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

# nolint start
#' @name Binomial
#' @template SDist
#' @templateVar ClassName Binomial
#' @templateVar DistName Binomial
#' @templateVar uses to model the number of successes out of a number of independent trials
#' @templateVar params number of trials, n, and probability of success, p,
#' @templateVar pdfpmf pmf
#' @templateVar pdfpmfeq \deqn{f(x) = C(n, x)p^x(1-p)^{n-x}}
#' @templateVar paramsupport \eqn{n = 0,1,2,\ldots} and probability \eqn{p}, where \eqn{C(a,b)} is the combination (or binomial coefficient) function
#' @templateVar distsupport \eqn{{0, 1,...,n}}
#' @templateVar default size = 10, prob = 0.5
# nolint end
#' @template param_prob
#' @template param_qprob
#' @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 discrete distributions
#' @family univariate distributions
#'
#' @export
Binomial <- R6Class("Binomial",
inherit = SDistribution, lock_objects = F,
public = list(
# Public fields
name = "Binomial",
short_name = "Binom",
description = "Binomial Probability Distribution.",
packages = "stats",

# Public methods
# initialize

#' @description
#' Creates a new instance of this [R6][R6::R6Class] class.
#' @param size (integer(1))\cr
#' Number of trials, defined on the positive Naturals.
initialize = function(size = NULL, prob = NULL, qprob = NULL, decorators = NULL) {
super$initialize( decorators = decorators, support = Set$new(0:10, class = "integer"),
type = Naturals$new(), symmetry = "sym" ) }, # stats #' @description #' The arithmetic mean of a (discrete) probability distribution X is the expectation #' \deqn{E_X(X) = \sum p_X(x)*x} #' with an integration analogue for continuous distributions. #' @param ... Unused. mean = function(...) { unlist(self$getParameterValue("size")) * unlist(self$getParameterValue("prob")) }, #' @description #' The mode of a probability distribution is the point at which the pdf is #' a local maximum, a distribution can be unimodal (one maximum) or multimodal (several #' maxima). mode = function(which = "all") { sapply((unlist(self$getParameterValue("size")) + 1) *
unlist(self$getParameterValue("prob")), floor) }, #' @description #' The variance of a distribution is defined by the formula #' \deqn{var_X = E[X^2] - E[X]^2} #' where \eqn{E_X} is the expectation of distribution X. If the distribution is multivariate the #' covariance matrix is returned. #' @param ... Unused. variance = function(...) { prob <- unlist(self$getParameterValue("prob"))
qprob <- 1 - prob

return(unlist(self$getParameterValue("size")) * prob * qprob) }, #' @description #' The skewness of a distribution is defined by the third standardised moment, #' \deqn{sk_X = E_X[\frac{x - \mu}{\sigma}^3]}{sk_X = E_X[((x - \mu)/\sigma)^3]} #' where \eqn{E_X} is the expectation of distribution X, \eqn{\mu} is the mean of the #' distribution and \eqn{\sigma} is the standard deviation of the distribution. #' @param ... Unused. skewness = function(...) { (1 - (2 * unlist(self$getParameterValue("prob")))) / self$stdev() }, #' @description #' The kurtosis of a distribution is defined by the fourth standardised moment, #' \deqn{k_X = E_X[\frac{x - \mu}{\sigma}^4]}{k_X = E_X[((x - \mu)/\sigma)^4]} #' where \eqn{E_X} is the expectation of distribution X, \eqn{\mu} is the mean of the #' distribution and \eqn{\sigma} is the standard deviation of the distribution. #' Excess Kurtosis is Kurtosis - 3. #' @param ... Unused. kurtosis = function(excess = TRUE, ...) { prob <- unlist(self$getParameterValue("prob"))
exkurtosis <- (1 - (6 * prob * (1 - prob))) / self$variance() if (excess) { return(exkurtosis) } else { return(exkurtosis + 3) } }, #' @description #' The entropy of a (discrete) distribution is defined by #' \deqn{- \sum (f_X)log(f_X)} #' where \eqn{f_X} is the pdf of distribution X, with an integration analogue for #' continuous distributions. #' @param ... Unused. entropy = function(base = 2, ...) { 0.5 * log(2 * pi * exp(1) * self$variance(), base)
},

#' @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, ...) {
(self$getParameterValue("qprob") + (self$getParameterValue("prob") * exp(t)))^self$getParameterValue("size") }, #' @description The characteristic function is defined by #' \deqn{cf_X(t) = E_X[exp(xti)]} #' where X is the distribution and \eqn{E_X} is the expectation of the distribution X. #' @param ... Unused. cf = function(t, ...) { (self$getParameterValue("qprob") +
(self$getParameterValue("prob") * exp((0 + 1i) * t)))^self$getParameterValue("size")
},

#' @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, ...) {
(self$getParameterValue("qprob") + (self$getParameterValue("prob") * z))^self$getParameterValue("size") } ), active = list( #' @field properties #' Returns distribution properties, including skewness type and symmetry. properties = function() { prop <- super$properties
prop$support <- Set$new(0:self$getParameterValue("size"), class = "integer") prop$symmetry <- if (self$getParameterValue("prob") == 0.5) { "symmetric" } else { "asymmetric" } prop } ), private = list( # dpqr .pdf = function(x, log = FALSE) { size <- self$getParameterValue("size")
prob <- self$getParameterValue("prob") call_C_base_pdqr( fun = "dbinom", x = x, args = list( size = unlist(size), prob = unlist(prob) ), log = log, vec = test_list(size) ) }, .cdf = function(x, lower.tail = TRUE, log.p = FALSE) { size <- self$getParameterValue("size")
prob <- self$getParameterValue("prob") call_C_base_pdqr( fun = "pbinom", x = x, args = list( size = unlist(size), prob = unlist(prob) ), lower.tail = lower.tail, log = log.p, vec = test_list(size) ) }, .quantile = function(p, lower.tail = TRUE, log.p = FALSE) { size <- self$getParameterValue("size")
prob <- self$getParameterValue("prob") call_C_base_pdqr( fun = "qbinom", x = p, args = list( size = unlist(size), prob = unlist(prob) ), lower.tail = lower.tail, log = log.p, vec = test_list(size) ) }, .rand = function(n) { size <- self$getParameterValue("size")
prob <- self$getParameterValue("prob") call_C_base_pdqr( fun = "rbinom", x = n, args = list( size = unlist(size), prob = unlist(prob) ), vec = test_list(size) ) }, # traits .traits = list(valueSupport = "discrete", variateForm = "univariate") ) ) .distr6$distributions <- rbind(
.distr6\$distributions,
data.table::data.table(
ShortName = "Binom", ClassName = "Binomial",
Type = "\u21150", ValueSupport = "discrete",
VariateForm = "univariate",
Package = "stats", Tags = "limits"
)
)


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