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François Pelletier 2014-01-02 21:17:20 -05:00
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# Characteristic function of GAL distribution
#
# Author: Francois Pelletier
#
# LGPL 3.0
###############################################################################
#' Characteristic function of GAL distribution
#' @param u Transform variate
#' @param param Parameter vector
#' @param type Choose between "mu" or "kappa" parametrization
#' @param log Boolean for log-parameters
#' @return Characteristic function value at point u for given parameter vector
#'
#' @author Francois Pelletier
characteristicfn <- function(u,param,type="mu",log=FALSE)
{
if(log)
{
if(type=="mu")
{
exp(1i*exp(param[1])*u)*(1+(exp(param[2])^2*u^2)/2-1i*exp(param[3])*u)^(-exp(param[4]))
}
if(type=="kappa")
{
exp(1i*exp(param[1])*u)*(1+(exp(param[2])^2*u^2)/2-(1/2*1i)*
exp(param[2])*sqrt(2)*(1/exp(param[3])-exp(param[3]))*u)^(-exp(param[4]))
}
}
else
{
if(type=="mu")
{
exp(1i*param[1]*u)*(1+(param[2]^2*u^2)/2-1i*param[3]*u)^(-param[4])
}
if(type=="kappa")
{
exp(1i*param[1]*u)*(1+(param[2]^2*u^2)/2-(1/2*1i)*
param[2]*sqrt(2)*(1/param[3]-param[3])*u)^(-param[4])
}
}
}