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

#' @name Rayleigh
#' @template SDist
#' @templateVar ClassName Rayleigh
#' @templateVar DistName Rayleigh
#' @templateVar uses to model random complex numbers.
#' @templateVar params mode (or scale), \eqn{\alpha},
#' @templateVar pdfpmf pdf
#' @templateVar pdfpmfeq \deqn{f(x) = x/\alpha^2 exp(-x^2/(2\alpha^2))}
#' @templateVar paramsupport \eqn{\alpha > 0}
#' @templateVar distsupport \eqn{[0, \infty)}
#' @templateVar default mode = 1
#'
#' @template class_distribution
#' @template method_mode
#' @template method_entropy
#' @template method_kurtosis
#' @template method_pgf
#' @template method_mgfcf
#' @template param_decorators
#' @template field_packages
#'
#' @family continuous distributions
#' @family univariate distributions
#'
#' @export
Rayleigh <- R6Class("Rayleigh",
inherit = SDistribution, lock_objects = F,
public = list(
# Public fields
name = "Rayleigh",
short_name = "Rayl",
description = "Rayleigh Probability Distribution.",

# Public methods
# initialize

#' @description
#' Creates a new instance of this [R6][R6::R6Class] class.
#' @param mode (numeric(1))\cr
#' Mode of the distribution, defined on the positive Reals. Scale parameter.
initialize = function(mode = NULL, decorators = NULL) {
super$initialize( decorators = decorators, support = PosReals$new(zero = T),
type = PosReals$new(zero = T) ) }, # stats #' @description #' The arithmetic mean of a (discrete) probability distribution X is the expectation #' \deqn{E_X(X) = \sum p_X(x)*x} #' with an integration analogue for continuous distributions. #' @param ... Unused. mean = function(...) { unlist(self$getParameterValue("mode")) * sqrt(pi / 2)
},

#' @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$getParameterValue("mode")) }, #' @description #' Returns the median of the distribution. If an analytical expression is available #' returns distribution median, otherwise if symmetric returns self$mean, otherwise
#' returns self$quantile(0.5). median = function() { unlist(self$getParameterValue("mode")) * sqrt(2 * 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(...) {
(4 - pi) / 2 * unlist(self$getParameterValue("mode"))^2 }, #' @description #' The skewness of a distribution is defined by the third standardised moment, #' \deqn{sk_X = E_X[\frac{x - \mu}{\sigma}^3]}{sk_X = E_X[((x - \mu)/\sigma)^3]} #' where \eqn{E_X} is the expectation of distribution X, \eqn{\mu} is the mean of the #' distribution and \eqn{\sigma} is the standard deviation of the distribution. #' @param ... Unused. skewness = function(...) { rep((2 * sqrt(pi) * (pi - 3)) / ((4 - pi)^(3 / 2)), length(self$getParameterValue("mode"))) # nolint
},

#' @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(-(6 * pi^2 - 24 * pi + 16) / (4 - pi)^2, length(self$getParameterValue("mode")))) # nolint } else { return(rep(-(6 * pi^2 - 24 * pi + 16) / (4 - pi)^2 + 3, # nolint length(self$getParameterValue("mode"))))
}
},

#' @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, ...) {
1 + log(unlist(self$getParameterValue("mode")) / sqrt(2), base) - digamma(1) / 2 }, #' @description The probability generating function is defined by #' \deqn{pgf_X(z) = E_X[exp(z^x)]} #' where X is the distribution and \eqn{E_X} is the expectation of the distribution X. #' @param ... Unused. pgf = function(z, ...) { return(NaN) } ), private = list( # dpqr .pdf = function(x, log = FALSE) { if (checkmate::testList(self$getParameterValue("mode"))) {
mapply(
sigma = self$getParameterValue("mode"), MoreArgs = list(x = x, log = log) ) } else { extraDistr::drayleigh( x, sigma = self$getParameterValue("mode"),
log = log
)
}
},
.cdf = function(x, lower.tail = TRUE, log.p = FALSE) {
if (checkmate::testList(self$getParameterValue("mode"))) { mapply( extraDistr::prayleigh, sigma = self$getParameterValue("mode"),
MoreArgs = list(
q = x,
lower.tail = lower.tail,
log.p = log.p
)
)
} else {
x,
sigma = self$getParameterValue("mode"), lower.tail = lower.tail, log.p = log.p ) } }, .quantile = function(p, lower.tail = TRUE, log.p = FALSE) { if (checkmate::testList(self$getParameterValue("mode"))) {
mapply(
sigma = self$getParameterValue("mode"), MoreArgs = list( p = p, lower.tail = lower.tail, log.p = log.p ) ) } else { extraDistr::qrayleigh( p, sigma = self$getParameterValue("mode"),
lower.tail = lower.tail,
log.p = log.p
)
}
},
.rand = function(n) {
if (checkmate::testList(self$getParameterValue("mode"))) { mapply( extraDistr::rrayleigh, sigma = self$getParameterValue("mode"),
MoreArgs = list(n = n)
)
} else {
n,
sigma = self$getParameterValue("mode") ) } }, # traits .traits = list(valueSupport = "continuous", variateForm = "univariate") ) ) .distr6$distributions <- rbind(
.distr6\$distributions,
data.table::data.table(
ShortName = "Rayl", ClassName = "Rayleigh",
Type = "\u211D+", ValueSupport = "continuous",
VariateForm = "univariate",
Package = "extraDistr", Tags = "scale"
)
)

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