# R/SDistribution_InverseGamma.R In distr6: The Complete R6 Probability Distributions Interface

# nolint start
#' @name InverseGamma
#' @template SDist
#' @templateVar ClassName InverseGamma
#' @templateVar DistName Inverse Gamma
#' @templateVar uses in Bayesian statistics as the posterior distribution from the unknown variance in a Normal distribution
#' @templateVar params shape, \eqn{\alpha}, and scale, \eqn{\beta},
#' @templateVar pdfpmf pdf
#' @templateVar pdfpmfeq \deqn{f(x) = (\beta^\alpha)/\Gamma(\alpha)x^{-\alpha-1}exp(-\beta/x)}
#' @templateVar paramsupport \eqn{\alpha, \beta > 0}, where \eqn{\Gamma} is the gamma function
#' @templateVar distsupport the Positive Reals
#' @templateVar default shape = 1, scale = 1
# nolint end
#' @template class_distribution
#' @template method_mode
#' @template method_entropy
#' @template method_kurtosis
#' @template method_pgf
#' @template method_mgfcf
#' @template param_decorators
#' @template param_shape
#' @template param_scale
#' @template field_packages
#'
#' @family continuous distributions
#' @family univariate distributions
#'
#' @export
InverseGamma <- R6Class("InverseGamma",
inherit = SDistribution, lock_objects = F,
public = list(
# Public fields
name = "InverseGamma",
short_name = "InvGamma",
description = "Inverse Gamma Probability Distribution.",

# Public methods
# initialize

#' @description
#' Creates a new instance of this [R6][R6::R6Class] class.
initialize = function(shape = NULL, scale = NULL, decorators = NULL) {
super$initialize( decorators = decorators, support = PosReals$new(),
type = PosReals$new() ) }, # stats #' @description #' The arithmetic mean of a (discrete) probability distribution X is the expectation #' \deqn{E_X(X) = \sum p_X(x)*x} #' with an integration analogue for continuous distributions. #' @param ... Unused. mean = function(...) { shape <- unlist(self$getParameterValue("shape"))
scale <- unlist(self$getParameterValue("scale")) mean <- rep(NaN, length(shape)) mean[shape > 1] <- scale[shape > 1] / (shape[shape > 1] - 1) return(mean) }, #' @description #' The mode of a probability distribution is the point at which the pdf is #' a local maximum, a distribution can be unimodal (one maximum) or multimodal (several #' maxima). mode = function(which = "all") { unlist(self$getParameterValue("scale")) / (unlist(self$getParameterValue("shape")) + 1) }, #' @description #' The variance of a distribution is defined by the formula #' \deqn{var_X = E[X^2] - E[X]^2} #' where \eqn{E_X} is the expectation of distribution X. If the distribution is multivariate the #' covariance matrix is returned. #' @param ... Unused. variance = function(...) { shape <- unlist(self$getParameterValue("shape"))
scale <- unlist(self$getParameterValue("scale")) var <- rep(NaN, length(shape)) var[shape > 2] <- scale[shape > 2]^2 / ((shape[shape > 2] - 1)^2 * (shape[shape > 2] - 2)) return(var) }, #' @description #' The skewness of a distribution is defined by the third standardised moment, #' \deqn{sk_X = E_X[\frac{x - \mu}{\sigma}^3]}{sk_X = E_X[((x - \mu)/\sigma)^3]} #' where \eqn{E_X} is the expectation of distribution X, \eqn{\mu} is the mean of the #' distribution and \eqn{\sigma} is the standard deviation of the distribution. #' @param ... Unused. skewness = function(...) { shape <- unlist(self$getParameterValue("shape"))
skew <- rep(NaN, length(shape))
skew[shape > 3] <- (4 * sqrt(shape[shape > 3] - 2)) / (shape[shape > 3] - 3)
return(skew)
},

#' @description
#' The kurtosis of a distribution is defined by the fourth standardised moment,
#' \deqn{k_X = E_X[\frac{x - \mu}{\sigma}^4]}{k_X = E_X[((x - \mu)/\sigma)^4]}
#' where \eqn{E_X} is the expectation of distribution X, \eqn{\mu} is the mean of the
#' distribution and \eqn{\sigma} is the standard deviation of the distribution.
#' Excess Kurtosis is Kurtosis - 3.
#' @param ... Unused.
kurtosis = function(excess = TRUE, ...) {
shape <- unlist(self$getParameterValue("shape")) kur <- rep(NaN, length(shape)) kur[shape > 4] <- (6 * (5 * shape[shape > 4] - 11)) / ((shape[shape > 4] - 3) * (shape[shape > 4] - 4)) if (excess) { return(kur) } else { return(kur + 3) } }, #' @description #' The entropy of a (discrete) distribution is defined by #' \deqn{- \sum (f_X)log(f_X)} #' where \eqn{f_X} is the pdf of distribution X, with an integration analogue for #' continuous distributions. #' @param ... Unused. entropy = function(base = 2, ...) { shape <- unlist(self$getParameterValue("shape"))
scale <- unlist(self$getParameterValue("scale")) return(shape + log(scale * gamma(shape), base) - (1 + shape) * digamma(shape)) }, #' @description The moment generating function is defined by #' \deqn{mgf_X(t) = E_X[exp(xt)]} #' where X is the distribution and \eqn{E_X} is the expectation of the distribution X. #' @param ... Unused. mgf = function(t, ...) { return(NaN) }, #' @description The probability generating function is defined by #' \deqn{pgf_X(z) = E_X[exp(z^x)]} #' where X is the distribution and \eqn{E_X} is the expectation of the distribution X. #' @param ... Unused. pgf = function(z, ...) { return(NaN) } ), private = list( # dpqr .pdf = function(x, log = FALSE) { if (checkmate::testList(self$getParameterValue("shape"))) {
mapply(
alpha = self$getParameterValue("shape"), beta = self$getParameterValue("scale"),
MoreArgs = list(x = x, log = log)
)
} else {
x,
alpha = self$getParameterValue("shape"), beta = self$getParameterValue("scale"),
log = log
)
}
},
.cdf = function(x, lower.tail = TRUE, log.p = FALSE) {
if (checkmate::testList(self$getParameterValue("shape"))) { mapply( extraDistr::pinvgamma, alpha = self$getParameterValue("shape"),
beta = self$getParameterValue("scale"), MoreArgs = list( q = x, lower.tail = lower.tail, log.p = log.p ) ) } else { extraDistr::pinvgamma( x, alpha = self$getParameterValue("shape"),
beta = self$getParameterValue("scale"), lower.tail = lower.tail, log.p = log.p ) } }, .quantile = function(p, lower.tail = TRUE, log.p = FALSE) { if (checkmate::testList(self$getParameterValue("shape"))) {
mapply(
alpha = self$getParameterValue("shape"), beta = self$getParameterValue("scale"),
MoreArgs = list(
p = p,
lower.tail = lower.tail,
log.p = log.p
)
)
} else {
p,
alpha = self$getParameterValue("shape"), beta = self$getParameterValue("scale"),
lower.tail = lower.tail,
log.p = log.p
)
}
},
.rand = function(n) {
if (checkmate::testList(self$getParameterValue("shape"))) { mapply( extraDistr::rinvgamma, alpha = self$getParameterValue("shape"),
beta = self$getParameterValue("scale"), MoreArgs = list(n = n) ) } else { extraDistr::rinvgamma( n, alpha = self$getParameterValue("shape"),
beta = self$getParameterValue("scale") ) } }, # traits .traits = list(valueSupport = "continuous", variateForm = "univariate") ) ) .distr6$distributions <- rbind(
.distr6\$distributions,
data.table::data.table(
ShortName = "InvGamma", ClassName = "InverseGamma",
Type = "\u211D+", ValueSupport = "continuous",
VariateForm = "univariate",
Package = "extraDistr", Tags = ""
)
)


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distr6 documentation built on March 28, 2022, 1:05 a.m.