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

# nolint start
#' @name Bernoulli
#' @template SDist
#'
#' @templateVar ClassName Bernoulli
#' @templateVar DistName Bernoulli
#' @templateVar uses to model a two-outcome scenario
#' @templateVar params probability of success, \eqn{p},
#' @templateVar pdfpmf pmf
#' @templateVar pdfpmfeq \deqn{f(x) = p, \ if \ x = 1}{f(x) = p, if x = 1}\deqn{f(x) = 1 - p, \ if \ x = 0}{f(x) = 1 - p, if x = 0}
#' @templateVar paramsupport probability \eqn{p}
#' @templateVar distsupport \eqn{\{0,1\}}{{0,1}}
#' @templateVar default 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 method_setParameterValue
#' @template param_decorators
#' @template field_packages
#'
#' @family discrete distributions
#' @family univariate distributions
#'
#' @export
Bernoulli <- R6Class("Bernoulli",
inherit = SDistribution, lock_objects = F,
public = list(
# Public fields
name = "Bernoulli",
short_name = "Bern",
description = "Bernoulli Probability Distribution.",
packages = "stats",

# Public methods
# initialize

#' @description
#' Creates a new instance of this [R6][R6::R6Class] class.
initialize = function(prob = NULL, qprob = NULL, decorators = NULL) {
super$initialize( decorators = decorators, support = Set$new(0, 1, 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("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") {
prob <- unlist(self$getParameterValue("prob")) if (length(prob) > 1) { if (which == "all") { stop("which cannot be 'all' when vectorising.") } else { mode <- numeric(length(prob)) mode[prob < 0.5] <- 0 mode[prob > 0.5] <- 1 mode[prob == 0.5] <- c(0, 1)[which] } } else { if (prob < 0.5) { mode <- 0 } else if (prob > 0.5) { mode <- 1 } else { if (which == "all") { mode <- c(0, 1) } else { mode <- c(0, 1)[which] } } } return(mode) }, #' @description #' Returns the median of the distribution. If an analytical expression is available #' returns distribution median, otherwise if symmetric returns self$mean, otherwise
#' returns self$quantile(0.5). median = function() { prob <- self$getParameterValue("prob")
median <- numeric(length(prob))
median[prob < 0.5] <- 0
median[prob > 0.5] <- 1
median[prob == 0.5] <- NaN

return(median)
},

#' @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$getParameterValue("prob")) * unlist(self$getParameterValue("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, ...) {
exkurtosis <- (1 - (6 * unlist(self$getParameterValue("prob")) * unlist(self$getParameterValue("qprob")))) / self$variance() if (excess) { return(exkurtosis) } else { return(exkurtosis + 3) } }, #' @description #' The entropy of a (discrete) distribution is defined by #' \deqn{- \sum (f_X)log(f_X)} #' where \eqn{f_X} is the pdf of distribution X, with an integration analogue for #' continuous distributions. #' @param ... Unused. entropy = function(base = 2, ...) { prob <- unlist(self$getParameterValue("prob"))
qprob <- 1 - prob

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

qprob + (prob * exp(1i * t))
},

#' @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, ...) {
prob <- self$getParameterValue("prob") qprob <- 1 - prob return(qprob + (prob * z)) } ), active = list( #' @field properties #' Returns distribution properties, including skewness type and symmetry. properties = function() { prop <- super$properties
prop$symmetry <- if (self$getParameterValue("prob") == 0.5) {
"symmetric"
} else {
"asymmetric"
}
prop
}
),

private = list(
# dpqr
.pdf = function(x, log = FALSE) {
prob <- self$getParameterValue("prob") call_C_base_pdqr( fun = "dbinom", x = x, args = list( size = 1, prob = unlist(prob) ), log = log, vec = test_list(prob) ) }, .cdf = function(x, lower.tail = TRUE, log.p = FALSE) { prob <- self$getParameterValue("prob")

call_C_base_pdqr(
fun = "pbinom",
x = x,
args = list(
size = 1,
prob = unlist(prob)
),
lower.tail = lower.tail,
log = log.p,
vec = test_list(prob)
)
},
.quantile = function(p, lower.tail = TRUE, log.p = FALSE) {
prob <- self$getParameterValue("prob") call_C_base_pdqr( fun = "qbinom", x = p, args = list( size = 1, prob = unlist(prob) ), lower.tail = lower.tail, log = log.p, vec = test_list(prob) ) }, .rand = function(n) { prob <- self$getParameterValue("prob")

call_C_base_pdqr(
fun = "rbinom",
x = n,
args = list(
size = 1,
prob = unlist(prob)
),
vec = test_list(prob)
)
},

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

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


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