ajout des fonction Crowder

.project

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+<?xml version="1.0" encoding="UTF-8"?>
+<projectDescription>
+	<name>QuadraticEstimatingEquations</name>
+	<comment></comment>
+	<projects>
+	</projects>
+	<buildSpec>
+		<buildCommand>
+			<name>de.walware.statet.r.builders.RSupport</name>
+			<arguments>
+			</arguments>
+		</buildCommand>
+	</buildSpec>
+	<natures>
+		<nature>de.walware.statet.base.StatetNature</nature>
+		<nature>de.walware.statet.r.RNature</nature>
+		<nature>de.walware.statet.r.RPkgNature</nature>
+	</natures>
+</projectDescription>

.settings/de.walware.r.core.prefs

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+RProjectBuild/Package.name=QuadraticEstimatingEquations
+eclipse.preferences.version=1

DESCRIPTION

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+Package: QuadraticEstimatingEquations
+Title: Quadratic Estimating Equations
+Version: 0.1
+Date: 2014-02-11
+Author: Francois Pelletier
+Maintainer: Francois Pelletier <francois@francoispelletier.org>
+Description: This is a package gathering different functions to work with
+    quadratic estimating equations used in Crowder (1987).
+Depends:
+    moments
+License: LGPL-3

R/M.Crowder.Mod.R

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+# M Matrix (Modified Crowder)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+
+#' M Matrix (Modified Crowder)
+#' 
+#' @param Y Individual data sample
+#' @param param Vector of parameters of the distribution function
+#' @param variancef Variance function of the distribution
+#' @param skewnessf Skewness function of the distribution
+#' @param kurtosisf Kurtosis function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution 
+#' @return M Matrix
+#' 
+#' @author Francois Pelletier
+M.Crowder.Mod <- function(param,Y,variancef,skewnessf,kurtosisf,dmean,dsd)
+{
+	-(a.Crowder.Mod(param,Y,variancef,dmean,dsd) %o% dmean(param) + 
+				2*sqrt(variancef(param)) * 
+				b.Crowder.Mod(param,Y,variancef,dmean,dsd) %*% t(dsd(param)))
+}

R/M.Crowder.R

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+# M Matrix (Crowder)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+
+#' M Matrix (Crowder)
+#' 
+#' Identical to the V matrix by definition
+#' @param Y Individual data sample
+#' @param param Vector of parameters of the distribution function
+#' @param variancef Variance function of the distribution
+#' @param skewnessf Skewness function of the distribution
+#' @param kurtosisf Kurtosis function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution 
+#' @return M Matrix
+#' 
+#' @author Francois Pelletier
+M.Crowder <- function(param,Y,variancef,skewnessf,kurtosisf,dmean,dsd)
+{
+	((dmean(param) %o% dmean(param))+
+				((skewnessf(param)*dmean(param)-2*dsd(param)) %o%
+					(skewnessf(param)*dmean(param)-2*dsd(param)))/
+				gammaf.Crowder(param,skewnessf,kurtosisf))/
+			variancef(param)
+}

R/M.gauss.R

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+# M Matrix (gaussian)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+#' M Matrix (gaussian)
+#' @param Y Individual data sample
+#' @param param Vector of parameters of the distribution function
+#' @param meanf Mean function of the distribution
+#' @param variancef Variance function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution
+#' @return M Matrix
+#' 
+#' @author Francois Pelletier
+M.gauss <- function(param,Y,meanf,variancef,dmean,dsd)
+{
+	-(a.gauss(param,variancef,dmean,dsd) %o% dmean(param) + 
+				2*sqrt(variancef(param)) * b.gauss(param,variancef,dmean,dsd) %*% t(dsd(param)))
+}

R/V.Crowder.Mod.R

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+# V Matrix (Modified Crowder)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+
+#' V Matrix (Modified Crowder)
+#' @param Y Individual data sample
+#' @param param Vector of parameters of the distribution function
+#' @param variancef Variance function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution 
+#' @return V Matrix
+#' 
+#' @author Francois Pelletier
+V.Crowder.Mod <- function(param,Y,variancef,dmean,dsd)
+{
+	(variancef(param)*(a.Crowder.Mod(param,Y,variancef,dmean,dsd) %o% 
+					a.Crowder.Mod(param,Y,variancef,dmean,dsd) + 
+					sqrt(variancef(param)) * skewness(Y) * 
+					(a.Crowder.Mod(param,Y,variancef,dmean,dsd) %o% 
+						b.Crowder.Mod(param,Y,variancef,dmean,dsd) + 
+						b.Crowder.Mod(param,Y,variancef,dmean,dsd) %o% 
+						a.Crowder.Mod(param,Y,variancef,dmean,dsd)) + 
+					variancef(param) * (kurtosis(Y)-3+2) * 
+					b.Crowder.Mod(param,Y,variancef,dmean,dsd) %*% 
+					t(b.Crowder.Mod(param,Y,variancef,dmean,dsd))))
+}

R/V.Crowder.R

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+# V Matrix (Crowder)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+
+#' V Matrix (Crowder)
+#' @param Y Individual data sample
+#' @param param Vector of parameters of the distribution function
+#' @param variancef Variance function of the distribution
+#' @param skewnessf Skewness function of the distribution
+#' @param kurtosisf Kurtosis function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution 
+#' @return V Matrix
+#' 
+#' @author Francois Pelletier
+V.Crowder <- function(param,Y,variancef,skewnessf,kurtosisf,dmean,dsd)
+{
+	((dmean(param) %o% dmean(param))+
+				((skewnessf(param)*dmean(param)-2*dsd(param)) %o%
+					(skewnessf(param)*dmean(param)-2*dsd(param)))/
+				gammaf.Crowder(param,skewnessf,kurtosisf))/
+			variancef(param)
+}

R/V.gauss.R

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+# V Matrix (gaussian)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+
+#' V Matrix (gaussian)
+#' @param Y Individual data sample
+#' @param param Vector of parameters of the distribution function
+#' @param meanf Mean function of the distribution
+#' @param variancef Variance function of the distribution
+#' @param skewnessf Skewness function of the distribution
+#' @param kurtosisf Kurtosis function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution 
+#' @return V Matrix
+#' 
+#' @author Francois Pelletier
+V.gauss <- function(param,Y,meanf,variancef,skewnessf,kurtosisf,dmean,dsd)
+{
+	(variancef(param)*(a.gauss(param,variancef,dmean,dsd) %o% 
+					a.gauss(param,variancef,dmean,dsd) + 
+					sqrt(variancef(param)) * skewnessf(param) * 
+					(a.gauss(param,variancef,dmean,dsd) %o% 
+						b.gauss(param,variancef,dmean,dsd) +
+						b.gauss(param,variancef,dmean,dsd) %o% 
+						a.gauss(param,variancef,dmean,dsd)) + 
+					variancef(param)*(kurtosis(param)+2) * 
+					b.gauss(param,variancef,dmean,dsd) %*% 
+					t(b.gauss(param,variancef,dmean,dsd))))
+}

R/a.Crowder.Mod.R

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+# First weighting vector of the modified quadratic estimating equation (Crowder)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+#' First weighting vector of the modified quadratic estimating equation (Crowder)
+#' 
+#' @param param Vector of parameters of the distribution function
+#' @param Y Individual data sample
+#' @param variancef Variance function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution
+#' @return First weighting vector
+#' 
+#' @author Francois Pelletier
+a.Crowder.Mod <- function(param,Y,variancef,dmean,dsd)
+{
+	(-(moments::kurtosis(Y)-1)*dmean(param)+
+				2*moments::skewness(Y)*dsd(param))/
+			(variancef(param)*gammaf.Crowder.Mod(Y))
+}

R/a.Crowder.R

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+# First weighting vector of the quadratic estimating equation (Crowder)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+#' First weighting vector of the quadratic estimating equation (Crowder)
+#' 
+#' @param param Vector of parameters of the distribution function
+#' @param variancef Variance function of the distribution
+#' @param skewnessf Skewness function of the distribution
+#' @param kurtosisf Kurtosis function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution
+#' @return First weighting vector
+#' 
+#' @author Francois Pelletier
+a.Crowder <- function(param,variancef,skewnessf,kurtosisf,dmean,dsd)
+{
+	(-(kurtosisf(param)+2)*dmean(param)+
+				2*skewnessf(param)*dsd(param))/
+			(variancef(param)*gammaf.Crowder(param,skewnessf,kurtosisf))
+}

R/a.gauss.R

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+# First weighting vector of the quadratic estimating equation (gaussian)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+#' First weighting vector of the quadratic estimating equation (gaussian)
+#' @param param Vector of parameters of the distribution function
+#' @param variancef Variance function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @return First weighting vector
+#' 
+#' @author Francois Pelletier
+a.gauss <- function(param,variancef,dmean)
+{
+	dmean(param)/variancef(param)
+}

R/b.Crowder.Mod.R

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+# Second weighting vector of the modified quadratic estimating equation (Crowder)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+#' Second weighting vector of the modified quadratic estimating equation (Crowder)
+#' 
+#' @param param Vector of parameters of the distribution function
+#' @param Y Individual data sample
+#' @param variancef Variance function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution
+#' @return First weighting vector
+#' 
+#' @author Francois Pelletier
+a.Crowder.Mod <- function(param,Y,variancef,dmean,dsd)
+{
+	(moments::skewness(Y)*dmean(param)-2*dsd(param)) /
+			(variancef(param)^(3/2)*gammaf.Crowder.Mod(Y))
+}

R/b.Crowder.R

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+# Second weighting vector of the quadratic estimating equation (Crowder)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+#' Second weighting vector of the quadratic estimating equation (Crowder)
+#' 
+#' @param param Vector of parameters of the distribution function
+#' @param variancef Variance function of the distribution
+#' @param skewnessf Skewness function of the distribution
+#' @param kurtosisf Kurtosis function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution
+#' @return First weighting vector
+#' 
+#' @author Francois Pelletier
+b.Crowder <- function(param,variancef,skewnessf,kurtosisf,dmean,dsd)
+{
+	(skewnessf(param)*dmean(param)-
+				2*dsd(param))/
+			(variancef(param)^(3/2)*gamma.Crowder(param,skewnessf,kurtosisf))	
+}

R/b.gauss.R

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+# Second weighting vector of the quadratic estimating equation (gaussian)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+#' Second weighting vector of the quadratic estimating equation (gaussian)
+#' @param param Vector of parameters of the distribution function
+#' @param variancef Variance function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution
+#' @return Second weighting vector
+#' 
+#' @author Francois Pelletier
+b.gauss <- function(param,variancef,dsd)
+{
+	dsd(param)/variancef(param)
+}
+
+

R/eqn.Crowder.Mod.R

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+# Modified Quadratic estimating equation (Crowder)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+
+#'  Modified Quadratic estimating equation (Crowder)
+#' @param Y Individual data sample
+#' @param param Vector of parameters of the distribution function
+#' @param meanf Mean function of the distribution
+#' @param variancef Variance function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution
+#' @return The vector value of the estimating equation
+#' 
+#' @author Francois Pelletier
+eqn.Crowder.Mod <- function(param,Y,meanf,variancef,dmean,dsd)
+{
+	a.Crowder.Mod(param,variancef,dmean,dsd) * sum(Y-meanf(param)) +
+			b.Crowder.Mod(param,variancef,dmean,dsd) * sum((Y-meanf(param))^2-variancef(param))
+}

R/eqn.Crowder.R

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+# Quadratic estimating equation (Crowder)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+
+#' Quadratic estimating equation (Crowder)
+#' @param Y Individual data sample
+#' @param param Vector of parameters of the distribution function
+#' @param meanf Mean function of the distribution
+#' @param variancef Variance function of the distribution
+#' @param skewnessf Skewness function of the distribution
+#' @param kurtosisf Kurtosis function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution
+#' @return The vector value of the estimating equation
+#' 
+#' @author Francois Pelletier
+eqn.Crowder <- function(param,Y,meanf,variancef,skewnessf,kurtosisf,dmean,dsd)
+{
+	a.Crowder(param,variancef,skewnessf,kurtosisf,dmean,dsd) * sum(Y-meanf(param)) +
+			b.Crowder(param,variancef,skewnessf,kurtosisf,dmean,dsd) * sum((Y-meanf(param))^2-variancef(param))
+}

R/eqn.gauss.R

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+# Quadratic estimating equation (gaussian)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+
+#' Quadratic estimating equation (gaussian)
+#' @param Y Individual data sample
+#' @param param Vector of parameters of the distribution function
+#' @param meanf Mean function of the distribution
+#' @param variancef Variance function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution
+#' @return The vector value of the estimating equation
+#' 
+#' @author Francois Pelletier
+eqn.gauss <- function(param,Y,meanf,variancef,dmean,dsd)
+{
+	a.gauss(param,variancef,dmean,dsd) * sum(Y-meanf(param)) +
+			b.gauss(param,variancef,dmean,dsd) * sum((Y-meanf(param))^2-variancef(param))
+}

R/gammaf.Crowder.Mod.R

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+# Gamma function used in Modified Crowder Estimating Equations
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+
+#' Gamma function used in Modified Crowder Estimating Equations
+#' @param Y Individual data sample
+#' @return Gamma function value
+#' 
+#' @author Francois Pelletier
+gammaf.Crowder.Mod <- function(Y)
+{
+	moments::kurtosis(Y)-1-moments::skewness(Y)^2
+}

R/gammaf.Crowder.R

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+# Gamma function used in Crowder Estimating Equations
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+
+#' Gamma function used in Crowder Estimating Equations
+#' @param param Vector of parameters of the distribution function
+#' @param skewnessf Skewness function of the distribution
+#' @param kurtosisf Kurtosis function of the distribution
+#' @return Gamma function value
+#' 
+#' @author Francois Pelletier
+gammaf.Crowder <- function(param,skewnessf,kurtosisf)
+{
+	kurtosisf(param)+2-skewnessf(param)^2
+}

R/obj.Crowder.Mod.R

@@ -0,0 +1,25 @@
+# Modified Quadratic form objective function for optimization of the parameter vector (Crowder)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+#' Modified Quadratic form objective function for optimization of the parameter vector (Crowder)
+#' @param Y Individual data sample
+#' @param param Vector of parameters of the distribution function
+#' @param meanf Mean function of the distribution
+#' @param variancef Variance function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution
+#' @param Q Weight matrix
+#' @return The value of the quadratic form
+#' 
+#' @author Francois Pelletier
+obj.Crowder.Mod <- function(param,Y,meanf,variancef,dmean,dsd,Q=diag(4))
+{
+	eqn.Crowder.Mod(param,Y,meanf,variancef,dmean,dsd) %*% Q %*% 
+			eqn.Crowder.Mod(param,Y,meanf,variancef,dmean,dsd)
+}
+
+

R/obj.Crowder.R

@@ -0,0 +1,27 @@
+# Quadratic form objective function for optimization of the parameter vector (Crowder)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+#' Quadratic form objective function for optimization of the parameter vector (Crowder)
+#' @param Y Individual data sample
+#' @param param Vector of parameters of the distribution function
+#' @param meanf Mean function of the distribution
+#' @param variancef Variance function of the distribution
+#' @param skewnessf Skewness function of the distribution
+#' @param kurtosisf Kurtosis function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution
+#' @param Q Weight matrix
+#' @return The value of the quadratic form
+#' 
+#' @author Francois Pelletier
+obj.Crowder <- function(param,Y,meanf,variancef,skewnessf,kurtosisf,dmean,dsd,Q=diag(4))
+{
+	eqn.Crowder(param,Y,meanf,variancef,skewnessf,kurtosisf,dmean,dsd) %*% Q %*% 
+			eqn.Crowder(param,Y,meanf,variancef,skewnessf,kurtosisf,dmean,dsd)
+}
+
+

R/obj.gauss.R

@@ -0,0 +1,25 @@
+# Quadratic form objective function for optimization of the parameter vector (gaussian)
+# 
+# Author: Francois Pelletier
+#
+# LGPL-3.0
+###############################################################################
+
+#' Quadratic form objective function for optimization of the parameter vector (gaussian)
+#' @param Y Individual data sample
+#' @param param Vector of parameters of the distribution function
+#' @param meanf Mean function of the distribution
+#' @param variancef Variance function of the distribution
+#' @param dmean Derivative in respect to the parameter vector of the mean function of the distribution
+#' @param dsd Derivative in respect to the parameter vector of the standard deviation function of the distribution
+#' @param Q Weight matrix
+#' @return The value of the quadratic form
+#' 
+#' @author Francois Pelletier
+obj.gauss <- function(param,Y,meanf,variancef,dmean,dsd,Q=diag(4))
+{
+	eqn.gauss(param,Y,meanf,variancef,dmean,dsd) %*% Q %*% 
+			eqn.gauss(param,Y,meanf,variancef,dmean,dsd)
+}
+
+

man/M.Crowder.Mod.Rd

@@ -0,0 +1,34 @@
+\name{M.Crowder.Mod}
+\alias{M.Crowder.Mod}
+\title{M Matrix (Modified Crowder)}
+\usage{
+M.Crowder.Mod(param, Y, variancef, skewnessf, kurtosisf, dmean, dsd)
+}
+\arguments{
+  \item{Y}{Individual data sample}
+
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{skewnessf}{Skewness function of the distribution}
+
+  \item{kurtosisf}{Kurtosis function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+}
+\value{
+M Matrix
+}
+\description{
+M Matrix (Modified Crowder)
+}
+\author{
+Francois Pelletier
+}
+

man/M.Crowder.Rd

@@ -0,0 +1,34 @@
+\name{M.Crowder}
+\alias{M.Crowder}
+\title{M Matrix (Crowder)}
+\usage{
+M.Crowder(param, Y, variancef, skewnessf, kurtosisf, dmean, dsd)
+}
+\arguments{
+  \item{Y}{Individual data sample}
+
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{skewnessf}{Skewness function of the distribution}
+
+  \item{kurtosisf}{Kurtosis function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+}
+\value{
+M Matrix
+}
+\description{
+Identical to the V matrix by definition
+}
+\author{
+Francois Pelletier
+}
+

man/M.gauss.Rd

@@ -0,0 +1,32 @@
+\name{M.gauss}
+\alias{M.gauss}
+\title{M Matrix (gaussian)}
+\usage{
+M.gauss(param, Y, meanf, variancef, dmean, dsd)
+}
+\arguments{
+  \item{Y}{Individual data sample}
+
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{meanf}{Mean function of the distribution}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+}
+\value{
+M Matrix
+}
+\description{
+M Matrix (gaussian)
+}
+\author{
+Francois Pelletier
+}
+

man/V.Crowder.Mod.Rd

@@ -0,0 +1,30 @@
+\name{V.Crowder.Mod}
+\alias{V.Crowder.Mod}
+\title{V Matrix (Modified Crowder)}
+\usage{
+V.Crowder.Mod(param, Y, variancef, dmean, dsd)
+}
+\arguments{
+  \item{Y}{Individual data sample}
+
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+}
+\value{
+V Matrix
+}
+\description{
+V Matrix (Modified Crowder)
+}
+\author{
+Francois Pelletier
+}
+

man/V.Crowder.Rd

@@ -0,0 +1,34 @@
+\name{V.Crowder}
+\alias{V.Crowder}
+\title{V Matrix (Crowder)}
+\usage{
+V.Crowder(param, Y, variancef, skewnessf, kurtosisf, dmean, dsd)
+}
+\arguments{
+  \item{Y}{Individual data sample}
+
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{skewnessf}{Skewness function of the distribution}
+
+  \item{kurtosisf}{Kurtosis function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+}
+\value{
+V Matrix
+}
+\description{
+V Matrix (Crowder)
+}
+\author{
+Francois Pelletier
+}
+

man/V.gauss.Rd

@@ -0,0 +1,36 @@
+\name{V.gauss}
+\alias{V.gauss}
+\title{V Matrix (gaussian)}
+\usage{
+V.gauss(param, Y, meanf, variancef, skewnessf, kurtosisf, dmean, dsd)
+}
+\arguments{
+  \item{Y}{Individual data sample}
+
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{meanf}{Mean function of the distribution}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{skewnessf}{Skewness function of the distribution}
+
+  \item{kurtosisf}{Kurtosis function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+}
+\value{
+V Matrix
+}
+\description{
+V Matrix (gaussian)
+}
+\author{
+Francois Pelletier
+}
+

man/a.Crowder.Mod.Rd

@@ -0,0 +1,53 @@
+\name{a.Crowder.Mod}
+\alias{a.Crowder.Mod}
+\title{First weighting vector of the modified quadratic estimating equation (Crowder)}
+\usage{
+a.Crowder.Mod(param, Y, variancef, dmean, dsd)
+
+a.Crowder.Mod(param, Y, variancef, dmean, dsd)
+}
+\arguments{
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{Y}{Individual data sample}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{Y}{Individual data sample}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+}
+\value{
+First weighting vector
+
+First weighting vector
+}
+\description{
+First weighting vector of the modified quadratic estimating
+equation (Crowder)
+
+Second weighting vector of the modified quadratic
+estimating equation (Crowder)
+}
+\author{
+Francois Pelletier
+
+Francois Pelletier
+}
+

man/a.Crowder.Rd

@@ -0,0 +1,33 @@
+\name{a.Crowder}
+\alias{a.Crowder}
+\title{First weighting vector of the quadratic estimating equation (Crowder)}
+\usage{
+a.Crowder(param, variancef, skewnessf, kurtosisf, dmean, dsd)
+}
+\arguments{
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{skewnessf}{Skewness function of the distribution}
+
+  \item{kurtosisf}{Kurtosis function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+}
+\value{
+First weighting vector
+}
+\description{
+First weighting vector of the quadratic estimating equation
+(Crowder)
+}
+\author{
+Francois Pelletier
+}
+

man/a.gauss.Rd

@@ -0,0 +1,26 @@
+\name{a.gauss}
+\alias{a.gauss}
+\title{First weighting vector of the quadratic estimating equation (gaussian)}
+\usage{
+a.gauss(param, variancef, dmean)
+}
+\arguments{
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+}
+\value{
+First weighting vector
+}
+\description{
+First weighting vector of the quadratic estimating equation
+(gaussian)
+}
+\author{
+Francois Pelletier
+}
+

man/b.Crowder.Rd

@@ -0,0 +1,33 @@
+\name{b.Crowder}
+\alias{b.Crowder}
+\title{Second weighting vector of the quadratic estimating equation (Crowder)}
+\usage{
+b.Crowder(param, variancef, skewnessf, kurtosisf, dmean, dsd)
+}
+\arguments{
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{skewnessf}{Skewness function of the distribution}
+
+  \item{kurtosisf}{Kurtosis function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+}
+\value{
+First weighting vector
+}
+\description{
+Second weighting vector of the quadratic estimating
+equation (Crowder)
+}
+\author{
+Francois Pelletier
+}
+

man/b.gauss.Rd

@@ -0,0 +1,26 @@
+\name{b.gauss}
+\alias{b.gauss}
+\title{Second weighting vector of the quadratic estimating equation (gaussian)}
+\usage{
+b.gauss(param, variancef, dsd)
+}
+\arguments{
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+}
+\value{
+Second weighting vector
+}
+\description{
+Second weighting vector of the quadratic estimating
+equation (gaussian)
+}
+\author{
+Francois Pelletier
+}
+

man/eqn.Crowder.Mod.Rd

@@ -0,0 +1,32 @@
+\name{eqn.Crowder.Mod}
+\alias{eqn.Crowder.Mod}
+\title{Modified Quadratic estimating equation (Crowder)}
+\usage{
+eqn.Crowder.Mod(param, Y, meanf, variancef, dmean, dsd)
+}
+\arguments{
+  \item{Y}{Individual data sample}
+
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{meanf}{Mean function of the distribution}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+}
+\value{
+The vector value of the estimating equation
+}
+\description{
+Modified Quadratic estimating equation (Crowder)
+}
+\author{
+Francois Pelletier
+}
+

man/eqn.Crowder.Rd

@@ -0,0 +1,36 @@
+\name{eqn.Crowder}
+\alias{eqn.Crowder}
+\title{Quadratic estimating equation (Crowder)}
+\usage{
+eqn.Crowder(param, Y, meanf, variancef, skewnessf, kurtosisf, dmean, dsd)
+}
+\arguments{
+  \item{Y}{Individual data sample}
+
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{meanf}{Mean function of the distribution}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{skewnessf}{Skewness function of the distribution}
+
+  \item{kurtosisf}{Kurtosis function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+}
+\value{
+The vector value of the estimating equation
+}
+\description{
+Quadratic estimating equation (Crowder)
+}
+\author{
+Francois Pelletier
+}
+

man/eqn.gauss.Rd

@@ -0,0 +1,32 @@
+\name{eqn.gauss}
+\alias{eqn.gauss}
+\title{Quadratic estimating equation (gaussian)}
+\usage{
+eqn.gauss(param, Y, meanf, variancef, dmean, dsd)
+}
+\arguments{
+  \item{Y}{Individual data sample}
+
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{meanf}{Mean function of the distribution}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+}
+\value{
+The vector value of the estimating equation
+}
+\description{
+Quadratic estimating equation (gaussian)
+}
+\author{
+Francois Pelletier
+}
+

man/gammaf.Crowder.Mod.Rd

@@ -0,0 +1,20 @@
+\name{gammaf.Crowder.Mod}
+\alias{gammaf.Crowder.Mod}
+\title{Gamma function used in Modified Crowder Estimating Equations}
+\usage{
+gammaf.Crowder.Mod(Y)
+}
+\arguments{
+  \item{Y}{Individual data sample}
+}
+\value{
+Gamma function value
+}
+\description{
+Gamma function used in Modified Crowder Estimating
+Equations
+}
+\author{
+Francois Pelletier
+}
+

man/gammaf.Crowder.Rd

@@ -0,0 +1,24 @@
+\name{gammaf.Crowder}
+\alias{gammaf.Crowder}
+\title{Gamma function used in Crowder Estimating Equations}
+\usage{
+gammaf.Crowder(param, skewnessf, kurtosisf)
+}
+\arguments{
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{skewnessf}{Skewness function of the distribution}
+
+  \item{kurtosisf}{Kurtosis function of the distribution}
+}
+\value{
+Gamma function value
+}
+\description{
+Gamma function used in Crowder Estimating Equations
+}
+\author{
+Francois Pelletier
+}
+

man/obj.Crowder.Mod.Rd

@@ -0,0 +1,35 @@
+\name{obj.Crowder.Mod}
+\alias{obj.Crowder.Mod}
+\title{Modified Quadratic form objective function for optimization of the parameter vector (Crowder)}
+\usage{
+obj.Crowder.Mod(param, Y, meanf, variancef, dmean, dsd, Q = diag(4))
+}
+\arguments{
+  \item{Y}{Individual data sample}
+
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{meanf}{Mean function of the distribution}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+
+  \item{Q}{Weight matrix}
+}
+\value{
+The value of the quadratic form
+}
+\description{
+Modified Quadratic form objective function for optimization
+of the parameter vector (Crowder)
+}
+\author{
+Francois Pelletier
+}
+

man/obj.Crowder.Rd

@@ -0,0 +1,40 @@
+\name{obj.Crowder}
+\alias{obj.Crowder}
+\title{Quadratic form objective function for optimization of the parameter vector (Crowder)}
+\usage{
+obj.Crowder(param, Y, meanf, variancef, skewnessf, kurtosisf, dmean, dsd,
+  Q = diag(4))
+}
+\arguments{
+  \item{Y}{Individual data sample}
+
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{meanf}{Mean function of the distribution}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{skewnessf}{Skewness function of the distribution}
+
+  \item{kurtosisf}{Kurtosis function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+
+  \item{Q}{Weight matrix}
+}
+\value{
+The value of the quadratic form
+}
+\description{
+Quadratic form objective function for optimization of the
+parameter vector (Crowder)
+}
+\author{
+Francois Pelletier
+}
+

man/obj.gauss.Rd

@@ -0,0 +1,35 @@
+\name{obj.gauss}
+\alias{obj.gauss}
+\title{Quadratic form objective function for optimization of the parameter vector (gaussian)}
+\usage{
+obj.gauss(param, Y, meanf, variancef, dmean, dsd, Q = diag(4))
+}
+\arguments{
+  \item{Y}{Individual data sample}
+
+  \item{param}{Vector of parameters of the distribution
+  function}
+
+  \item{meanf}{Mean function of the distribution}
+
+  \item{variancef}{Variance function of the distribution}
+
+  \item{dmean}{Derivative in respect to the parameter
+  vector of the mean function of the distribution}
+
+  \item{dsd}{Derivative in respect to the parameter vector
+  of the standard deviation function of the distribution}
+
+  \item{Q}{Weight matrix}
+}
+\value{
+The value of the quadratic form
+}
+\description{
+Quadratic form objective function for optimization of the
+parameter vector (gaussian)
+}
+\author{
+Francois Pelletier
+}
+