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ajout fonction caractéristique processus

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François Pelletier 2014-02-13 23:46:32 -05:00
parent 6572808b1b
commit 1e20a6a809
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46
R/cfLM.R Normal file
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# Characteristic function of Laplace motion
#
# Author: Francois Pelletier
#
# LGPL 3.0
###############################################################################
#' Characteristic function of Laplace motion
#' @param u Transform variate
#' @param param Parameter vector
#' @param 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 Characteristic function value at point u for given parameter vector
#'
#' @author Francois Pelletier
cfLM <- function(u,param,time,type="mu",log=FALSE,start=0)
{
testparGAL(param,type,log)
if(log)
{
if(type=="mu")
{
exp(1i*(start+exp(param[1])*time)*u)*(1+(exp(param[2])^2*u^2)/2-1i*exp(param[3])*u)^(-exp(param[4])*time)
}
if(type=="kappa")
{
exp(1i*(start+exp(param[1])*time)*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])*time)
}
}
else
{
if(type=="mu")
{
exp(1i*(start+param[1]*time)*u)*(1+(param[2]^2*u^2)/2-1i*param[3]*u)^(-param[4]*time)
}
if(type=="kappa")
{
exp(1i*(start+param[1]*time)*u)*(1+(param[2]^2*u^2)/2-(1/2*1i)*
param[2]*sqrt(2)*(1/param[3]-param[3])*u)^(-param[4]*time)
}
}
}

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R/startparamGAL.R Normal file
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# Method of moments with a twist for GAL distribution
#
# Author: Francois Pelletier
#
# LGPL 3.0
###############################################################################
#' Method of moments with a twist for GAL distribution
#'
#' Estimating the parameters of GAL distribution using a
#' twist on method of moments by Seneta (2004)
#' @param data Sample
#' @param type Choose between "mu" or "kappa" parametrization
#' @param log Logical for log-parameters
#' @return a vector of estimated parameters
#'
#' @author Francois Pelletier
startparamGAL <- function(data,type="mu",log=FALSE)
{
if(type=="mu")
{
mom <- c(mean(data),var(data),moments::skewness(data),moments::kurtosis(data)-3)
tau <- 3/(mom[4])
sigma <- sqrt(mom[2]/(2*tau))
mu <- mom[3]*sigma*sqrt(2/(3*(mom[4])))
theta <- mom[1]-tau*mu
if(log==FALSE)
c(theta,sigma,mu,tau)
else
log(c(theta,sigma,mu,tau))
}
if(type=="kappa")
{
changetypeGAL(startparamGAL(data,type="mu",log),type="kappa",target="mu",log)
}
}