# jMEF.MultinomialFixedN Class Reference

List of all members.

## Public Member Functions

MultinomialFixedN ()
Class constructor.
MultinomialFixedN (int n)
Class constructor.
double F (PVector T)
Computes .
Computes .
double G (PVector H)
Computes .
Computes .
PVector t (PVector x)
Computes the sufficient statistic .
double k (PVector x)
Computes the carrier measure .
PVector Lambda2Theta (PVector L)
Converts source parameters to natural parameters.
PVector Theta2Lambda (PVector T)
Converts natural parameters to source parameters.
PVector Lambda2Eta (PVector L)
Converts source parameters to expectation parameters.
PVector Eta2Lambda (PVector H)
Converts expectation parameters to source parameters.
double density (PVector x, PVector param)
Computes the density value .
PVector drawRandomPoint (PVector L)
Draws a point from the considered distribution.
double KLD (PVector LA, PVector LB)
Computes the Kullback-Leibler divergence between two Binomial distributions.

Version:
1.0

## Description

The Multinomial distribution, with fixed, is an exponential family and, as a consequence, the probability density function is given by

where are the natural parameters. This class implements the different functions allowing to express a Multinomial distribution as a member of an exponential family.

## Parameters

The parameters of a given distribution are:
• Source parameters
• Natural parameters
• Expectation parameters

## Constructor & Destructor Documentation

 jMEF.MultinomialFixedN.MultinomialFixedN ( )

Class constructor.

 jMEF.MultinomialFixedN.MultinomialFixedN ( int n )

Class constructor.

Parameters:
 n parameter n

## Member Function Documentation

 double jMEF.MultinomialFixedN.density ( PVector x, PVector param )

Computes the density value .

Parameters:
 x point param parameters (source, natural, or expectation)
Returns:

 PVector jMEF.MultinomialFixedN.drawRandomPoint ( PVector L )

Draws a point from the considered distribution.

Parameters:
 L source parameters
Returns:
a point

 PVector jMEF.MultinomialFixedN.Eta2Lambda ( PVector H )

Converts expectation parameters to source parameters.

Parameters:
 H natural parameters
Returns:
source parameters

 double jMEF.MultinomialFixedN.F ( PVector T )

Computes .

Parameters:
 T parameters
Returns:

 double jMEF.MultinomialFixedN.G ( PVector H )

Computes .

Parameters:
 H expectation parameters
Returns:

 PVector jMEF.MultinomialFixedN.gradF ( PVector T )

Computes .

Parameters:
 T naturel parameters
Returns:

 PVector jMEF.MultinomialFixedN.gradG ( PVector H )

Computes .

Parameters:
 H expectation parameters
Returns:

 double jMEF.MultinomialFixedN.k ( PVector x )

Computes the carrier measure .

Parameters:
 x a point
Returns:

 double jMEF.MultinomialFixedN.KLD ( PVector LA, PVector LB )

Computes the Kullback-Leibler divergence between two Binomial distributions.

Parameters:
 LA source parameters LB source parameters
Returns:

 PVector jMEF.MultinomialFixedN.Lambda2Eta ( PVector L )

Converts source parameters to expectation parameters.

Parameters:
 L source parameters
Returns:
expectation parameters

 PVector jMEF.MultinomialFixedN.Lambda2Theta ( PVector L )

Converts source parameters to natural parameters.

Parameters:
 L source parameters
Returns:
natural parameters

 PVector jMEF.MultinomialFixedN.t ( PVector x )

Computes the sufficient statistic .

Parameters:
 x a point
Returns:

 PVector jMEF.MultinomialFixedN.Theta2Lambda ( PVector T )

Converts natural parameters to source parameters.

Parameters:
 T natural parameters
Returns:
source parameters

The documentation for this class was generated from the following file:

Generated on Mon Nov 23 15:46:26 2009 for jMEF by  1.5.9