diff --git a/.project b/.project new file mode 100644 index 0000000..98c9ace --- /dev/null +++ b/.project @@ -0,0 +1,19 @@ + + + QuadraticEstimatingEquations + + + + + + de.walware.statet.r.builders.RSupport + + + + + + de.walware.statet.base.StatetNature + de.walware.statet.r.RNature + de.walware.statet.r.RPkgNature + + diff --git a/.settings/de.walware.r.core.prefs b/.settings/de.walware.r.core.prefs new file mode 100644 index 0000000..736c810 --- /dev/null +++ b/.settings/de.walware.r.core.prefs @@ -0,0 +1,2 @@ +RProjectBuild/Package.name=QuadraticEstimatingEquations +eclipse.preferences.version=1 diff --git a/DESCRIPTION b/DESCRIPTION new file mode 100644 index 0000000..5bb647c --- /dev/null +++ b/DESCRIPTION @@ -0,0 +1,11 @@ +Package: QuadraticEstimatingEquations +Title: Quadratic Estimating Equations +Version: 0.1 +Date: 2014-02-11 +Author: Francois Pelletier +Maintainer: Francois Pelletier +Description: This is a package gathering different functions to work with + quadratic estimating equations used in Crowder (1987). +Depends: + moments +License: LGPL-3 diff --git a/NAMESPACE b/NAMESPACE new file mode 100644 index 0000000..e69de29 diff --git a/R/M.Crowder.Mod.R b/R/M.Crowder.Mod.R new file mode 100644 index 0000000..964edf0 --- /dev/null +++ b/R/M.Crowder.Mod.R @@ -0,0 +1,26 @@ +# 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))) +} \ No newline at end of file diff --git a/R/M.Crowder.R b/R/M.Crowder.R new file mode 100644 index 0000000..1e23c9f --- /dev/null +++ b/R/M.Crowder.R @@ -0,0 +1,29 @@ +# 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) +} \ No newline at end of file diff --git a/R/M.gauss.R b/R/M.gauss.R new file mode 100644 index 0000000..fb82ab0 --- /dev/null +++ b/R/M.gauss.R @@ -0,0 +1,22 @@ +# 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))) +} \ No newline at end of file diff --git a/R/V.Crowder.Mod.R b/R/V.Crowder.Mod.R new file mode 100644 index 0000000..438652f --- /dev/null +++ b/R/V.Crowder.Mod.R @@ -0,0 +1,30 @@ +# 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)))) +} diff --git a/R/V.Crowder.R b/R/V.Crowder.R new file mode 100644 index 0000000..7b729e2 --- /dev/null +++ b/R/V.Crowder.R @@ -0,0 +1,27 @@ +# 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) +} diff --git a/R/V.gauss.R b/R/V.gauss.R new file mode 100644 index 0000000..3abe89f --- /dev/null +++ b/R/V.gauss.R @@ -0,0 +1,33 @@ +# 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)))) +} diff --git a/R/a.Crowder.Mod.R b/R/a.Crowder.Mod.R new file mode 100644 index 0000000..7307539 --- /dev/null +++ b/R/a.Crowder.Mod.R @@ -0,0 +1,23 @@ +# 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)) +} \ No newline at end of file diff --git a/R/a.Crowder.R b/R/a.Crowder.R new file mode 100644 index 0000000..dea9e36 --- /dev/null +++ b/R/a.Crowder.R @@ -0,0 +1,24 @@ +# 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)) +} \ No newline at end of file diff --git a/R/a.gauss.R b/R/a.gauss.R new file mode 100644 index 0000000..1a4c223 --- /dev/null +++ b/R/a.gauss.R @@ -0,0 +1,18 @@ +# 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) +} \ No newline at end of file diff --git a/R/b.Crowder.Mod.R b/R/b.Crowder.Mod.R new file mode 100644 index 0000000..e92c735 --- /dev/null +++ b/R/b.Crowder.Mod.R @@ -0,0 +1,22 @@ +# 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)) +} \ No newline at end of file diff --git a/R/b.Crowder.R b/R/b.Crowder.R new file mode 100644 index 0000000..0d3ea21 --- /dev/null +++ b/R/b.Crowder.R @@ -0,0 +1,24 @@ +# 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)) +} \ No newline at end of file diff --git a/R/b.gauss.R b/R/b.gauss.R new file mode 100644 index 0000000..e2824d6 --- /dev/null +++ b/R/b.gauss.R @@ -0,0 +1,20 @@ +# 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) +} + + diff --git a/R/eqn.Crowder.Mod.R b/R/eqn.Crowder.Mod.R new file mode 100644 index 0000000..dd551db --- /dev/null +++ b/R/eqn.Crowder.Mod.R @@ -0,0 +1,23 @@ +# 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)) +} diff --git a/R/eqn.Crowder.R b/R/eqn.Crowder.R new file mode 100644 index 0000000..aa189ae --- /dev/null +++ b/R/eqn.Crowder.R @@ -0,0 +1,25 @@ +# 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)) +} diff --git a/R/eqn.gauss.R b/R/eqn.gauss.R new file mode 100644 index 0000000..7fca039 --- /dev/null +++ b/R/eqn.gauss.R @@ -0,0 +1,23 @@ +# 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)) +} diff --git a/R/gammaf.Crowder.Mod.R b/R/gammaf.Crowder.Mod.R new file mode 100644 index 0000000..8542005 --- /dev/null +++ b/R/gammaf.Crowder.Mod.R @@ -0,0 +1,17 @@ +# 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 +} diff --git a/R/gammaf.Crowder.R b/R/gammaf.Crowder.R new file mode 100644 index 0000000..5ab90ec --- /dev/null +++ b/R/gammaf.Crowder.R @@ -0,0 +1,19 @@ +# 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 +} diff --git a/R/obj.Crowder.Mod.R b/R/obj.Crowder.Mod.R new file mode 100644 index 0000000..1c736a1 --- /dev/null +++ b/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) +} + + diff --git a/R/obj.Crowder.R b/R/obj.Crowder.R new file mode 100644 index 0000000..659e789 --- /dev/null +++ b/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) +} + + diff --git a/R/obj.gauss.R b/R/obj.gauss.R new file mode 100644 index 0000000..a8560c0 --- /dev/null +++ b/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) +} + + diff --git a/man/M.Crowder.Mod.Rd b/man/M.Crowder.Mod.Rd new file mode 100644 index 0000000..3b0a23c --- /dev/null +++ b/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 +} + diff --git a/man/M.Crowder.Rd b/man/M.Crowder.Rd new file mode 100644 index 0000000..bd181d4 --- /dev/null +++ b/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 +} + diff --git a/man/M.gauss.Rd b/man/M.gauss.Rd new file mode 100644 index 0000000..37c978e --- /dev/null +++ b/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 +} + diff --git a/man/V.Crowder.Mod.Rd b/man/V.Crowder.Mod.Rd new file mode 100644 index 0000000..1606a3d --- /dev/null +++ b/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 +} + diff --git a/man/V.Crowder.Rd b/man/V.Crowder.Rd new file mode 100644 index 0000000..83f25cd --- /dev/null +++ b/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 +} + diff --git a/man/V.gauss.Rd b/man/V.gauss.Rd new file mode 100644 index 0000000..175f56a --- /dev/null +++ b/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 +} + diff --git a/man/a.Crowder.Mod.Rd b/man/a.Crowder.Mod.Rd new file mode 100644 index 0000000..c194011 --- /dev/null +++ b/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 +} + diff --git a/man/a.Crowder.Rd b/man/a.Crowder.Rd new file mode 100644 index 0000000..8e09951 --- /dev/null +++ b/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 +} + diff --git a/man/a.gauss.Rd b/man/a.gauss.Rd new file mode 100644 index 0000000..bcf08be --- /dev/null +++ b/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 +} + diff --git a/man/b.Crowder.Rd b/man/b.Crowder.Rd new file mode 100644 index 0000000..aadb0b1 --- /dev/null +++ b/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 +} + diff --git a/man/b.gauss.Rd b/man/b.gauss.Rd new file mode 100644 index 0000000..5e1660c --- /dev/null +++ b/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 +} + diff --git a/man/eqn.Crowder.Mod.Rd b/man/eqn.Crowder.Mod.Rd new file mode 100644 index 0000000..3fba227 --- /dev/null +++ b/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 +} + diff --git a/man/eqn.Crowder.Rd b/man/eqn.Crowder.Rd new file mode 100644 index 0000000..1352112 --- /dev/null +++ b/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 +} + diff --git a/man/eqn.gauss.Rd b/man/eqn.gauss.Rd new file mode 100644 index 0000000..d5f8718 --- /dev/null +++ b/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 +} + diff --git a/man/gammaf.Crowder.Mod.Rd b/man/gammaf.Crowder.Mod.Rd new file mode 100644 index 0000000..4bc06d4 --- /dev/null +++ b/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 +} + diff --git a/man/gammaf.Crowder.Rd b/man/gammaf.Crowder.Rd new file mode 100644 index 0000000..97b6e63 --- /dev/null +++ b/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 +} + diff --git a/man/obj.Crowder.Mod.Rd b/man/obj.Crowder.Mod.Rd new file mode 100644 index 0000000..7f0f409 --- /dev/null +++ b/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 +} + diff --git a/man/obj.Crowder.Rd b/man/obj.Crowder.Rd new file mode 100644 index 0000000..a180b70 --- /dev/null +++ b/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 +} + diff --git a/man/obj.gauss.Rd b/man/obj.gauss.Rd new file mode 100644 index 0000000..4466ca3 --- /dev/null +++ b/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 +} +