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

# nolint start
#' @name Frechet
#' @template SDist
#' @templateVar ClassName Frechet
#' @templateVar DistName Frechet
#' @templateVar uses as a special case of the Generalised Extreme Value distribution
#' @templateVar params shape, \eqn{\alpha}, scale, \eqn{\beta}, and minimum, \eqn{\gamma},
#' @templateVar pdfpmf pdf
#' @templateVar pdfpmfeq \deqn{f(x) = (\alpha/\beta)((x-\gamma)/\beta)^{-1-\alpha}exp(-(x-\gamma)/\beta)^{-\alpha}}
#' @templateVar paramsupport \eqn{\alpha, \beta \epsilon R^+} and \eqn{\gamma \epsilon R}
#' @templateVar distsupport \eqn{x > \gamma}
#' @templateVar aka Inverse Weibull
#' @templateVar default shape = 1, scale = 1, minimum = 0
#' @aliases InverseWeibull
# nolint end
#' @template class_distribution
#' @template method_mode
#' @template method_entropy
#' @template method_kurtosis
#' @template method_pgf
#' @template method_mgfcf
#' @template method_setParameterValue
#' @template param_decorators
#' @template param_shape
#' @template param_scale
#' @template field_packages
#'
#' @family continuous distributions
#' @family univariate distributions
#'
#' @export
Frechet <- R6Class("Frechet",
inherit = SDistribution, lock_objects = F,
public = list(
# Public fields
name = "Frechet",
short_name = "Frec",
description = "Frechet Probability Distribution.",

# Public methods
# initialize

#' @description
#' Creates a new instance of this [R6][R6::R6Class] class.
#' @param minimum (numeric(1))\cr
#' Minimum of the distribution, defined on the Reals.
initialize = function(shape = NULL, scale = NULL, minimum = NULL, decorators = NULL) {
super$initialize( decorators = decorators, support = Interval$new(0, Inf, type = "()"),
type = Reals$new() ) }, # stats #' @description #' The arithmetic mean of a (discrete) probability distribution X is the expectation #' \deqn{E_X(X) = \sum p_X(x)*x} #' with an integration analogue for continuous distributions. #' @param ... Unused. mean = function(...) { shape <- unlist(self$getParameterValue("shape"))
minimum <- unlist(self$getParameterValue("minimum")) scale <- unlist(self$getParameterValue("scale"))
mean <- rep(Inf, length(shape))
mean[shape > 1] <- minimum[shape > 1] + scale[shape > 1] * gamma(1 - 1 / shape[shape > 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") {
shape <- unlist(self$getParameterValue("shape")) minimum <- unlist(self$getParameterValue("minimum"))
scale <- unlist(self$getParameterValue("scale")) return(minimum + scale * (shape / (1 + shape))^(1 / shape)) # nolint }, #' @description #' Returns the median of the distribution. If an analytical expression is available #' returns distribution median, otherwise if symmetric returns self$mean, otherwise
#' returns self$quantile(0.5). median = function() { m <- unlist(self$getParameterValue("minimum"))
s <- unlist(self$getParameterValue("scale")) a <- unlist(self$getParameterValue("shape"))

return(m + s / (log(2)^(1 / a))) # nolint
},

#' @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$getParameterValue("shape")) minimum <- unlist(self$getParameterValue("minimum"))
scale <- unlist(self$getParameterValue("scale")) var <- rep(Inf, length(shape)) var[shape > 2] <- scale[shape > 2]^2 * (gamma(1 - 2 / shape[shape > 2]) - gamma(1 - 1 / shape[shape > 2])^2) return(var) }, #' @description #' The skewness of a distribution is defined by the third standardised moment, #' \deqn{sk_X = E_X[\frac{x - \mu}{\sigma}^3]}{sk_X = E_X[((x - \mu)/\sigma)^3]} #' where \eqn{E_X} is the expectation of distribution X, \eqn{\mu} is the mean of the #' distribution and \eqn{\sigma} is the standard deviation of the distribution. #' @param ... Unused. skewness = function(...) { shape <- unlist(self$getParameterValue("shape"))
minimum <- unlist(self$getParameterValue("minimum")) scale <- unlist(self$getParameterValue("scale"))
skew <- rep(Inf, length(shape))
skew[shape > 3] <- (gamma(1 - 3 / shape[shape > 3]) - 3 *
gamma(1 - 2 / shape[shape > 3]) * gamma(1 - 1 / shape[shape > 3]) + 2
* gamma(1 - 1 / shape[shape > 3])^3) /
((gamma(1 - 2 / shape[shape > 3]) - gamma(1 - 1 / shape[shape > 3])^2)^(3 / 2)) # nolint
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$getParameterValue("shape")) minimum <- unlist(self$getParameterValue("minimum"))
scale <- unlist(self$getParameterValue("scale")) kur <- rep(Inf, length(shape)) kur[shape > 4] <- (gamma(1 - 4 / shape[shape > 4]) - 4 * gamma(1 - 3 / shape[shape > 4]) * gamma(1 - 1 / shape[shape > 4]) + 3 * gamma(1 - 2 / shape[shape > 4])^2) / ((gamma(1 - 2 / shape[shape > 4]) - gamma(1 - 1 / shape[shape > 4])^2)^2) if (excess) { return(kur - 6) } else { return(kur - 3) } }, #' @description #' The entropy of a (discrete) distribution is defined by #' \deqn{- \sum (f_X)log(f_X)} #' where \eqn{f_X} is the pdf of distribution X, with an integration analogue for #' continuous distributions. #' @param ... Unused. entropy = function(base = 2, ...) { shape <- unlist(self$getParameterValue("shape"))
minimum <- unlist(self$getParameterValue("minimum")) scale <- unlist(self$getParameterValue("scale"))

return(1 - digamma(1) / shape - digamma(1) + log(scale / shape, base))
},

#' @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)
}
),

active = list(
#' @field properties
#' Returns distribution properties, including skewness type and symmetry.
properties = function() {
prop <- super$properties prop$support <- Interval$new(self$getParameterValue("minimum"),
Inf, type = "()")
prop
}
),

private = list(
# dpqr
.pdf = function(x, log = FALSE) {
if (checkmate::testList(self$getParameterValue("shape"))) { mapply( extraDistr::dfrechet, lambda = self$getParameterValue("shape"),
mu = self$getParameterValue("minimum"), sigma = self$getParameterValue("scale"),
MoreArgs = list(x = x, log = log)
)
} else {
x,
lambda = self$getParameterValue("shape"), mu = self$getParameterValue("minimum"),
sigma = self$getParameterValue("scale"), log = log ) } }, .cdf = function(x, lower.tail = TRUE, log.p = FALSE) { if (checkmate::testList(self$getParameterValue("shape"))) {
mapply(
lambda = self$getParameterValue("shape"), mu = self$getParameterValue("minimum"),
sigma = self$getParameterValue("scale"), MoreArgs = list( q = x, lower.tail = lower.tail, log.p = log.p ) ) } else { extraDistr::pfrechet( x, lambda = self$getParameterValue("shape"),
mu = self$getParameterValue("minimum"), sigma = self$getParameterValue("scale"),
lower.tail = lower.tail,
log.p = log.p
)
}
},
.quantile = function(p, lower.tail = TRUE, log.p = FALSE) {
if (checkmate::testList(self$getParameterValue("shape"))) { mapply( extraDistr::qfrechet, lambda = self$getParameterValue("shape"),
mu = self$getParameterValue("minimum"), sigma = self$getParameterValue("scale"),
MoreArgs = list(
p = p,
lower.tail = lower.tail,
log.p = log.p
)
)
} else {
p,
lambda = self$getParameterValue("shape"), mu = self$getParameterValue("minimum"),
sigma = self$getParameterValue("scale"), lower.tail = lower.tail, log.p = log.p ) } }, .rand = function(n) { if (checkmate::testList(self$getParameterValue("shape"))) {
mapply(
lambda = self$getParameterValue("shape"), mu = self$getParameterValue("minimum"),
sigma = self$getParameterValue("scale"), MoreArgs = list(n = n) ) } else { extraDistr::rfrechet( n, lambda = self$getParameterValue("shape"),
mu = self$getParameterValue("minimum"), sigma = self$getParameterValue("scale")
)
}
},

# traits
.traits = list(valueSupport = "continuous", variateForm = "univariate")
)
)

.distr6$distributions <- rbind( .distr6$distributions,
data.table::data.table(
ShortName = "Frec", ClassName = "Frechet",
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.