Ajout de plusieurs fonctions concernant l'approximation de la

distribution GAL

man/cfLM.Rd

@@ -2,7 +2,7 @@
 \alias{cfLM}
 \title{Characteristic function of Laplace motion}
 \usage{
-cfLM(u, param, time, type = "mu", log = FALSE, start = 0)
+cfLM(u, param, time = 1, type = "mu", log = FALSE, start = 0)
 }
 \arguments{
   \item{u}{Transform variate}

man/cgfEsscherGAL.Rd

@@ -0,0 +1,31 @@
+\name{cgfEsscherGAL}
+\alias{cgfEsscherGAL}
+\title{Cumulant generating function of the
+Esscher transform with parameter 1 of GAL distribution}
+\usage{
+cgfEsscherGAL(u, param, eval.time = 1, type = "mu", log = FALSE)
+}
+\arguments{
+  \item{u}{Transform variate}
+
+  \item{param}{Parameter vector}
+
+  \item{eval.time}{Time of the process}
+
+  \item{type}{Choose between "mu" or "kappa"
+  parametrization}
+
+  \item{log}{Logical for log-parameters}
+}
+\value{
+Cumulant generating function value at point u for given
+parameter vector
+}
+\description{
+Cumulant generating function of the Esscher transform with
+parameter 1 of GAL distribution
+}
+\author{
+Francois Pelletier
+}
+

man/diffcgfEsscherGAL.Rd

@@ -0,0 +1,34 @@
+\name{diffcgfEsscherGAL}
+\alias{diffcgfEsscherGAL}
+\title{Differenciation of the cumulant generating fonction of the
+Esscher transform with parameter 1 of the GAL distribution}
+\usage{
+diffcgfEsscherGAL(u, order, param, eval.time = 1, type = "mu",
+  log = FALSE)
+}
+\arguments{
+  \item{u}{Transform variate point of evaluation}
+
+  \item{order}{Order of differenciation}
+
+  \item{param}{Parameters of the GAL distirbution}
+
+  \item{eval.time}{Time of the process}
+
+  \item{type}{Choose between "mu" or "kappa"
+  parametrization}
+
+  \item{log}{Logical for log-parameters}
+}
+\value{
+The value of the derivative at the transform variate point
+of evaluation
+}
+\description{
+Differenciation of the cumulant generating fonction of the
+Esscher transform with parameter 1 of the GAL distribution
+}
+\author{
+Francois Pelletier
+}
+

man/diffcgfGAL.Rd

@@ -0,0 +1,33 @@
+\name{diffcgfGAL}
+\alias{diffcgfGAL}
+\title{Differenciation of the cumulant generating fonction of the
+GAL distribution}
+\usage{
+diffcgfGAL(u, order, param, eval.time = 1, type = "mu", log = FALSE)
+}
+\arguments{
+  \item{u}{Transform variate point of evaluation}
+
+  \item{order}{Order of differenciation}
+
+  \item{param}{Parameters of the GAL distirbution}
+
+  \item{eval.time}{Time of the process}
+
+  \item{type}{Choose between "mu" or "kappa"
+  parametrization}
+
+  \item{log}{Logical for log-parameters}
+}
+\value{
+The value of the derivative at the transform variate point
+of evaluation
+}
+\description{
+Differenciation of the cumulant generating fonction of the
+GAL distribution
+}
+\author{
+Francois Pelletier
+}
+

man/dnormapproxEsscherLM.Rd

@@ -0,0 +1,33 @@
+\name{dnormapproxEsscherLM}
+\alias{dnormapproxEsscherLM}
+\title{Normal approximation of the density function of the
+Esscher transform of a Laplace Motion}
+\usage{
+dnormapproxEsscherLM(x, param, hEsscher = 0, eval.time = 1, type = "mu",
+  log = FALSE, start = 0)
+}
+\arguments{
+  \item{x}{vector of quantiles}
+
+  \item{param}{Parameter vector}
+
+  \item{hEsscher}{Esscher transform parameter}
+
+  \item{eval.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{
+Normal density function approximation of the Esscher
+transform of the specified Laplace motion
+}
+\description{
+Normal approximation of the density function of the Esscher
+transform of a Laplace Motion
+}
+

man/dsaddleapproxGAL.Rd

@@ -0,0 +1,27 @@
+\name{dsaddleapproxGAL}
+\alias{dsaddleapproxGAL}
+\title{Saddlepoint approximation of the density function of the
+GAL distribution}
+\usage{
+dsaddleapproxGAL(x, param, eval.time = 1, type = "mu", log = FALSE)
+}
+\arguments{
+  \item{x}{vector of quantiles}
+
+  \item{param}{Parameter vector}
+
+  \item{eval.time}{Time of the process}
+
+  \item{type}{Choose between "mu" or "kappa"
+  parametrization}
+
+  \item{log}{Logical for log-parameters}
+}
+\value{
+Saddlepoint approximation of the density function
+}
+\description{
+Saddlepoint approximation of the density function of the
+GAL distribution
+}
+

man/pnormapproxEsscherLM.Rd

@@ -0,0 +1,32 @@
+\name{pnormapproxEsscherLM}
+\alias{pnormapproxEsscherLM}
+\title{Normal approximation of the distribution function of the
+Esscher transform of a Laplace Motion}
+\usage{
+pnormapproxEsscherLM(x, param, hEsscher = 0, eval.time = 1, type = "mu",
+  log = FALSE, start = 0)
+}
+\arguments{
+  \item{x}{vector of quantiles}
+
+  \item{param}{Parameter vector}
+
+  \item{hEsscher}{Esscher transform parameter}
+
+  \item{eval.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{
+Normal distribution function approximation
+}
+\description{
+Normal approximation of the distribution function of the
+Esscher transform of a Laplace Motion
+}
+

man/psaddleapproxEsscherGAL.Rd

@@ -0,0 +1,27 @@
+\name{psaddleapproxEsscherGAL}
+\alias{psaddleapproxEsscherGAL}
+\title{Saddlepoint approximation of the distribution function of the Esscher
+transform of the GAL distribution}
+\usage{
+psaddleapproxEsscherGAL(x, param, eval.time = 1, type = "mu", log = FALSE)
+}
+\arguments{
+  \item{x}{vector of quantiles}
+
+  \item{param}{Parameter vector}
+
+  \item{eval.time}{Time of the process}
+
+  \item{type}{Choose between "mu" or "kappa"
+  parametrization}
+
+  \item{log}{Logical for log-parameters}
+}
+\value{
+Saddlepoint approximation of the distribution function
+}
+\description{
+Saddlepoint approximation of the distribution function of
+the Esscher transform of the GAL distribution
+}
+

man/psaddleapproxGAL.Rd

@@ -0,0 +1,27 @@
+\name{psaddleapproxGAL}
+\alias{psaddleapproxGAL}
+\title{Saddlepoint approximation of the distribution function of the
+GAL distribution}
+\usage{
+psaddleapproxGAL(x, param, eval.time = 1, type = "mu", log = FALSE)
+}
+\arguments{
+  \item{x}{vector of quantiles}
+
+  \item{param}{Parameter vector}
+
+  \item{eval.time}{Time of the process}
+
+  \item{type}{Choose between "mu" or "kappa"
+  parametrization}
+
+  \item{log}{Logical for log-parameters}
+}
+\value{
+Saddlepoint approximation of the distribution function
+}
+\description{
+Saddlepoint approximation of the distribution function of
+the GAL distribution
+}
+

man/saddlepointEsscherGAL.Rd

@@ -0,0 +1,32 @@
+\name{saddlepointEsscherGAL}
+\alias{saddlepointEsscherGAL}
+\title{Evaluation of the saddlepoint of the Esscher transform with
+parameter 1 of the GAL distribution for given quantiles}
+\usage{
+saddlepointEsscherGAL(x, param, eval.time = 1, type = "mu", log = FALSE)
+}
+\arguments{
+  \item{x}{vector of quantiles}
+
+  \item{param}{Parameters of the underlying GAL
+  distribution}
+
+  \item{eval.time}{Time of the process}
+
+  \item{type}{Choose between "mu" or "kappa"
+  parametrization}
+
+  \item{log}{Logical for log-parameters}
+}
+\value{
+The value of the saddlepoint for each point of the vector
+of quantiles
+}
+\description{
+Evaluation of the saddlepoint of the Esscher transform with
+parameter 1 of the GAL distribution for given quantiles
+}
+\author{
+Francois Pelletier
+}
+

man/saddlepointGAL.Rd

@@ -0,0 +1,30 @@
+\name{saddlepointGAL}
+\alias{saddlepointGAL}
+\title{Evaluation of the saddlepoint of the GAL distribution for given quantiles}
+\usage{
+saddlepointGAL(x, param, eval.time = 1, type = "mu", log = FALSE)
+}
+\arguments{
+  \item{x}{vector of quantiles}
+
+  \item{param}{Parameters of the GAL distribution}
+
+  \item{eval.time}{Time of the process}
+
+  \item{type}{Choose between "mu" or "kappa"
+  parametrization}
+
+  \item{log}{Logical for log-parameters}
+}
+\value{
+The value of the saddlepoint for each point of the vector
+of quantiles
+}
+\description{
+Evaluation of the saddlepoint of the GAL distribution for
+given quantiles
+}
+\author{
+Francois Pelletier
+}
+