SDistribution_StudentTNoncentral.R

# 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 field_alias
#' @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.",
    alias = "STNC",
    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 = "", Alias = "STNC"
  )
)