R/non_central_t_distribution.R

In boostmath: 'R' Bindings for the 'Boost' Math Functions

#' @title Noncentral T Distribution Functions
#' @name non_central_t_distribution
#' @description Functions to compute the probability density function, cumulative distribution function, and quantile function for the Noncentral T distribution.
#' @param x quantile
#' @param df degrees of freedom (df > 0)
#' @param delta noncentrality parameter (delta >= 0)
#' @param p probability (0 <= p <= 1)
#' @return A single numeric value with the computed probability density, log-probability density, cumulative distribution, log-cumulative distribution, or quantile depending on the function called.
#' @seealso [Boost Documentation](https://www.boost.org/doc/libs/latest/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_t_dist.html) for more details on the mathematical background.
#' @examples
#' # Noncentral T distribution with 5 degrees of freedom and noncentrality parameter 1
#' dist <- non_central_t_distribution(5, 1)
#' # Apply generic functions
#' cdf(dist, 0.5)
#' logcdf(dist, 0.5)
#' pdf(dist, 0.5)
#' logpdf(dist, 0.5)
#' hazard(dist, 0.5)
#' chf(dist, 0.5)
#' mean(dist)
#' median(dist)
#' mode(dist)
#' range(dist)
#' quantile(dist, 0.2)
#' standard_deviation(dist)
#' support(dist)
#' variance(dist)
#' skewness(dist)
#' kurtosis(dist)
#' kurtosis_excess(dist)
#'
#' # Convenience functions
#' non_central_t_pdf(0, 5, 1)
#' non_central_t_lpdf(0, 5, 1)
#' non_central_t_cdf(0, 5, 1)
#' non_central_t_lcdf(0, 5, 1)
#' non_central_t_quantile(0.5, 5, 1)
NULL

#' @rdname non_central_t_distribution
#' @export
non_central_t_distribution <- function(df, delta) {
  structure(
    list(
      extptr = .Call(`non_central_t_init_`, df, delta),
      degrees_of_freedom = df,
      non_centrality = delta
    ),
    class = c("non_central_t_distribution", "boost_distribution")
  )
}

#' @rdname non_central_t_distribution
#' @export
non_central_t_pdf <- function(x, df, delta) {
  pdf(non_central_t_distribution(df, delta), x)
}

#' @rdname non_central_t_distribution
#' @export
non_central_t_lpdf <- function(x, df, delta) {
  logpdf(non_central_t_distribution(df, delta), x)
}

#' @rdname non_central_t_distribution
#' @export
non_central_t_cdf <- function(x, df, delta) {
  cdf(non_central_t_distribution(df, delta), x)
}

#' @rdname non_central_t_distribution
#' @export
non_central_t_lcdf <- function(x, df, delta) {
  logcdf(non_central_t_distribution(df, delta), x)
}

#' @rdname non_central_t_distribution
#' @export
non_central_t_quantile <- function(p, df, delta) {
  quantile(non_central_t_distribution(df, delta), p)
}