ajout des fonction Crowder

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

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+# 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)
+}
+
+