27 lines
912 B
R
27 lines
912 B
R
# Normal approximation of the distribution function of the Esscher
|
|
# transform of a Laplace Motion
|
|
#
|
|
# Author: Francois Pelletier
|
|
#
|
|
# LGPL 3.0
|
|
###############################################################################
|
|
|
|
#' Normal approximation of the distribution function of the
|
|
#' Esscher transform of a Laplace Motion
|
|
#' @param x vector of quantiles
|
|
#' @param param Parameter vector
|
|
#' @param hEsscher Esscher transform parameter
|
|
#' @param eval.time Time of the process
|
|
#' @param type Choose between "mu" or "kappa" parametrization
|
|
#' @param log Logical for log-parameters
|
|
#' @param start Starting value of the process
|
|
|
|
#' @return Normal distribution function approximation
|
|
pnormapproxEsscherLM <- function(x,param,hEsscher=0,eval.time=1,type="mu",log=FALSE,start=0)
|
|
{
|
|
pnorm(x,start+eval.time*(mGAL(1,param,type,log)+hEsscher*cmGAL(2,param,type,log)),
|
|
sqrt(eval.time*cmGAL(2,param,type,log)))
|
|
}
|
|
|
|
|
|
|