R/drpexpow.R

In powdist: Power and Reversal Power Distributions

#' @title The Reversal Power Exponential Power Distribution
#' @name ReversalPowerExponentialPower
#' @description Density, distribution function,
#' quantile function and random generation for
#' the reversal power exponential power distribution with parameters mu, sigma, lambda and k.
#' @param x,q vector of quantiles.
#' @param p vector of probabilities.
#' @param n number of observations.
#' @param k,lambda shape parameters.
#' @param mu,sigma location and scale parameters.
#' @param log,log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are \eqn{P[X \le x ]}, otherwise, P[X > x].
#' @importFrom stats runif
#' @importFrom normalp dnormp
#' @importFrom normalp pnormp
#' @importFrom normalp qnormp
#' @details The reversal power exponential power distribution has density
#'
#' \eqn{f(x)=[\lambda/\sigma][f((x-\mu)/\sigma)][F((x-\mu)/\sigma)] ^(\lambda-1)},
#'
#' where \eqn{-\infty<\mu<\infty} is the location paramether, \eqn{\sigma^2>0} the scale parameter and \eqn{\lambda>0} and k the shape parameters.
#'
#' @examples
#' drpexpow(1, 1, 3, 4, 1)
#' @export
drpexpow <- function(x, lambda = 1, mu = 0, sigma = 1, k = 0, log = FALSE){
  d = (lambda/sigma) * dnormp( ((x-mu)/sigma), p = (2/(k+1)) ) * (pnormp( ((-x+mu)/sigma), p = (2/(k+1)) )**(lambda-1))
  if (log == TRUE) {
    d = log( (lambda/sigma) * dnormp( ((x-mu)/sigma), p = (2/(k+1)) ) * (pnormp( ((-x+mu)/sigma), p = (2/(k+1)) )**(lambda-1)) )
  }
  return(d)
}