp = log, log = function(x, base = exp(1)) base ^ x, log2 = function(x) 2^x, log10 = function(x) 10^x, expm1 = log1p, log1p = expm1, cos = acos, sin = asin, tan = atan, acos = cos, asin = sin, atan = tan, cosh = acosh, sinh = asinh, tanh = atanh, acosh = cosh, asinh = sinh, atanh = tanh, invert_fail ) } #' Attempt to get the inverse of f(x, constant) by name. Returns invert_fail #' (a function that raises an error if called) if there is no known inverse. #' @param f string. Name of a function. #' @param constant a constant value #' @noRd get_binary_inverse_1 <- function(f, constant) { force(constant) switch(f, `+` = function(x) x - constant, `-` = function(x) x + constant, `*` = function(x) x / constant, `/` = function(x) x * constant, `^` = function(x) x ^ (1/constant), invert_fail ) } #' Attempt to get the inverse of f(constant, x) by name. Returns invert_fail #' (a function that raises an error if called) if there is no known inverse. #' @param f string. Name of a function. #' @param constant a constant value #' @noRd get_binary_inverse_2 <- function(f, constant) { force(constant) switch(f, `+` = function(x) x - constant, `-` = function(x) constant - x, `*` = function(x) x / constant, `/` = function(x) constant / x, `^` = function(x) log(x, base = constant), invert_fail ) } #' @method Math dist_default #' @export Math.dist_default <- function(x, ...) { if(dim(x) > 1) stop("Transformations of multivariate distributions are not yet supported.") trans <- new_function(exprs(x = ), body = expr((!!sym(.Generic))(x, !!!dots_list(...)))) inverse_fun <- get_unary_inverse(.Generic) inverse <- new_function(exprs(x = ), body = expr((!!inverse_fun)(x, !!!dots_list(...)))) vec_data(dist_transformed(wrap_dist(list(x)), trans, inverse))[[1]] } #' @method Ops dist_default #' @export Ops.dist_default <- function(e1, e2) { is_dist <- c(inherits(e1, "dist_default"), inherits(e2, "dist_default")) if(any(vapply(list(e1, e2)[is_dist], dim, numeric(1L)) > 1)){ stop("Transformations of multivariate distributions are not yet supported.") } trans <- if(all(is_dist)) { if(identical(e1$dist, e2$dist)){ new_function(exprs(x = ), expr((!!sym(.Generic))((!!e1$transform)(x), (!!e2$transform)(x)))) } else { stop(sprintf("The %s operation is not supported for <%s> and <%s>", .Generic, class(e1)[1], class(e2)[1])) } } else if(is_dist[1]){ new_function(exprs(x = ), body = expr((!!sym(.Generic))(x, !!e2))) } else { new_function(exprs(x = ), body = expr((!!sym(.Generic))(!!e1, x))) } inverse <- if(all(is_dist)) { invert_fail } else if(is_dist[1]){ get_binary_inverse_1(.Generic, e2) } else { get_binary_inverse_2(.Generic, e1) } vec_data(dist_transformed(wrap_dist(list(e1,e2)[which(is_dist)]), trans, inverse))[[1]] } distributional/R/dist_geometric.R0000644000176200001440000000550714304314245016642 0ustar liggesusers#' The Geometric Distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' The Geometric distribution can be thought of as a generalization #' of the [dist_bernoulli()] distribution where we ask: "if I keep flipping a #' coin with probability `p` of heads, what is the probability I need #' \eqn{k} flips before I get my first heads?" The Geometric #' distribution is a special case of Negative Binomial distribution. #' #' @inheritParams stats::dgeom #' #' @details #' #' We recommend reading this documentation on #' , where the math #' will render nicely. #' #' In the following, let \eqn{X} be a Geometric random variable with #' success probability `p` = \eqn{p}. Note that there are multiple #' parameterizations of the Geometric distribution. #' #' **Support**: 0 < p < 1, \eqn{x = 0, 1, \dots} #' #' **Mean**: \eqn{\frac{1-p}{p}} #' #' **Variance**: \eqn{\frac{1-p}{p^2}} #' #' **Probability mass function (p.m.f)**: #' #' \deqn{ #' P(X = x) = p(1-p)^x, #' } #' #' **Cumulative distribution function (c.d.f)**: #' #' \deqn{ #' P(X \le x) = 1 - (1-p)^{x+1} #' } #' #' **Moment generating function (m.g.f)**: #' #' \deqn{ #' E(e^{tX}) = \frac{pe^t}{1 - (1-p)e^t} #' }{ #' E(e^{tX}) = \frac{pe^t}{1 - (1-p)e^t} #' } #' #' @seealso [stats::Geometric] #' #' @examples #' dist <- dist_geometric(prob = c(0.2, 0.5, 0.8)) #' #' dist #' mean(dist) #' variance(dist) #' skewness(dist) #' kurtosis(dist) #' #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' @name dist_geometric #' @export dist_geometric <- function(prob){ prob <- vec_cast(prob, double()) if(any((prob < 0) | (prob > 1))){ abort("The prob parameter of an Geometric distribution must be between 0 and 1.") } new_dist(p = prob, class = "dist_geometric") } #' @export format.dist_geometric <- function(x, digits = 2, ...){ sprintf( "Geometric(%s)", format(x[["p"]], digits = digits, ...) ) } #' @export density.dist_geometric <- function(x, at, ...){ stats::dgeom(at, x[["p"]]) } #' @export log_density.dist_geometric <- function(x, at, ...){ stats::dgeom(at, x[["p"]], log = TRUE) } #' @export quantile.dist_geometric <- function(x, p, ...){ stats::qgeom(p, x[["p"]]) } #' @export cdf.dist_geometric <- function(x, q, ...){ stats::pgeom(q, x[["p"]]) } #' @export generate.dist_geometric <- function(x, times, ...){ stats::rgeom(times, x[["p"]]) } #' @export mean.dist_geometric <- function(x, ...){ 1/x[["p"]] - 1 } #' @export covariance.dist_geometric <- function(x, ...){ (1 - x[["p"]])/x[["p"]]^2 } #' @export skewness.dist_geometric <- function(x, ...) (2 - x[["p"]]) / sqrt(1 - x[["p"]]) #' @export kurtosis.dist_geometric <- function(x, ...) 6 + (x[["p"]]^2 / (1 - x[["p"]])) distributional/R/hdr.R0000644000176200001440000000412114304176634014415 0ustar liggesusers#' Construct hdr intervals #' #' @param lower,upper A list of numeric vectors specifying the region's lower #' and upper bounds. #' @param size A numeric vector specifying the coverage size of the region. #' #' @return A "hdr" vector #' #' @author Mitchell O'Hara-Wild #' #' @examples #' #' new_hdr(lower = list(1, c(3,6)), upper = list(10, c(5, 8)), size = c(80, 95)) #' #' @export new_hdr <- function(lower = list_of(.ptype = double()), upper = list_of(.ptype = double()), size = double()) { lower <- as_list_of(lower) upper <- as_list_of(upper) vec_assert(lower, list_of(.ptype = double())) vec_assert(upper, list_of(.ptype = double())) vec_assert(size, double()) if (any(size < 0 | size > 100, na.rm = TRUE)) abort("'size' must be between [0, 100].") out <- vec_recycle_common(lower = lower, upper = upper) mapply( function(l,u) if (any(u 1){ abort("The inflation probability must be between 0 and 1.") } new_dist(dist = dist, x = x, p = prob, dimnames = dimnames(dist), class = "dist_inflated") } #' @export format.dist_inflated <- function(x, ...){ sprintf( "%s+%s", format(x[["x"]]), format(x[["dist"]]) ) } #' @export density.dist_inflated <- function(x, at, ...){ x[["p"]]*(at==x[["x"]]) + (1-x[["p"]])*density(x[["dist"]], at, ...) } #' @export quantile.dist_inflated <- function(x, p, ...){ qt <- quantile(x[["dist"]], pmax(0, (p - x[["p"]]) / (1-x[["p"]])), ...) if(qt >= x[["x"]]) return(qt) qt <- quantile(x[["dist"]], p, ...) if(qt < x[["x"]]) qt else x[["x"]] } #' @export cdf.dist_inflated <- function(x, q, ...){ x[["p"]]*(q>=x[["x"]]) + (1-x[["p"]])*cdf(x[["dist"]], q, ...) } #' @export generate.dist_inflated <- function(x, times, ...){ p <- x[["p"]] inf <- stats::runif(times) < p r <- vec_init(x[["x"]], times) r[inf] <- x[["x"]] r[!inf] <- generate(x[["dist"]], sum(!inf)) r } #' @export mean.dist_inflated <- function(x, ...){ # Can't compute if inflation value is not numeric if(!vec_is(x[["x"]], numeric())) return(NA_real_) p <- x[["p"]] p*x[["x"]] + (1-p)*mean(x[["dist"]]) } #' @export covariance.dist_inflated <- function(x, ...){ # Can't compute if inflation value is not numeric if(!vec_is(x[["x"]], numeric())) return(NA_real_) # Can't (easily) compute if inflation value is not zero if(x[["x"]] != 0) return(NA_real_) m1 <- mean(x[["dist"]]) v <- variance(x[["dist"]]) m2 <- v + m1^2 p <- x[["p"]] (1-p)*v + p*(1-p)*m1^2 } distributional/R/dist_pareto.R0000644000176200001440000000401514304314623016147 0ustar liggesusers#' The Pareto distribution #' #' @description #' `r lifecycle::badge('stable')` #' #' @inheritParams actuar::dpareto #' #' @seealso [actuar::Pareto] #' #' @examples #' dist <- dist_pareto(shape = c(10, 3, 2, 1), scale = rep(1, 4)) #' dist #' #' @examplesIf requireNamespace("actuar", quietly = TRUE) #' mean(dist) #' variance(dist) #' support(dist) #' generate(dist, 10) #' #' density(dist, 2) #' density(dist, 2, log = TRUE) #' #' cdf(dist, 4) #' #' quantile(dist, 0.7) #' #' @name dist_pareto #' @export dist_pareto <- function(shape, scale){ shape <- vec_cast(shape, double()) scale <- vec_cast(scale, double()) if(any(shape < 0)){ abort("The shape parameter of a Pareto distribution must be non-negative.") } if(any(scale <= 0)){ abort("The scale parameter of a Pareto distribution must be strictly positive.") } new_dist(shape = shape, scale = scale, class = "dist_pareto") } #' @export format.dist_pareto <- function(x, digits = 2, ...){ sprintf( "Pareto(%s, %s)", format(x[["shape"]], digits = digits, ...), format(x[["scale"]], digits = digits, ...) ) } #' @export density.dist_pareto <- function(x, at, ...){ require_package("actuar") actuar::dpareto(at, x[["shape"]], x[["scale"]]) } #' @export log_density.dist_pareto <- function(x, at, ...){ require_package("actuar") actuar::dpareto(at, x[["shape"]], x[["scale"]], log = TRUE) } #' @export quantile.dist_pareto <- function(x, p, ...){ require_package("actuar") actuar::qpareto(p, x[["shape"]], x[["scale"]]) } #' @export cdf.dist_pareto <- function(x, q, ...){ require_package("actuar") actuar::ppareto(q, x[["shape"]], x[["scale"]]) } #' @export generate.dist_pareto <- function(x, times, ...){ require_package("actuar") actuar::rpareto(times, x[["shape"]], x[["scale"]]) } #' @export mean.dist_pareto <- function(x, ...){ actuar::mpareto(1, x[["shape"]], x[["scale"]]) } #' @export covariance.dist_pareto <- function(x, ...){ actuar::mpareto(2, x[["shape"]], x[["scale"]]) - actuar::mpareto(1, x[["shape"]], x[["scale"]])^2 } distributional/NEWS.md0000644000176200001440000002527214560651321014417 0ustar liggesusers# distributional 0.4.0 ## Breaking changes * All graphics related functionality has been removed from the package in favour of the ggdist (https://cran.r-project.org/package=ggdist) package. This breaking change was done to substantially reduce the package's dependencies, focusing the functionality on representing vectors of distributions. # distributional 0.3.2 Small patch to resolve issues with CRAN checks. ## Bug fixes * Fixed object structure resulting from transforming sample distributions (#81). * Improved reliability of `quantile()`. * Defined `cdf()` as Pr(X <= x), not Pr(X < x). * Fixed S3 generic argument name `p` for `log_quantile()`. # distributional 0.3.1 ## New features * Add Math and Ops methods for sample distribution, which applies the functions directly to the samples. * Added `mean` and `sd` as aliases for `mu` and `sigma` respectively in `dist_normal()` and `dist_student_t()` to match arguments of the stats package interface (#76). * Added `scale` argument for alternative specification for `dist_burr()` and `dist_gamma()`. ## Improvements * Generics introduced by this package now allow `na.rm` and other parameters to be passed to distribution methods, even if these parameters aren't used. The package no longer checks the usage of `...` with the `ellipsis` package, if you'd like to check that all `...` are used, you can write your own wrapping functions. * Lists of functions can now be used in `dist_transformed()`, allowing the transformation to differ for each distribution. * `covariance()` and other matrix output functions of multivariate distributions now name the result using the distribution's dimension names. * Improve handling of mixture distribution quantiles at boundaries {0,1}. ## Bug fixes * Fixed issue with computing multiple values from a univariate distribution with named dimensions (#79). # distributional 0.3.0 ## New features ### Probability distributions * Added `dist_categorical()` for the Categorical distribution. * Added `dist_lognormal()` for the log-normal distribution. Mathematical conversion shortcuts have also been added, so `exp(dist_normal())` produces `dist_lognormal()`. ### Generics * Added `parameters()` generic for obtaining the distribution's parameters. * Added `family()` for getting the distribution's family name. * Added `covariance()` to return the covariance of a distribution. * Added `support()` to identify the distribution's region of support (#8). * Added `log_likelihood()` for computing the log-likelihood of observing a sample from a distribution. ## Improvements * `variance()` now always returns a variance. It will not default to providing a covariance matrix for matrices. This also applies to multivariate distributions such as `dist_multivariate_normal()`. The covariance can now be obtained using the `covariance()` function. * `dist_wrap()` can now search for distribution functions in any environment, not just packages. If the `package` argument is `NULL`, it will search the calling environment for the functions. You can also provide a package name as before, and additionally an arbitrary environment to this argument. * `median()` methods will now ignore the `na.rm` option when it does not apply to that distribution type (#72). * `dist_sample()` now allows for missing values to be stored. Note that `density()`, `quantile()` and `cdf()` will remove these missing values by default. This behaviour can be changed with the `na.rm` argument. * `` objects now support non-numeric and multivariate distributions. `` vectors that have different bound types cannot be mixed (#74). * Improved performance of default methods of `mean()` and `variance()`, which no longer use sampling based means and variances for univariate continuous distributions (#71, @mjskay) * `dist_binomial()` distributions now return integers for `quantile()` and `generate()` methods. * Added conditional examples for distributions using functions from supported packages. ## Bug fixes * Fixed fallback `format()` function for distributions classes that have not defined this method (#67). ## Breaking changes * `variance()` on a `dist_multivariate_normal()` will now return the diagonal instead of the complete variance-covariance matrix. * `dist_bernoulli()` will now return logical values for `quantile()` and `generate()`. # distributional 0.2.2 ## New features * Added `is_distribution()` to identify if an object is a distribution. ## Improvements * Improved NA structure of distributions, allowing it to work with `is.na()` and `vctrs` vector resizing / filling functionality. * Added `as.character()` method, allowing datasets containing `hilo()` objects to be saved as a text file (#57). ## Bug fixes * Fixed issue with `hdr()` range `size` incorrectly being treated as `100-size`, giving 5% ranges for 95% sizes and vice-versa (#61). # distributional 0.2.1 A small performance and methods release. Some issues with truncated distributions have been fixed, and some more distribution methods have been added which improve performance of common tasks. ## New features ### Probability distributions * Added `dist_missing()` for representing unknown or missing (NA) distributions. ## Improvements * Documentation improvements. * Added `cdf()` method for `dist_sample()` which uses the emperical cdf. * `dist_mixture()` now preserves `dimnames()` if all distributions have the same `dimnames()`. * Added `density()` and `generate()` methods for sample distributions. * Added `skewness()` method for `dist_sample()`. * Improved performance for truncated Normal and sample distributions (#49). * Improved vectorisation of distribution methods. ## Bug fixes * Fixed issue with computing the median of `dist_truncated()` distributions. * Fixed format method for `dist_truncated()` distributions with no upper or lower limit. * Fixed issue with naming objects giving an invalid structure. It now gives an informative error (#23). * Fixed documentation for Negative Binomial distribution (#46). # distributional 0.2.0 ## New features ### Probability distributions * Added `dist_wrap()` for wrapping distributions not yet added in the package. ### Methods * Added `likelihood()` for computing the likelihood of observing a sample from a distribution. * Added `skewness()` for computing the skewness of a distribution. * Added `kurtosis()` for computing the kurtosis of a distribution. * The `density()`, `cdf()` and `quantile()` methods now accept a `log` argument which will use/return probabilities as log probabilities. ## Improvements * Improved documentation for most distributions to include equations for the region of support, summary statistics, density functions and moments. This is the work of @alexpghayes in the `distributions3` package. * Documentation improvements * Added support for displaying distributions with `View()`. * `hilo()` intervals can no longer be added to other intervals, as this is a common mistake when aggregating forecasts. * Incremented `d` for `numDeriv::hessian()` when computing mean and variance of transformed distributions. ## Deprecated features * Graphics functionality provided by `autoplot.distribution()` is now deprecated in favour of using the `ggdist` package. The `ggdist` package allows distributions produced by distributional to be used directly with ggplot2 as aesthetics. # distributional 0.1.0 First release. ## New features ### Object classes * `distribution`: Distributions are represented in a vectorised format using the [vctrs](https://cran.r-project.org/package=vctrs) package. This makes distributions suitable for inclusion in model prediction output. A `distribution` is a container for distribution-specific S3 classes. * `hilo`: Intervals are also stored in a vector. A `hilo` consists of a `lower` bound, `upper` bound, and confidence `level`. Each numerical element can be extracted using `$`, for example my_hilo$lower to obtain the lower bounds. * `hdr`: Highest density regions are currently stored as lists of `hilo` values. This is an experimental feature, and is likely to be expanded upon in an upcoming release. ### Generic functions Values of interest can be computed from the distribution using generic functions. The first release provides 9 functions for interacting with distributions: * `density()`: The probability density/mass function (equivalent to `d...()`). * `cdf()`: The cumulative distribution function (equivalent to `p...()`). * `generate()`: Random generation from the distribution (equivalent to `r...()`). * `quantile()`: Compute quantiles of the distribution (equivalent to `q...()`). * `hilo()`: Compute probability intervals of probability distribution(s). * `hdr()`: Compute highest density regions of probability distribution(s). * `mean()`: Obtain the mean(s) of probability distribution(s). * `median()`: Obtain the median(s) of probability distribution(s). * `variance()`: Obtain the variance(s) of probability distribution(s). ### Graphics * Added an `autoplot()` method for visualising the probability density function ([`density()`]) or cumulative distribution function ([`cdf()`]) of one or more distribution. * Added `geom_hilo_ribbon()` and `geom_hilo_linerange()` geometries for ggplot2. These geoms allow uncertainty to be shown graphically with `hilo()` intervals. ### Probability distributions * Added 20 continuous probability distributions: `dist_beta()`, `dist_burr()`, `dist_cauchy()`, `dist_chisq()`, `dist_exponential()`, `dist_f()`, `dist_gamma()`, `dist_gumbel()`, `dist_hypergeometric()`, `dist_inverse_exponential()`, `dist_inverse_gamma()`, `dist_inverse_gaussian()`, `dist_logistic()`, `dist_multivariate_normal()`, `dist_normal()`, `dist_pareto()`, `dist_student_t()`, `dist_studentized_range()`, `dist_uniform()`, `dist_weibull()` * Added 8 discrete probability distributions: `dist_bernoulli()`, `dist_binomial()`, `dist_geometric()`, `dist_logarithmic()`, `dist_multinomial()`, `dist_negative_binomial()`, `dist_poisson()`, `dist_poisson_inverse_gaussian()` * Added 3 miscellaneous probability distributions: `dist_degenerate()`, `dist_percentile()`, `dist_sample()` ### Distribution modifiers * Added `dist_inflated()` which inflates a specific value of a distribution by a given probability. 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