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

# nolint start
#' @name Gumbel
#' @template SDist
#' @templateVar ClassName Gumbel
#' @templateVar DistName Gumbel
#' @templateVar uses to model the maximum (or minimum) of a number of samples of different distributions, and is a special case of the Generalised Extreme Value distribution
#' @templateVar params location, \eqn{\mu}, and scale, \eqn{\beta},
#' @templateVar pdfpmf pdf
#' @templateVar pdfpmfeq \deqn{f(x) = exp(-(z + exp(-z)))/\beta}
#' @templateVar paramsupport \eqn{z = (x-\mu)/\beta}, \eqn{\mu \epsilon R} and \eqn{\beta > 0}
#' @templateVar distsupport the Reals
#' @templateVar default location = 0, 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_locationscale
#' @template field_packages
#'
#' @family continuous distributions
#' @family univariate distributions
#'
#' @export
Gumbel <- R6Class("Gumbel",
inherit = SDistribution, lock_objects = F,
public = list(
# Public fields
name = "Gumbel",
short_name = "Gumb",
description = "Gumbel Probability Distribution.",

# Public methods
# initialize

#' @description
#' Creates a new instance of this [R6][R6::R6Class] class.
initialize = function(location = NULL, scale = NULL, decorators = NULL) {
super$initialize( decorators = decorators, support = Reals$new(),
type = Reals$new() ) }, # stats #' @description #' The arithmetic mean of a (discrete) probability distribution X is the expectation #' \deqn{E_X(X) = \sum p_X(x)*x} #' with an integration analogue for continuous distributions. #' @param ... Unused. mean = function(...) { unlist(self$getParameterValue("location")) -
digamma(1) * unlist(self$getParameterValue("scale")) }, #' @description #' The mode of a probability distribution is the point at which the pdf is #' a local maximum, a distribution can be unimodal (one maximum) or multimodal (several #' maxima). mode = function(which = "all") { unlist(self$getParameterValue("location"))
},

#' @description
#' Returns the median of the distribution. If an analytical expression is available
#' returns distribution median, otherwise if symmetric returns self$mean, otherwise #' returns self$quantile(0.5).
median = function() {
unlist(self$getParameterValue("location")) - unlist(self$getParameterValue("scale")) * log(log(2))
},

#' @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(...) {
(pi * unlist(self$getParameterValue("scale")))^2 / 6 }, #' @description #' The skewness of a distribution is defined by the third standardised moment, #' \deqn{sk_X = E_X[\frac{x - \mu}{\sigma}^3]}{sk_X = E_X[((x - \mu)/\sigma)^3]} #' where \eqn{E_X} is the expectation of distribution X, \eqn{\mu} is the mean of the #' distribution and \eqn{\sigma} is the standard deviation of the distribution. #' #' Apery's Constant to 16 significant figures is used in the calculation. #' @param ... Unused. skewness = function(...) { rep( (12 * sqrt(6) * 1.202056903159594285399738161511449990764986292) / pi^3, length(self$getParameterValue("scale"))
)
},

#' @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, ...) {
if (excess) {
return(rep(2.4, length(self$getParameterValue("scale")))) } else { return(rep(5.4, length(self$getParameterValue("scale"))))
}
},

#' @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, ...) {
log(unlist(self$getParameterValue("scale")), base) - digamma(1) + 1 }, #' @description The moment generating function is defined by #' \deqn{mgf_X(t) = E_X[exp(xt)]} #' where X is the distribution and \eqn{E_X} is the expectation of the distribution X. #' @param ... Unused. mgf = function(t, ...) { return(gamma(1 - self$getParameterValue("scale") * t) *
exp(self$getParameterValue("location") * t)) }, #' @description The characteristic function is defined by #' \deqn{cf_X(t) = E_X[exp(xti)]} #' where X is the distribution and \eqn{E_X} is the expectation of the distribution X. #' #' [pracma::gammaz()] is used in this function to allow complex inputs. #' @param ... Unused. cf = function(t, ...) { return(pracma::gammaz(1 - self$getParameterValue("scale") * t * 1i) *
exp(1i * self$getParameterValue("location") * t)) }, #' @description The probability generating function is defined by #' \deqn{pgf_X(z) = E_X[exp(z^x)]} #' where X is the distribution and \eqn{E_X} is the expectation of the distribution X. #' @param ... Unused. pgf = function(z, ...) { return(NaN) } ), private = list( # dpqr .pdf = function(x, log = FALSE) { if (checkmate::testList(self$getParameterValue("location"))) {
mapply(
mu = self$getParameterValue("location"), sigma = self$getParameterValue("scale"),
MoreArgs = list(x = x, log = log)
)
} else {
x,
mu = self$getParameterValue("location"), sigma = self$getParameterValue("scale"),
log = log
)
}
},
.cdf = function(x, lower.tail = TRUE, log.p = FALSE) {
if (checkmate::testList(self$getParameterValue("location"))) { mapply( extraDistr::pgumbel, mu = self$getParameterValue("location"),
sigma = self$getParameterValue("scale"), MoreArgs = list( q = x, lower.tail = lower.tail, log.p = log.p ) ) } else { extraDistr::pgumbel( x, mu = self$getParameterValue("location"),
sigma = 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("location"))) {
mapply(
mu = self$getParameterValue("location"), sigma = self$getParameterValue("scale"),
MoreArgs = list(
p = p,
lower.tail = lower.tail,
log.p = log.p
)
)
} else {
p,
mu = self$getParameterValue("location"), sigma = self$getParameterValue("scale"),
lower.tail = lower.tail,
log.p = log.p
)
}
},
.rand = function(n) {
if (checkmate::testList(self$getParameterValue("location"))) { mapply( extraDistr::rgumbel, mu = self$getParameterValue("location"),
sigma = self$getParameterValue("scale"), MoreArgs = list(n = n) ) } else { extraDistr::rgumbel( n, mu = self$getParameterValue("location"),
sigma = self$getParameterValue("scale") ) } }, # traits .traits = list(valueSupport = "continuous", variateForm = "univariate") ) ) .distr6$distributions <- rbind(
.distr6\$distributions,
data.table::data.table(
ShortName = "Gumb", ClassName = "Gumbel",
Type = "\u211D+", ValueSupport = "continuous",
VariateForm = "univariate",
Package = "extraDistr", Tags = "locscale"
)
)


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