40 lines
No EOL
1.1 KiB
R
40 lines
No EOL
1.1 KiB
R
# Moment generating function of GAL distribution
|
|
#
|
|
# Author: Francois Pelletier
|
|
#
|
|
# LGPL 3.0
|
|
###############################################################################
|
|
|
|
#' Moment generating function of GAL distribution
|
|
#' @param u Transform variate
|
|
#' @param param Parameter vector
|
|
#' @param type Choose between "mu" or "kappa" parametrization
|
|
#' @param log Logical for log-parameters
|
|
#' @return Moment generating function value at point u for given parameter vector
|
|
#'
|
|
#' @author Francois Pelletier
|
|
mgfGAL <- function(u,param,type="mu",log=FALSE)
|
|
{
|
|
if(log)
|
|
{
|
|
if(type=="mu")
|
|
{
|
|
exp(exp(param[1])*u)*(1-(1/2)*exp(param[2])^2*u^2-exp(param[3])*u)^(-exp(param[4]))
|
|
}
|
|
if(type=="kappa")
|
|
{
|
|
exp(exp(param[1])*u)*((exp(param[2])^2*u^2)/2+(exp(param[3])*exp(param[2])*u)/sqrt(2)-(exp(param[2])*u)/(sqrt(2)*exp(param[3]))+1)^(-exp(param[4]))
|
|
}
|
|
}
|
|
else
|
|
{
|
|
if(type=="mu")
|
|
{
|
|
exp(param[1]*u)*(1-(1/2)*param[2]^2*u^2-param[3]*u)^(-param[4])
|
|
}
|
|
if(type=="kappa")
|
|
{
|
|
exp(param[1]*u)*((param[2]^2*u^2)/2+(param[3]*param[2]*u)/sqrt(2)-(param[2]*u)/(sqrt(2)*param[3])+1)^(-param[4])
|
|
}
|
|
}
|
|
} |