R/order_betaexpg.R

In orders: Sampling from k-th Order Statistics of New Families of Distributions

#' Random Sampling of k-th Order Statistics from a Beta Exponential G Distribution
#'
#'\code{order_betaexpg} is used to obtain a random sample of the k-th order statistic from a Beta Exponential G Distribution.
#' @param size numeric, represents the size of the sample.
#' @param spec character, represents an specific G distribution. Possible values "norm", "exp","lnorm","chisq".
#' @param lambda numeric, represents the first shape parameter. Default value is 1.
#' @param a numeric, represents the second shape parameter. Default value is 1.
#' @param b numeric, represents the third 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 to compute the order statistic from.
#' @param p numeric, represents the 100p percentile for the distribution of the k-th order statistic. Default value is population median, p = 0.5.
#' @param alpha numeric, (1 - alpha) represents the confidence of an interval for the population percentile p of the distribution of the k-th order statistic. Default value is 0.05.
#' @param ... represents others parameters of the G distribution.
#' @return A list with a random sample of order statistics from a Beta Exponential G Distribution and the value of its join probability density function evaluated in the random sample
#' and an approximate (1 - alpha) confidence interval for the population percentile p of the distribution of the k-th order statistic.
#' @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
#' library(orders)
#' # A sample of size 10 of the 3-th order statistics from
#' # a Beta Exponential Exponential Distribution
#' order_betaexpg(10,"exp",1,1,1,k=3,50,alpha=0.02)
#' # A sample of size 10 of the 3-th order statistics from
#' # a Beta Exponential Normal Distribution
#' order_betaexpg(10,"norm",1,1,1,k=3,50)
#' # A sample of size 10 of the 3-th order statistics from
#' # a Beta Exponential Log-normal Distribution
#' order_betaexpg(10,"lnorm",1,1,1,k=3,50)
#' # A sample of size 10 of the 3-th order statistics from
#' # a Beta Exponential Chi-square Distribution
#' order_betaexpg(10,"chisq",1,1,1,k=3,50,df=3)
#' @importFrom Newdistns qbetaexpg dbetaexpg
#' @importFrom stats rbeta
#' @export order_betaexpg

order_betaexpg <- function(size,spec,lambda,a,b,k,n,p=0.5,alpha=0.05,...){
  sample       <- qbetaexpg(initial_order(size,k,n),spec,lambda,a,b,...)
  pdf          <- factorial(size)*cumprod(dbetaexpg(sample,spec,...))[size]
  log_pdf     <- sum(log(2:size)) + sum(log(dbetaexpg(sample,spec,...)))
  if(size>5){
    int_perc_est <- interval_percentile_est(p,size,sample,alpha)
    return(list(sample = sample,
                pdf = pdf,
                log_pdf = log_pdf,
                point_percentile_est = point_percentile_est(p,size,sample),
                confidence_percentile_est = int_perc_est[1:2],
                aprox_coverage_prob = int_perc_est[3]))
  }
  cat("---------------------------------------------------------------------------------------------\n")
  cat("We cannot report the confidence interval. The size of the sample is less or equal than five.\n")
  return(list(sample=sample,pdf=pdf))
}