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ajout des fonction Crowder

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François Pelletier 2014-02-23 21:05:36 -05:00
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34
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\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
}

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\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
}

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\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
}

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\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
}

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\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
}

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\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
}

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\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
}

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\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
}

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\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
}

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\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
}

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\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
}

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\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
}

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\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
}

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\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
}

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\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
}

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\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
}

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\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
}

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\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
}

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\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
}