Nothing
#' @export
dskellam.sp <- function(x, lambda1, lambda2=lambda1, log=FALSE){
# saddlepoint density (PMF) for Skellam distribution
terms=1
if (missing(x)|missing(lambda1)) stop("first 2 arguments are required")
s <- log(0.5*(x+sqrt(x^2+4*lambda1*lambda2))/lambda1)# the saddlepoint
K <- lambda1*(exp(s)-1)+lambda2*(exp(-s)-1) # CGF(s)
K2 <- lambda1*exp(s)+lambda2*exp(-s) # CGF''(s)
if (terms<1) {
ret <- exp(K-x*s)/sqrt(2*pi*K2) # saddlepoint density
} else {
c <- (1-((lambda1*exp(s)-lambda2*exp(-s))/K2)^2*5/3)/K2*0.125+1
ret <- exp(K-x*s)/sqrt(2*pi*K2)*(1+c)*0.5
}
ret
}
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