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#' The probability mass function (PMF) for Discrete Transmuted Generalized Inverse Weibull (DTGIW) distribution.
#'
#' This function calculated the PMF of the DTGIW distribution.
#'
#' The PMF of the DTGIW distribution is shown in Theorem 1 based on the research paper in references.
#'
#' @param x vector of quantiles.
#' @param alpha shape parameter#1.
#' @param beta scale parameter.
#' @param lambda shape pameter#2.
#' @param theta the transmuted parameter.
#' @param log logical(TRUE or FALSE); if log=FALSE, then return the PMF; if log=TRUE, then return the natural logarithms of the PMF.
#' @references Atchanut Rattanalertnusorn and Sirinapa Aryuyuen (2021).
#' The zero-truncated discrete transmuted generalized inverse Weibull distribution and its applications,
#' Songklanakarin Journal of Science and Technology (SJST), Volume 43 No.4 (July - August 2021), pp. 1140 - 1151. DOI: 10.14456/sjst-psu.2021.149
#'
#' @return the PMF of DTGIW distribution
#' @export
#'
#' @examples
#' x <- c(0:10)
#' dDTGIW(x,3.45,0.7,1.05,0)
dDTGIW <- function(x,alpha,beta,lambda,theta,log=FALSE){
m<- length(x)
if (m>=1){
p <- c()
for(j in 1:m){
A <- exp(-lambda*((beta*x[j]+beta)^(-alpha)))
B <- exp(-lambda*((beta*x[j])^(-alpha)))
C <- exp(-2*lambda*((beta*x[j]+beta)^(-alpha)))
D <- exp(-2*lambda*((beta*x[j])^(-alpha)))
p[j]<- (1+theta)*(A-B)-theta*(C-D)
}
if(log==FALSE){
return(p)
}else{
return(log(p))
}
}else{
errmsg <- c("Error in first argument x, that is NULL or empty quantile")
return(errmsg)
}
}#end dDTGIW
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