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

# nolint start
#' @name Multinomial
#' @template SDist
#' @templateVar ClassName Multinomial
#' @templateVar DistName Multinomial
#' @templateVar uses to extend the binomial distribution to multiple variables, for example to model the rolls of multiple dice multiple times
#' @templateVar params number of trials, \eqn{n}, and probabilities of success, \eqn{p_1,...,p_k},
#' @templateVar pdfpmf pmf
#' @templateVar pdfpmfeq \deqn{f(x_1,x_2,\ldots,x_k) = n!/(x_1! * x_2! * \ldots * x_k!) * p_1^{x_1} * p_2^{x_2} * \ldots * p_k^{x_k}}
#' @templateVar paramsupport \eqn{p_i, i = {1,\ldots,k}; \sum p_i = 1} and \eqn{n = {1,2,\ldots}}
#' @templateVar distsupport \eqn{\sum x_i = N}
#' @templateVar omittedDPQR \code{cdf} and \code{quantile}
#' @templateVar default size = 10, probs = c(0.5, 0.5)
# 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 field_packages
#'
#' @family discrete distributions
#' @family multivariate distributions
#'
#' @export
Multinomial <- R6Class("Multinomial",
inherit = SDistribution, lock_objects = F,
public = list(
# Public fields
name = "Multinomial",
short_name = "Multinom",
description = "Multinomial Probability Distribution.",

# 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.
#' @param probs (numeric())\cr
#' Vector of probabilities. Automatically normalised by
#' probs = probs/sum(probs).
initialize = function(size = NULL, probs = NULL, decorators = NULL) {
super$initialize( decorators = decorators, support = setpower(Set$new(0:10, class = "integer"), 2),
type = setpower(Naturals$new(), "n") ) }, # stats #' @description #' The arithmetic mean of a (discrete) probability distribution X is the expectation #' \deqn{E_X(X) = \sum p_X(x)*x} #' with an integration analogue for continuous distributions. #' @param ... Unused. mean = function(...) { size <- self$getParameterValue("size")
probs <- self$getParameterValue("probs") if (checkmate::testList(probs)) { return(t(mapply( function(s, p) s * p, size, probs ))) } else { return(size * probs) } }, #' @description #' The variance of a distribution is defined by the formula #' \deqn{var_X = E[X^2] - E[X]^2} #' where \eqn{E_X} is the expectation of distribution X. If the distribution is multivariate the #' covariance matrix is returned. #' @param ... Unused. variance = function(...) { size <- self$getParameterValue("size")
probs <- self$getParameterValue("probs") if (checkmate::testList(probs)) { covar <- array(dim = c(length(probs[[1]]), length(probs[[1]]), length(probs))) for (i in seq_along(size)) { covar[, , i] <- probs[[i]] %*% t(probs[[i]]) * -size[[i]] diag(covar[, , i]) <- size[[i]] * probs[[i]] * (1 - probs[[i]]) } return(covar) } else { cov <- probs %*% t(probs) * -size diag(cov) <- size * probs * (1 - probs) return(cov) } }, #' @description #' The skewness of a distribution is defined by the third standardised moment, #' \deqn{sk_X = E_X[\frac{x - \mu}{\sigma}^3]}{sk_X = E_X[((x - \mu)/\sigma)^3]} #' where \eqn{E_X} is the expectation of distribution X, \eqn{\mu} is the mean of the #' distribution and \eqn{\sigma} is the standard deviation of the distribution. #' @param ... Unused. skewness = function(...) { rep(NaN, length(self$getParameterValue("size")))
},

#' @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, ...) {
rep(NaN, length(self$getParameterValue("size"))) }, #' @description #' The entropy of a (discrete) distribution is defined by #' \deqn{- \sum (f_X)log(f_X)} #' where \eqn{f_X} is the pdf of distribution X, with an integration analogue for #' continuous distributions. #' @param ... Unused. entropy = function(base = 2, ...) { size <- self$getParameterValue("size")
probs <- self$getParameterValue("probs") if (checkmate::testList(size)) { K <- length(probs[[1]]) ent <- c() for (k in seq_along(size)) { s1 <- -log(factorial(size[[k]]), base) s2 <- -size[[k]] * sum(probs[[k]] * log(probs[[k]], base)) s3 <- 0 for (i in 1:K) { for (j in 0:size[[k]]) { s3 <- s3 + (choose(size[[k]], j) * (probs[[k]][[i]]^j) * # nolint ((1 - probs[[k]][[i]])^(size[[k]] - j)) * (log(factorial(j), base))) # nolint } } ent <- c(ent, s1 + s2 + s3) } } else { K <- length(probs) s1 <- -log(factorial(size), base) s2 <- -size * sum(probs * log(probs, base)) s3 <- 0 for (i in 1:K) { for (j in 0:size) { s3 <- s3 + (choose(size, j) * (probs[[i]]^j) * ((1 - probs[[i]])^(size - j)) * (log(factorial(j), base))) # nolint } } ent <- s1 + s2 + s3 } return(ent) }, #' @description The moment generating function is defined by #' \deqn{mgf_X(t) = E_X[exp(xt)]} #' where X is the distribution and \eqn{E_X} is the expectation of the distribution X. #' @param ... Unused. mgf = function(t, ...) { probs <- self$getParameterValue("probs")
checkmate::assert(length(t) == length(probs))
return(sum(exp(t) * probs)^self$getParameterValue("size")) }, #' @description The characteristic function is defined by #' \deqn{cf_X(t) = E_X[exp(xti)]} #' where X is the distribution and \eqn{E_X} is the expectation of the distribution X. #' @param ... Unused. cf = function(t, ...) { probs <- self$getParameterValue("probs")
checkmate::assert(length(t) == length(probs))
return(sum(exp(1i * t) * probs)^self$getParameterValue("size")) }, #' @description The probability generating function is defined by #' \deqn{pgf_X(z) = E_X[exp(z^x)]} #' where X is the distribution and \eqn{E_X} is the expectation of the distribution X. #' @param ... Unused. pgf = function(z, ...) { probs <- self$getParameterValue("probs")
checkmate::assert(length(z) == length(probs))
return(sum(probs * z)^self$getParameterValue("size")) }, # optional setParameterValue #' @description #' Sets the value(s) of the given parameter(s). setParameterValue = function(..., lst = list(...), error = "warn", resolveConflicts = FALSE) { super$setParameterValue(lst = lst)
private$.variates <- length(self$getParameterValue("probs"))
invisible(self)
}
),

active = list(
#' @field properties
#' Returns distribution properties, including skewness type and symmetry.
properties = function() {
prop <- super$properties prop$support <- setpower(Set$new(0:self$getParameterValue("size"),
class = "integer"),
length(self$getParameterValue("probs"))) prop } ), private = list( # dpqr .pdf = function(x, log = FALSE) { probs <- self$getParameterValue("probs")

if (checkmate::testList(probs)) {
checkmate::assertMatrix(x, ncols = length(probs[[1]]))
size = self$getParameterValue("size"), prob = probs, MoreArgs = list(x = x, log = log) ) } else { checkmate::assertMatrix(x, ncols = length(probs)) extraDistr::dmnom(x, size = self$getParameterValue("size"),
prob = probs,
log = log
)
}
},
.rand = function(n) {
if (checkmate::testList(self$getParameterValue("probs"))) { mapply(extraDistr::rmnom, size = self$getParameterValue("size"),
prob = self$getParameterValue("probs"), MoreArgs = list(n = n), SIMPLIFY = FALSE ) } else { extraDistr::rmnom(n, size = self$getParameterValue("size"),
prob = self$getParameterValue("probs") ) } }, .variates = 2, # traits .traits = list(valueSupport = "discrete", variateForm = "multivariate"), .isCdf = FALSE, .isQuantile = FALSE ) ) .distr6$distributions <- rbind(
.distr6\$distributions,
data.table::data.table(
ShortName = "Multinom", ClassName = "Multinomial",
Type = "\u21150^K", ValueSupport = "discrete",
VariateForm = "multivariate",
Package = "extraDistr", Tags = "limits"
)
)


## Try the distr6 package in your browser

Any scripts or data that you put into this service are public.

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