R/pk_order_glg.R

In sglg: Fitting Semi-Parametric Generalized log-Gamma Regression Models

#' Cumulative Probability Distribution of a K-th Order Statistic from a Generalized Log-gamma Distribution
#'
#'\code{pk_order_glg} is used to obtain the cumulative probability distribution of the k-th order statistic from a generalized log-gamma distribution.
#' @param x numeric, represents a real value.
#' @param mu numeric, represents the location parameter. Default value is 0.
#' @param sigma numeric, represents the scale parameter. Default value is 1.
#' @param lambda numeric, represents the shape parameter. Default value is 1.
#' @param k numeric, represents the K-th smallest value from a sample.
#' @param n numeric, represents the size of the sample of the generalized log-gamma distribution.
#' @return A list of values of the cumulative probability function of the k-th order statistic from a generalized log-gamma distribution.
#' @references Gentle, J, Computational Statistics, First Edition. Springer - Verlag, 2009.
#' @references Naradajah, S. and Rocha, R. (2016) Newdistns: An R Package for New Families of Distributions, Journal of Statistical Software.
#' @author Carlos Alberto Cardozo Delgado <cardozorpackages@gmail.com>.
#' @examples
#' # The cumulative probability distribution of 10-th order statistics at 0
#' # from a random sample of extreme value distribution with n=20.
#' pk_order_glg(0,0,1,1,k=10,n=20)
#' @importFrom stats rbeta
#' @export pk_order_glg

pk_order_glg <- function(x,mu=0,sigma=1,lambda=1,k,n){
  p <- rep(pglg(x,mu,sigma,lambda),n-k+1)
  cpdf    <-  sum(choose(n,k:n)*(p^(k:n))*((1 - p)^((n-k):0)))
  return(cpdf)
}