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

# nolint start
#' @name StudentTNoncentral
#' @author Jordan Deenichin
#' @template SDist
#' @templateVar ClassName StudentTNoncentral
#' @templateVar DistName Noncentral Student's T
#' @templateVar uses to estimate the mean of populations with unknown variance from a small sample size, as well as in t-testing for difference of means and regression analysis
#' @templateVar params degrees of freedom, \eqn{\nu} and location, \eqn{\lambda},
#' @templateVar pdfpmf pdf
#' @templateVar pdfpmfeq \deqn{f(x) = (\nu^{\nu/2}exp(-(\nu\lambda^2)/(2(x^2+\nu)))/(\sqrt{\pi} \Gamma(\nu/2) 2^{(\nu-1)/2} (x^2+\nu)^{(\nu+1)/2}))\int_{0}^{\infty} y^\nu exp(-1/2(y-x\lambda/\sqrt{x^2+\nu})^2)}
#' @templateVar paramsupport \eqn{\nu > 0}, \eqn{\lambda \epsilon R}
#' @templateVar distsupport the 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 param_decorators
#' @template param_df
#' @template param_location
#' @template field_packages
#'
#' @family continuous distributions
#' @family univariate distributions
#'
#' @export
StudentTNoncentral <- R6Class("StudentTNoncentral",
inherit = SDistribution, lock_objects = F,
public = list(
# Public fields
name = "StudentTNoncentral",
short_name = "TNS",
description = "Non-central Student's T 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$initialize( decorators = decorators, support = Reals$new(),
symmetry = "sym",
type = Reals$new() ) }, # stats #' @description #' The arithmetic mean of a (discrete) probability distribution X is the expectation #' \deqn{E_X(X) = \sum p_X(x)*x} #' with an integration analogue for continuous distributions. #' @param ... Unused. mean = function(...) { df <- unlist(self$getParameterValue("df"))
location <- unlist(self$getParameterValue("location")) mean <- rep(NaN, length(location)) mean[df > 1] <- location[df > 1] * sqrt(df[df > 1] / 2) * gamma((df[df > 1] - 1) / 2) / gamma(df[df > 1] / 2) return(mean) }, #' @description #' The variance of a distribution is defined by the formula #' \deqn{var_X = E[X^2] - E[X]^2} #' where \eqn{E_X} is the expectation of distribution X. If the distribution is multivariate the #' covariance matrix is returned. #' @param ... Unused. variance = function(...) { df <- unlist(self$getParameterValue("df"))
mu <- unlist(self$getParameterValue("location")) var <- rep(NaN, length(mu)) var[df > 2] <- df[df > 2] * (1 + mu[df > 2]^2) / (df[df > 2] - 2) - (mu[df > 2]^2 * df[df > 2] / 2) * (gamma((df[df > 2] - 1) / 2) / gamma(df[df > 2] / 2))^2 return(var) } ), private = list( # dpqr .pdf = function(x, log = FALSE) { df <- self$getParameterValue("df")
ncp <- self$getParameterValue("location") call_C_base_pdqr( fun = "dt", x = x, args = list( df = unlist(df), ncp = unlist(ncp) ), log = log, vec = test_list(df) ) }, .cdf = function(x, lower.tail = TRUE, log.p = FALSE) { df <- self$getParameterValue("df")
ncp <- self$getParameterValue("location") call_C_base_pdqr( fun = "pt", x = x, args = list( df = unlist(df), ncp = unlist(ncp) ), lower.tail = lower.tail, log = log.p, vec = test_list(df) ) }, .quantile = function(p, lower.tail = TRUE, log.p = FALSE) { df <- self$getParameterValue("df")
ncp <- self$getParameterValue("location") call_C_base_pdqr( fun = "qt", x = p, args = list( df = unlist(df), ncp = unlist(ncp) ), lower.tail = lower.tail, log = log.p, vec = test_list(df) ) }, .rand = function(n) { df <- self$getParameterValue("df")
ncp <- self$getParameterValue("location") call_C_base_pdqr( fun = "rt", x = n, args = list( df = unlist(df), ncp = unlist(ncp) ), vec = test_list(df) ) }, # traits .traits = list(valueSupport = "continuous", variateForm = "univariate") ) ) .distr6$distributions <- rbind(
.distr6\$distributions,
data.table::data.table(
ShortName = "TNC", ClassName = "StudentTNoncentral",
Type = "\u211D", ValueSupport = "continuous",
VariateForm = "univariate",
Package = "stats", Tags = ""
)
)


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