# jMEF.UnivariateGaussian Class Reference

List of all members.

## Public Member Functions

double F (PVector T)
Computes the log normalizer .
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 LP, PVector LQ)
Computes the Kullback-Leibler divergence between two univariate Gaussian distributions.

## Static Public Member Functions

static double Rand (double mu, double sigma)
Box-Muller transform/generator.
static double Rand ()
Box-Muller transform/generator.

Version:
1.0

## Description

The univariate Gaussian distribution 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 univariate Gaussian distribution as a member of an exponential family.

## Parameters

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

## Member Function Documentation

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

Computes the density value .

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

 PVector jMEF.UnivariateGaussian.drawRandomPoint ( PVector L )

Draws a point from the considered distribution.

Parameters:
 L source parameters
Returns:
a point

 PVector jMEF.UnivariateGaussian.Eta2Lambda ( PVector H )

Converts expectation parameters to source parameters.

Parameters:
 H natural parameters
Returns:
source parameters

 double jMEF.UnivariateGaussian.F ( PVector T )

Computes the log normalizer .

Parameters:
 T parameters
Returns:

 double jMEF.UnivariateGaussian.G ( PVector H )

Computes .

Parameters:
 H expectation parameters
Returns:

 PVector jMEF.UnivariateGaussian.gradF ( PVector T )

Computes .

Parameters:
 T natural parameters
Returns:

 PVector jMEF.UnivariateGaussian.gradG ( PVector H )

Computes .

Parameters:
 H expectation parameters
Returns:

 double jMEF.UnivariateGaussian.k ( PVector x )

Computes the carrier measure .

Parameters:
 x a point
Returns:

 double jMEF.UnivariateGaussian.KLD ( PVector LP, PVector LQ )

Computes the Kullback-Leibler divergence between two univariate Gaussian distributions.

Parameters:
 LP source parameters LQ source parameters
Returns:

 PVector jMEF.UnivariateGaussian.Lambda2Eta ( PVector L )

Converts source parameters to expectation parameters.

Parameters:
 L source parameters
Returns:
expectation parameters

 PVector jMEF.UnivariateGaussian.Lambda2Theta ( PVector L )

Converts source parameters to natural parameters.

Parameters:
 L source parameters
Returns:
natural parameters

 static double jMEF.UnivariateGaussian.Rand ( ) [static]

Box-Muller transform/generator.

Returns:
where

 static double jMEF.UnivariateGaussian.Rand ( double mu, double sigma ) [static]

Box-Muller transform/generator.

Parameters:
 mu mean sigma variance
Returns:
where

 PVector jMEF.UnivariateGaussian.t ( PVector x )

Computes the sufficient statistic .

Parameters:
 x a point
Returns:

 PVector jMEF.UnivariateGaussian.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