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

# nolint start
#' @name Triangular
#' @template SDist
#' @aliases SymmetricTriangular
#' @templateVar ClassName Triangular
#' @templateVar DistName Triangular
#' @templateVar uses to model population data where only the minimum, mode and maximum are known (or can be reliably estimated), also to model the sum of standard uniform distributions
#' @templateVar params lower limit, \eqn{a}, upper limit, \eqn{b}, and mode, \eqn{c},
#' @templateVar pdfpmf pdf
#' @templateVar pdfpmfeq \cr\cr \eqn{f(x) = 0, x < a} \cr \eqn{f(x) = 2(x-a)/((b-a)(c-a)), a \le x < c} \cr \eqn{f(x) = 2/(b-a), x = c} \cr \eqn{f(x) = 2(b-x)/((b-a)(b-c)), c < x \le b} \cr \eqn{f(x) = 0, x > b}
#' @templateVar paramsupport \eqn{a,b,c \ \in \ R}{a,b,c \epsilon R}, \eqn{a \le c \le b}
#' @templateVar distsupport \eqn{[a, b]}
#' @templateVar default lower = 0, upper = 1, mode = 0.5, symmetric = FALSE
# nolint end
#'
#' @template param_lower
#' @template param_upper
#' @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 continuous distributions
#' @family univariate distributions
#'
#' @export
Triangular <- R6Class("Triangular",
inherit = SDistribution, lock_objects = F,
public = list(
# Public fields
name = "Triangular",
short_name = "Tri",
description = "Triangular 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, if symmetric = TRUE then determined automatically.
#' @param symmetric (logical(1))\cr
#' If TRUE then the symmetric Triangular distribution is constructed, where the mode is
#' automatically calculated. Otherwise mode can be set manually. Cannot be changed after
#' construction.
#'
#' @examples
#' Triangular$new(lower = 2, upper = 5, symmetric = TRUE) #' Triangular$new(lower = 2, upper = 5, mode = 4, symmetric = FALSE)
#'
#' # You can view the type of Triangular distribution with $description #' Triangular$new(symmetric = TRUE)$description #' Triangular$new(symmetric = FALSE)$description initialize = function(lower = NULL, upper = NULL, mode = NULL, symmetric = NULL, decorators = NULL) { super$initialize(
decorators = decorators,
support = Interval$new(0, 1), type = Reals$new(),
symmetry = "sym"
)

if (self$getParameterValue("symmetric")) { private$.type <- "symmetric"
self$description <- "Symmetric Triangular Probability Distribution." } else { self$description <- "Triangular Probability Distribution."
}

invisible(self)
},

# 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$getParameterValue("lower")) + unlist(self$getParameterValue("upper")) +
unlist(self$getParameterValue("mode"))) / 3 }, #' @description #' The mode of a probability distribution is the point at which the pdf is #' a local maximum, a distribution can be unimodal (one maximum) or multimodal (several #' maxima). mode = function(which = "all") { unlist(self$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() {
lower <- unlist(self$getParameterValue("lower")) upper <- unlist(self$getParameterValue("upper"))
mode <- unlist(self$getParameterValue("mode")) median <- numeric(length(lower)) ind <- mode >= (lower + upper) / 2 median[ind] <- lower[ind] + sqrt((upper[ind] - lower[ind]) * (mode[ind] - lower[ind])) / sqrt(2) median[!ind] <- upper[!ind] - sqrt((upper[!ind] - lower[!ind]) * (upper[!ind] - mode[!ind])) / sqrt(2) return(median) }, #' @description #' The variance of a distribution is defined by the formula #' \deqn{var_X = E[X^2] - E[X]^2} #' where \eqn{E_X} is the expectation of distribution X. If the distribution is multivariate the #' covariance matrix is returned. #' @param ... Unused. variance = function(...) { lower <- unlist(self$getParameterValue("lower"))
upper <- unlist(self$getParameterValue("upper")) mode <- unlist(self$getParameterValue("mode"))

return((lower^2 + upper^2 + mode^2 - lower * upper - lower * mode - upper * mode) / 18)
},

#' @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(...) {
lower <- unlist(self$getParameterValue("lower")) upper <- unlist(self$getParameterValue("upper"))
mode <- unlist(self$getParameterValue("mode")) num <- sqrt(2) * (lower + upper - 2 * mode) * (2 * lower - upper - mode) * (lower - 2 * upper + mode) den <- 5 * (lower^2 + upper^2 + mode^2 - lower * upper - lower * mode - upper * mode)^1.5 return(num / den) }, #' @description #' The kurtosis of a distribution is defined by the fourth standardised moment, #' \deqn{k_X = E_X[\frac{x - \mu}{\sigma}^4]}{k_X = E_X[((x - \mu)/\sigma)^4]} #' where \eqn{E_X} is the expectation of distribution X, \eqn{\mu} is the mean of the #' distribution and \eqn{\sigma} is the standard deviation of the distribution. #' Excess Kurtosis is Kurtosis - 3. #' @param ... Unused. kurtosis = function(excess = TRUE, ...) { if (excess) { return(rep(-0.6, length(self$getParameterValue("lower"))))
} else {
return(rep(2.4, length(self$getParameterValue("lower")))) } }, #' @description #' The entropy of a (discrete) distribution is defined by #' \deqn{- \sum (f_X)log(f_X)} #' where \eqn{f_X} is the pdf of distribution X, with an integration analogue for #' continuous distributions. #' @param ... Unused. entropy = function(base = 2, ...) { 0.5 * log((unlist(self$getParameterValue("upper")) -
unlist(self$getParameterValue("lower"))) / 2, base) }, #' @description The moment generating function is defined by #' \deqn{mgf_X(t) = E_X[exp(xt)]} #' where X is the distribution and \eqn{E_X} is the expectation of the distribution X. #' @param ... Unused. mgf = function(t, ...) { lower <- self$getParameterValue("lower")
upper <- self$getParameterValue("upper") mode <- self$getParameterValue("mode")

num <- 2 * ((upper - mode) * exp(lower * t) - (upper - lower) * exp(mode * t) + (mode - lower)
* exp(upper * t))
den <- (upper - lower) * (mode - lower) * (upper - mode) * t^2

return(num / den)
},

#' @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, ...) {
lower <- self$getParameterValue("lower") upper <- self$getParameterValue("upper")
mode <- self$getParameterValue("mode") num <- -2 * ((upper - mode) * exp(1i * lower * t) - (upper - lower) * exp(1i * mode * t) + (mode - lower) * exp(1i * upper * t)) den <- (upper - lower) * (mode - lower) * (upper - mode) * t^2 return(num / den) }, #' @description The probability generating function is defined by #' \deqn{pgf_X(z) = E_X[exp(z^x)]} #' where X is the distribution and \eqn{E_X} is the expectation of the distribution X. #' @param ... Unused. pgf = function(z, ...) { return(NaN) } ), active = list( #' @field properties #' Returns distribution properties, including skewness type and symmetry. properties = function() { lower <- self$getParameterValue("lower")
upper <- self$getParameterValue("upper") prop <- super$properties
prop$support <- Interval$new(lower, upper)
if (private$.type != "symmetric") { if (self$getParameterValue("mode") == (lower + upper) / 2) {
prop$symmetry <- "symmetric" } else { prop$symmetry <- "asymmetric"
}
}

prop
}
),

private = list(
# dpqr
.pdf = function(x, log = FALSE) {
if (checkmate::testList(self$getParameterValue("lower"))) { mapply( extraDistr::dtriang, a = self$getParameterValue("lower"),
b = self$getParameterValue("upper"), c = self$getParameterValue("mode"),
MoreArgs = list(x = x, log = log)
)
} else {
x,
a = self$getParameterValue("lower"), b = self$getParameterValue("upper"),
c = self$getParameterValue("mode"), log = log ) } }, .cdf = function(x, lower.tail = TRUE, log.p = FALSE) { if (checkmate::testList(self$getParameterValue("lower"))) {
mapply(
a = self$getParameterValue("lower"), b = self$getParameterValue("upper"),
c = self$getParameterValue("mode"), MoreArgs = list( q = x, lower.tail = lower.tail, log.p = log.p ) ) } else { extraDistr::ptriang( x, a = self$getParameterValue("lower"),
b = self$getParameterValue("upper"), c = self$getParameterValue("mode"),
lower.tail = lower.tail,
log.p = log.p
)
}
},
.quantile = function(p, lower.tail = TRUE, log.p = FALSE) {
if (checkmate::testList(self$getParameterValue("lower"))) { mapply( extraDistr::qtriang, a = self$getParameterValue("lower"),
b = self$getParameterValue("upper"), c = self$getParameterValue("mode"),
MoreArgs = list(
p = p,
lower.tail = lower.tail,
log.p = log.p
)
)
} else {
p,
a = self$getParameterValue("lower"), b = self$getParameterValue("upper"),
c = self$getParameterValue("mode"), lower.tail = lower.tail, log.p = log.p ) } }, .rand = function(n) { if (checkmate::testList(self$getParameterValue("lower"))) {
mapply(
a = self$getParameterValue("lower"), b = self$getParameterValue("upper"),
c = self$getParameterValue("mode"), MoreArgs = list(n = n) ) } else { extraDistr::rtriang( n, a = self$getParameterValue("lower"),
b = self$getParameterValue("upper"), c = self$getParameterValue("mode")
)
}
},

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

.type = "asymmetric"
)
)

.distr6$distributions <- rbind( .distr6$distributions,
data.table::data.table(
ShortName = "Tri", ClassName = "Triangular",
Type = "\u211D", ValueSupport = "continuous",
VariateForm = "univariate",
Package = "extraDistr", Tags = "limits"
)
)


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