R/Gompertz.R

In kyoustat/T4mle: What the Package Does Using Title Case

#' (Weighted) MLE of Gompertz Distribution
#' 
#' Gompertz distribution is characterized by the following probability density function,
#' \deqn{f(x;\eta, b) = b\eta \exp(bx) \exp(\eta) \exp(-\eta e^{bx})}
#' where the domain is \eqn{x \in [0,\infty)} with two parameters \eqn{\eta > 0} for shape and \eqn{b > 0} for scale.
#' 
#' @param x a length-\eqn{n} vector of nonnegative real numbers.
#' @param weight a length-\eqn{n} weight vector. If set as \code{NULL}, it gives an equal weight, leading to standard MLE.
#' 
#' @return a named list containing (weighted) MLE of \describe{
#' \item{eta}{shape parameter \eqn{\eta}.}
#' \item{b}{scale parameter \eqn{b}.}
#' }
#' 
#' @examples
#' #  generate data from half normal
#' x = abs(stats::rnorm(100))
#' 
#' #  fit unweighted
#' Gompertz(x)
#' 
#' \dontrun{
#' # put random weights to see effect of weights
#' niter = 500
#' ndata = 200
#' 
#' # generate data as above and fit unweighted MLE
#' x    = abs(stats::rnorm(ndata))
#' xmle = Gompertz(x)
#' 
#' # iterate
#' vec.eta = rep(0,niter)
#' vec.b   = rep(0,niter)
#' for (i in 1:niter){
#'   # random weight
#'   ww = abs(stats::rnorm(ndata))
#' 
#'   MLE = Gompertz(x, weight=ww)
#'   vec.eta[i] = MLE$eta
#'   vec.b[i]   = MLE$b
#'   if ((i%%10) == 0){
#'     print(paste0(" iteration ",i,"/",niter," complete.."))
#'   }
#' }
#' 
#' # distribution of weighted estimates + standard MLE
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(1,2))
#' hist(vec.eta, main="shape 'eta'")
#' abline(v=xmle$eta, lwd=3, col="red")
#' hist(vec.b, main="scale 'b'")
#' abline(v=xmle$b, lwd=3, col="blue")
#' par(opar)
#' } 
#' 
#' @author Kisung You
#' @export
Gompertz <- function(x, weight=NULL){
  #############################################
  # Preprocessing
  x      = handle_cts_nonneg("Gompertz", x)
  nx     = length(x)
  weight = handle_weight("Gompertz", weight, nx)
  maceps = 10*.Machine$double.eps
  
  #############################################
  # Optimize : DEoptim
  fopt.Gompertz <- function(pars){
    # parameters
    eta = pars[1]
    b   = pars[2]
    # log-likelihood
    term1 = log(b) + log(eta)
    term2 = (b*x + eta)
    term3 = -eta*exp(b*x)
    loglkd = term1+term2+term3
    # return
    return(-sum(loglkd*weight))
  }
  mylower = c(maceps, maceps)
  myupper = c(1e+5, 1e+5)
  sol = DEoptim::DEoptim(fopt.Gompertz, lower=mylower, upper=myupper, 
                         control=DEoptim::DEoptim.control(trace=FALSE))$optim$bestmem
  
  #############################################
  # Return
  output = list()
  output$eta = as.double(sol[1])
  output$b   = as.double(sol[2])
  return(output)
}