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#'
#' @title
#' PMF of Conditional Negative Binomial
#'
#'
#' @description
#' Probability mass function of the conditional distribution of X given X + Y = D,
#' where X ~ NB(r1, p1) and Y ~ NB(r2, p2) are drawn from two negative binomials,
#' independent of each other,
#' and assuming p1/p2 = lambda.
#'
#' @details
#' Need to specify full list of arguments, as default values have not been set.
#'
#' @author Xiaotian Zhu, \email{xiaotian.zhu.psualum@@gmail.com}
#'
#' @param x a nonempty vector of non-negative integer(s) <= D.
#' @param D a positive integer.
#' @param r1 a positive value.
#' @param r2 a positive value.
#' @param lambda a positive value.
#'
#' @return A vector providing values of Pr(X = x | X + Y = D) for each element in x.
#'
#' @examples
#' dcnb(980, 2000, 120, 90, 0.994)
#' dcnb(0:7, 7, 2, 0.4, 0.6)
#'
#' @seealso
#' \code{\link{pcnb}, \link{qcnb}, \link{rcnb}.}
#'
#'
#' @export
"dcnb" <- function(x, D, r1, r2, lambda){
if (missing(x) || missing(D) || missing(r1) || missing(r2) || missing(lambda))
stop("Need to specify a full set of arguments: x, D, r1, r2, lambda.")
if (!is.numeric(D) || length(D)!=1 || !D%%1==0 || D<=0)
stop("D needs to be a positive integer.")
if (!is.numeric(x) || length(x)<1 || any(!x%%1==0) || any(x<0) || any(x>D))
stop("x needs to be a nonempty vector of non-negative integer(s) <= D.")
if (!is.numeric(r1) || length(r1)!=1 || r1<=0)
stop("r1 needs to be a positive value.")
if (!is.numeric(r2) || length(r2)!=1 || r2<=0)
stop("r2 needs to be a positive value.")
if (!is.numeric(lambda) || length(lambda)!=1 || lambda<=0)
stop("lambda needs to be a positive value.")
return_value <- rep(0, length(x))
if (lambda <= 1) {
tmpbase <- lgamma(D + 1) - lgamma(r1) - lgamma(D + r2) -
log(Re(hypergeo::hypergeo(-D, r1, -D-r2+1, lambda)))
for (i in 1:length(x)){
lnvalue <- tmpbase - lgamma(x[i] + 1) - lgamma(D - x[i] + 1) +
lgamma(x[i] + r1) + lgamma(D - x[i] + r2) + log(lambda) * x[i]
return_value[i] <- exp(lnvalue)
}
}else{
return_value <- dcnb(D-x, D, r2, r1, 1/lambda)
}
return_value
}
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