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

# nolint start
#' @name ChiSquaredNoncentral
#' @author Jordan Deenichin
#' @template SDist
#' @templateVar ClassName ChiSquaredNoncentral
#' @templateVar DistName Noncentral Chi-Squared
#' @templateVar uses to model the sum of independent squared Normal distributions and for confidence intervals
#' @templateVar params degrees of freedom, \eqn{\nu}, and location, \eqn{\lambda},
#' @templateVar pdfpmf pdf
#' @templateVar pdfpmfeq \deqn{f(x) = exp(-\lambda/2) \sum_{r=0}^\infty ((\lambda/2)^r/r!) (x^{(\nu+2r)/2-1}exp(-x/2))/(2^{(\nu+2r)/2}\Gamma((\nu+2r)/2))}
#' @templateVar paramsupport \eqn{\nu \ge 0}, \eqn{\lambda \ge 0}
#' @templateVar distsupport the Positive Reals
#' @templateVar default df = 1, location = 0
# 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 param_df
#' @template param_poslocation
#' @template field_packages
#'
#' @family continuous distributions
#' @family univariate distributions
#'
#' @export
ChiSquaredNoncentral <- R6Class("ChiSquaredNoncentral",
inherit = SDistribution, lock_objects = F,
public = list(
# Public fields
name = "ChiSquaredNoncentral",
short_name = "ChiSqNC",
description = "Non-central ChiSquared Probability Distribution.",
packages = "stats",

# Public methods
# initialize

#' @description
#' Creates a new instance of this [R6][R6::R6Class] class.
initialize = function(df = NULL, location = NULL, decorators = NULL) {
super$initialize( decorators = decorators, support = PosReals$new(zero = F),
type = PosReals$new(zero = TRUE) ) }, # stats #' @description #' The arithmetic mean of a (discrete) probability distribution X is the expectation #' \deqn{E_X(X) = \sum p_X(x)*x} #' with an integration analogue for continuous distributions. #' @param ... Unused. mean = function(...) { unlist(self$getParameterValue("df")) + unlist(self$getParameterValue("location")) }, #' @description #' The variance of a distribution is defined by the formula #' \deqn{var_X = E[X^2] - E[X]^2} #' where \eqn{E_X} is the expectation of distribution X. If the distribution is multivariate the #' covariance matrix is returned. #' @param ... Unused. variance = function(...) { 2 * (unlist(self$getParameterValue("df")) + 2 * unlist(self$getParameterValue("location"))) }, #' @description #' The skewness of a distribution is defined by the third standardised moment, #' \deqn{sk_X = E_X[\frac{x - \mu}{\sigma}^3]}{sk_X = E_X[((x - \mu)/\sigma)^3]} #' where \eqn{E_X} is the expectation of distribution X, \eqn{\mu} is the mean of the #' distribution and \eqn{\sigma} is the standard deviation of the distribution. #' @param ... Unused. skewness = function(...) { df <- unlist(self$getParameterValue("df"))
ncp <- unlist(self$getParameterValue("location")) skew <- rep(NaN, length(df)) skew[df + ncp != 0] <- ((2^(3 / 2)) * (df + 3 * ncp)) / ((df + 2 * ncp)^(3 / 2)) # nolint return(skew) }, #' @description #' The kurtosis of a distribution is defined by the fourth standardised moment, #' \deqn{k_X = E_X[\frac{x - \mu}{\sigma}^4]}{k_X = E_X[((x - \mu)/\sigma)^4]} #' where \eqn{E_X} is the expectation of distribution X, \eqn{\mu} is the mean of the #' distribution and \eqn{\sigma} is the standard deviation of the distribution. #' Excess Kurtosis is Kurtosis - 3. #' @param ... Unused. kurtosis = function(excess = TRUE, ...) { df <- unlist(self$getParameterValue("df"))
ncp <- unlist(self$getParameterValue("location")) kur <- rep(NaN, length(df)) kur[df + ncp != 0] <- (12 * (df + 4 * ncp)) / ((df + 2 * ncp)^2) if (excess) { return(kur) } else { return(kur + 3) } }, #' @description The moment generating function is defined by #' \deqn{mgf_X(t) = E_X[exp(xt)]} #' where X is the distribution and \eqn{E_X} is the expectation of the distribution X. #' @param ... Unused. mgf = function(t, ...) { if (t < 0.5) { return(exp(self$getParameterValue("location") * t / (1 - 2 * t)) / ((1 - 2 * t)^(self$getParameterValue("df") / 2))) # nolint } else { return(NaN) } }, #' @description The characteristic function is defined by #' \deqn{cf_X(t) = E_X[exp(xti)]} #' where X is the distribution and \eqn{E_X} is the expectation of the distribution X. #' @param ... Unused. cf = function(t, ...) { return(exp(self$getParameterValue("location") * 1i * t / (1 - 2i * t)) / ((1 - 2i * t)^(self$getParameterValue("df") / 2))) # nolint } ), active = list( #' @field properties #' Returns distribution properties, including skewness type and symmetry. properties = function() { prop <- super$properties
prop$support <- if (self$getParameterValue("df") <= 1) {
PosReals$new(zero = F) } else { PosReals$new(zero = T)
}
prop
}
),

private = list(
# dpqr
.pdf = function(x, log = FALSE) {
df <- self$getParameterValue("df") ncp <- self$getParameterValue("location")
call_C_base_pdqr(
fun = "dchisq",
x = x,
args = list(
df = unlist(df),
ncp = unlist(ncp)
),
log = log,
vec = test_list(df)
)
},
.cdf = function(x, lower.tail = TRUE, log.p = FALSE) {
df <- self$getParameterValue("df") ncp <- self$getParameterValue("location")
call_C_base_pdqr(
fun = "pchisq",
x = x,
args = list(
df = unlist(df),
ncp = unlist(ncp)
),
lower.tail = lower.tail,
log = log.p,
vec = test_list(df)
)
},
.quantile = function(p, lower.tail = TRUE, log.p = FALSE) {
df <- self$getParameterValue("df") ncp <- self$getParameterValue("location")
call_C_base_pdqr(
fun = "qchisq",
x = p,
args = list(
df = unlist(df),
ncp = unlist(ncp)
),
lower.tail = lower.tail,
log = log.p,
vec = test_list(df)
)
},
.rand = function(n) {
df <- self$getParameterValue("df") ncp <- self$getParameterValue("location")
call_C_base_pdqr(
fun = "rchisq",
x = n,
args = list(
df = unlist(df),
ncp = unlist(ncp)
),
vec = test_list(df)
)
},

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

.distr6$distributions <- rbind( .distr6$distributions,
data.table::data.table(
ShortName = "ChiSqNC", ClassName = "ChiSquaredNoncentral",
Type = "\u211D+", ValueSupport = "continuous",
VariateForm = "univariate",
Package = "stats", Tags = ""
)
)


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