ajout fonction caractéristique processus

R/cfLM.R

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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)
+		}
+	}
+}
+

R/startparamGAL.R

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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)
+	}
+}

man/cfLM.Rd

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+\name{cfLM}
+\alias{cfLM}
+\title{Characteristic function of Laplace motion}
+\usage{
+cfLM(u, param, time, type = "mu", log = FALSE, start = 0)
+}
+\arguments{
+  \item{u}{Transform variate}
+
+  \item{param}{Parameter vector}
+
+  \item{time}{Time of the process}
+
+  \item{type}{Choose between "mu" or "kappa"
+  parametrization}
+
+  \item{log}{Logical for log-parameters}
+
+  \item{start}{Starting value of the process}
+}
+\value{
+Characteristic function value at point u for given
+parameter vector
+}
+\description{
+Characteristic function of Laplace motion
+}
+\author{
+Francois Pelletier
+}
+

man/scaleGAL.Rd

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+\name{scaleGAL}
+\alias{scaleGAL}
+\title{Apply scale and location transform to the GAL distribution}
+\usage{
+scaleGAL(param, type = "kappa", location, scale)
+}
+\arguments{
+  \item{param}{Parameter vector}
+
+  \item{type}{Choose between "mu" or "kappa"
+  parametrization}
+
+  \item{location}{Location shift (unitary)}
+
+  \item{scale}{Scale shift (in standard deviations)}
+}
+\value{
+The transformed parameter vector
+}
+\description{
+Apply scale and location transform to the GAL distribution
+}
+\author{
+Francois Pelletier
+}
+

man/startparamGAL.Rd

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+\name{startparamGAL}
+\alias{startparamGAL}
+\title{Method of moments with a twist for GAL distribution}
+\usage{
+startparamGAL(data, type = "mu", log = FALSE)
+}
+\arguments{
+  \item{data}{Sample}
+
+  \item{type}{Choose between "mu" or "kappa"
+  parametrization}
+
+  \item{log}{Logical for log-parameters}
+}
+\value{
+a vector of estimated parameters
+}
+\description{
+Estimating the parameters of GAL distribution using a twist
+on method of moments by Seneta (2004)
+}
+\author{
+Francois Pelletier
+}
+