GeneralizedAsymmetricLaplace/R/psaddleapproxGAL.R

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# Saddlepoint approximation of the distribution function of the
# GAL distribution
#
# Author: Francois Pelletier
#
# LGPL 3.0
###############################################################################
#' Saddlepoint approximation of the distribution function of the
#' GAL distribution
#' @param x vector of quantiles
#' @param param Parameter vector
#' @param eval.time Time of the process
#' @param type Choose between "mu" or "kappa" parametrization
#' @param log Logical for log-parameters
#' @return Saddlepoint approximation of the distribution function
#' @export psaddleapproxGAL
#' @author Francois Pelletier
psaddleapproxGAL <- function(x,param,eval.time=1,type="mu",log=FALSE)
{
s <- saddlepointGAL(x,param,eval.time,type,log)
u <- s * sqrt(diffcgfGAL(s,2,param,eval.time,type,log))
w <- sign(s)*sqrt(2*(s*x-cgfGAL(s,param,type,log)))
if(x==mGAL(1,param,type,log))
{
return(1/2 + diffcgfGAL(0,3,param,eval.time,type,log)/
(6*sqrt(2*pi)*diffcgfGAL(0,2,param,eval.time,type,log)^(3/2)))
}
else
{
return(pnorm(w)+dnorm(w)*(1/w-1/u))
}
}