R/pmle_tpexp.R

In twopexp: The Two Parameter Exponential Distribution

#' Penalized maximum likelihood estimation for the two-parameter exponential dist.
#'
#' To estimate the location (or shift) and scale parameters for  the two-parameter exponential distribution
#' based on penalized maximum likelihood method. See detail in \code{source}
#'
#' @param x       vector of quantile (or a data set).
#' @param theta   location parameter, where \eqn{\theta > 0}.
#' @param beta    scale parameter, where \eqn{\beta > 0} and \eqn{rate=1/\beta}.
#'
#' @return the estimate three values for the two-parameter exponential dist. as follows:
#' \code{ptheta.hat}  gives the estimate location parameter,
#' \code{pbeta.hat}   gives the estimate scale parameter,
#' and \code{plamda.hat} gives the estimate the rate.
#'
#' @source Zheng, M. (2013). \emph{Penalized Maximum Likelihood Estimation of Two-Parameter Exponential Distributions [Master’s thesis]}.
#'  \url{https://scse.d.umn.edu/sites/scse.d.umn.edu/files/mengjie-thesis_masters-1.pdf}
#'
#' @export
#'
#' @examples
#' x1 <- c(25,43,53,65,76,86,95,115,132,150) # test a data set
#' pmle_tpexp(x1)
#' x2 <- c(20,15,10,25,35,30,40,70,50,60,90,100,80,5) # test a data set
#' pmle_tpexp(x2)
#'
pmle_tpexp <- function(x,theta=0,beta=1){
  xs <- sort(x)
  n <- length(xs)
  ptheta.hat <- (n*xs[1]-mean(xs))/(n-1)
  pbeta.hat <- (sum(xs)-n*xs[1])/(n-1)
  plamda.hat <- 1/pbeta.hat
  return(c(ptheta.hat,pbeta.hat,plamda.hat))
}