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

# nolint start
#' @name Poisson
#' @template SDist
#' @templateVar ClassName Poisson
#' @templateVar DistName Poisson
#' @templateVar uses to model the number of events occurring in at a constant, independent rate over an interval of time or space
#' @templateVar params arrival rate, \eqn{\lambda},
#' @templateVar pdfpmf pmf
#' @templateVar pdfpmfeq \deqn{f(x) = (\lambda^x * exp(-\lambda))/x!}
#' @templateVar paramsupport \eqn{\lambda} > 0
#' @templateVar distsupport the Naturals
#' @templateVar default rate = 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_rate
#' @template field_packages
#'
#' @family continuous distributions
#' @family univariate distributions
#'
#' @export
Poisson <- R6Class("Poisson",
inherit = SDistribution, lock_objects = F,
public = list(
# Public fields
name = "Poisson",
short_name = "Pois",
description = "Poisson Probability Distribution.",
packages = "stats",

# Public methods
# initialize

#' @description
#' Creates a new instance of this [R6][R6::R6Class] class.
initialize = function(rate = NULL, decorators = NULL) {
super$initialize( decorators = decorators, support = Naturals$new(),
type = Naturals$new() ) }, # stats #' @description #' The arithmetic mean of a (discrete) probability distribution X is the expectation #' \deqn{E_X(X) = \sum p_X(x)*x} #' with an integration analogue for continuous distributions. #' @param ... Unused. mean = function(...) { unlist(self$getParameterValue("rate"))
},

#' @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(self$getParameterValue("rate"), floor) }, #' @description #' The variance of a distribution is defined by the formula #' \deqn{var_X = E[X^2] - E[X]^2} #' where \eqn{E_X} is the expectation of distribution X. If the distribution is multivariate the #' covariance matrix is returned. #' @param ... Unused. variance = function(...) { unlist(self$getParameterValue("rate"))
},

#' @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(...) {
unlist(self$getParameterValue("rate"))^(-0.5) # nolint }, #' @description #' The kurtosis of a distribution is defined by the fourth standardised moment, #' \deqn{k_X = E_X[\frac{x - \mu}{\sigma}^4]}{k_X = E_X[((x - \mu)/\sigma)^4]} #' where \eqn{E_X} is the expectation of distribution X, \eqn{\mu} is the mean of the #' distribution and \eqn{\sigma} is the standard deviation of the distribution. #' Excess Kurtosis is Kurtosis - 3. #' @param ... Unused. kurtosis = function(excess = TRUE, ...) { if (excess) { return(1 / unlist(self$getParameterValue("rate")))
} else {
return(1 / unlist(self$getParameterValue("rate")) + 3) } }, #' @description The moment generating function is defined by #' \deqn{mgf_X(t) = E_X[exp(xt)]} #' where X is the distribution and \eqn{E_X} is the expectation of the distribution X. #' @param ... Unused. mgf = function(t, ...) { return(exp(self$getParameterValue("rate") * (exp(t) - 1)))
},

#' @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, ...) {
return(exp(self$getParameterValue("rate") * (exp(1i * t) - 1))) }, #' @description The probability generating function is defined by #' \deqn{pgf_X(z) = E_X[exp(z^x)]} #' where X is the distribution and \eqn{E_X} is the expectation of the distribution X. #' @param ... Unused. pgf = function(z, ...) { return(exp(self$getParameterValue("rate") * (z - 1)))
}
),

private = list(
# dpqr
.pdf = function(x, log = FALSE) {
lambda <- self$getParameterValue("rate") call_C_base_pdqr( fun = "dpois", x = x, args = list(lambda = unlist(lambda)), log = log, vec = test_list(lambda) ) }, .cdf = function(x, lower.tail = TRUE, log.p = FALSE) { lambda <- self$getParameterValue("rate")
call_C_base_pdqr(
fun = "ppois",
x = x,
args = list(lambda = unlist(lambda)),
lower.tail = lower.tail,
log = log.p,
vec = test_list(lambda)
)
},
.quantile = function(p, lower.tail = TRUE, log.p = FALSE) {
lambda <- self$getParameterValue("rate") call_C_base_pdqr( fun = "qpois", x = p, args = list(lambda = unlist(lambda)), lower.tail = lower.tail, log = log.p, vec = test_list(lambda) ) }, .rand = function(n) { lambda <- self$getParameterValue("rate")
call_C_base_pdqr(
fun = "rpois",
x = n,
args = list(lambda = unlist(lambda)),
vec = test_list(lambda)
)
},

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

.distr6$distributions <- rbind( .distr6$distributions,
data.table::data.table(
ShortName = "Pois", ClassName = "Poisson",
Type = "\u21150", ValueSupport = "discrete",
VariateForm = "univariate",
Package = "stats", Tags = ""
)
)


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