statalign.utils
Class GammaDistribution

java.lang.Object
  org.apache.commons.math3.distribution.AbstractRealDistribution
      statalign.utils.GammaDistribution

All Implemented Interfaces:

java.io.Serializable, org.apache.commons.math3.distribution.RealDistribution

public class GammaDistribution
extends org.apache.commons.math3.distribution.AbstractRealDistribution

Implementation of the Gamma distribution. Adapted from Apache Commons Math v3.0, but modified to use Utils.generator as the random number source.

Version:

$Id: GammaDistribution.java 1382904 2012-09-10 14:47:45Z luc $

See Also:

Gamma distribution (Wikipedia), Gamma distribution (MathWorld), Serialized Form

Field Summary

static double

DEFAULT_INVERSE_ABSOLUTE_ACCURACY Default inverse cumulative probability accuracy.

Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

SOLVER_DEFAULT_ABSOLUTE_ACCURACY

Constructor Summary

GammaDistribution(double shape, double scale)
Creates a new gamma distribution with specified values of the shape and scale parameters.

GammaDistribution(double shape, double scale, double inverseCumAccuracy)
Creates a new gamma distribution with specified values of the shape and scale parameters.

GammaDistribution(org.apache.commons.math3.random.RandomGenerator rng, double shape, double scale, double inverseCumAccuracy)
Creates a Gamma distribution.

Method Summary

double	cumulativeProbability(double x) The implementation of this method is based on: Chi-Squared Distribution, equation (9).
double	density(double x)
double	getAlpha() Deprecated. as of version 3.1, getShape() should be preferred. This method will be removed in version 4.0.
double	getBeta() Deprecated. as of version 3.1, getScale() should be preferred. This method will be removed in version 4.0.
double	getNumericalMean() For shape parameter alpha and scale parameter beta, the mean is alpha * beta.
double	getNumericalVariance() For shape parameter alpha and scale parameter beta, the variance is alpha * beta^2.
double	getScale() Returns the scale parameter of this distribution.
double	getShape() Returns the shape parameter of this distribution.
double	getSupportLowerBound() The lower bound of the support is always 0 no matter the parameters.
double	getSupportUpperBound() The upper bound of the support is always positive infinity no matter the parameters.
boolean	isSupportConnected() The support of this distribution is connected.
boolean	isSupportLowerBoundInclusive()
boolean	isSupportUpperBoundInclusive()
double	sample() This implementation uses the following algorithms: For 0 < shape < 1: Ahrens, J.

Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

cumulativeProbability, inverseCumulativeProbability, probability, probability, reseedRandomGenerator, sample

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Default inverse cumulative probability accuracy.

Since:

2.1

See Also:

Constant Field Values

Constructor Detail

GammaDistribution

public GammaDistribution(double shape,
                         double scale)
                  throws org.apache.commons.math3.exception.NotStrictlyPositiveException

Creates a new gamma distribution with specified values of the shape and scale parameters.

Parameters:

shape - the shape parameter

scale - the scale parameter

Throws:

org.apache.commons.math3.exception.NotStrictlyPositiveException - if shape <= 0 or scale <= 0.

GammaDistribution

public GammaDistribution(double shape,
                         double scale,
                         double inverseCumAccuracy)
                  throws org.apache.commons.math3.exception.NotStrictlyPositiveException

Creates a new gamma distribution with specified values of the shape and scale parameters.

Parameters:

shape - the shape parameter

scale - the scale parameter

inverseCumAccuracy - the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).

Throws:

org.apache.commons.math3.exception.NotStrictlyPositiveException - if shape <= 0 or scale <= 0.

Since:

2.1

GammaDistribution

public GammaDistribution(org.apache.commons.math3.random.RandomGenerator rng,
                         double shape,
                         double scale,
                         double inverseCumAccuracy)
                  throws org.apache.commons.math3.exception.NotStrictlyPositiveException

Creates a Gamma distribution.

Parameters:

rng - Random number generator.

shape - the shape parameter

scale - the scale parameter

inverseCumAccuracy - the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).

Throws:

org.apache.commons.math3.exception.NotStrictlyPositiveException - if shape <= 0 or scale <= 0.

Since:

3.1

Method Detail

getAlpha

@Deprecated
public double getAlpha()

Deprecated. as of version 3.1, getShape() should be preferred. This method will be removed in version 4.0.

Returns the shape parameter of this distribution.

Returns:

the shape parameter

getShape

public double getShape()

Returns the shape parameter of this distribution.

Returns:

the shape parameter

getBeta

@Deprecated
public double getBeta()

Deprecated. as of version 3.1, getScale() should be preferred. This method will be removed in version 4.0.

Returns the scale parameter of this distribution.

Returns:

the scale parameter

getScale

public double getScale()

Returns the scale parameter of this distribution.

Returns:

the scale parameter

density

public double density(double x)

cumulativeProbability

public double cumulativeProbability(double x)

The implementation of this method is based on:

• Chi-Squared Distribution, equation (9).
• Casella, G., & Berger, R. (1990). Statistical Inference. Belmont, CA: Duxbury Press.

getNumericalMean

public double getNumericalMean()

For shape parameter alpha and scale parameter beta, the mean is alpha * beta.

getNumericalVariance

public double getNumericalVariance()

For shape parameter alpha and scale parameter beta, the variance is alpha * beta^2.

Returns:

getSupportLowerBound

public double getSupportLowerBound()

The lower bound of the support is always 0 no matter the parameters.

Returns:

lower bound of the support (always 0)

getSupportUpperBound

public double getSupportUpperBound()

The upper bound of the support is always positive infinity no matter the parameters.

Returns:

upper bound of the support (always Double.POSITIVE_INFINITY)

isSupportLowerBoundInclusive

public boolean isSupportLowerBoundInclusive()

isSupportUpperBoundInclusive

public boolean isSupportUpperBoundInclusive()

isSupportConnected

public boolean isSupportConnected()

The support of this distribution is connected.

Returns:

true

sample

public double sample()

This implementation uses the following algorithms:

For 0 < shape < 1:
Ahrens, J. H. and Dieter, U., Computer methods for sampling from gamma, beta, Poisson and binomial distributions. Computing, 12, 223-246, 1974.

For shape >= 1:
Marsaglia and Tsang, A Simple Method for Generating Gamma Variables. ACM Transactions on Mathematical Software, Volume 26 Issue 3, September, 2000.

Specified by:

sample in interface org.apache.commons.math3.distribution.RealDistribution

Overrides:

sample in class org.apache.commons.math3.distribution.AbstractRealDistribution

Returns:

random value sampled from the Gamma(shape, scale) distribution