de.lmu.ifi.dbs.elki.math.statistics.distribution

Class ChiSquaredDistribution

java.lang.Object

de.lmu.ifi.dbs.elki.math.statistics.distribution.AbstractDistribution

de.lmu.ifi.dbs.elki.math.statistics.distribution.GammaDistribution

de.lmu.ifi.dbs.elki.math.statistics.distribution.ChiSquaredDistribution

All Implemented Interfaces:

Distribution

public class ChiSquaredDistribution
extends GammaDistribution

Chi-Squared distribution (a specialization of the Gamma distribution).

Since:

0.5.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	ChiSquaredDistribution.Parameterizer Parameterization class

Field Summary

Fields inherited from class de.lmu.ifi.dbs.elki.math.statistics.distribution.GammaDistribution

EULERS_CONST, LANCZOS, MAX_ITERATIONS, NUM_PRECISION

Fields inherited from class de.lmu.ifi.dbs.elki.math.statistics.distribution.AbstractDistribution

random

Constructor Summary

Constructors

Constructor and Description
ChiSquaredDistribution(double dof) Constructor.
ChiSquaredDistribution(double dof, java.util.Random random) Constructor.
ChiSquaredDistribution(double dof, RandomFactory random) Constructor.

Method Summary

Modifier and Type	Method and Description
static double	cdf(double val, double dof) The CDF, static version.
static double	logpdf(double x, double dof) Chi-Squared distribution PDF (with 0.0 for x < 0)
static double	pdf(double x, double dof) Chi-Squared distribution PDF (with 0.0 for x < 0)
static double	quantile(double x, double dof) Return the quantile function for this distribution Reference: D.
java.lang.String	toString() Simple toString explaining the distribution parameters.

Methods inherited from class de.lmu.ifi.dbs.elki.math.statistics.distribution.GammaDistribution

cdf, cdf, chisquaredProbitApproximation, digamma, gamma, gammaQuantileNewtonRefinement, getK, getTheta, logcdf, logGamma, logpdf, logpdf, logregularizedGammaP, nextRandom, nextRandom, pdf, pdf, quantile, quantile, regularizedGammaP, regularizedGammaQ, trigamma

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

ChiSquaredDistribution

public ChiSquaredDistribution(double dof)

Constructor.

Parameters:

dof - Degrees of freedom.

ChiSquaredDistribution

public ChiSquaredDistribution(double dof,
                              java.util.Random random)

Constructor.

Parameters:

dof - Degrees of freedom.

random - Random generator.

ChiSquaredDistribution

public ChiSquaredDistribution(double dof,
                              RandomFactory random)

Constructor.

Parameters:

dof - Degrees of freedom.

random - Random generator.

Method Detail

cdf

public static double cdf(double val,
                         double dof)

The CDF, static version.

Parameters:

val - Value

dof - Degrees of freedom.

Returns:

cdf value

pdf

public static double pdf(double x,
                         double dof)

Chi-Squared distribution PDF (with 0.0 for x < 0)

Parameters:

x - query value

dof - Degrees of freedom.

Returns:

probability density

logpdf

public static double logpdf(double x,
                            double dof)

Chi-Squared distribution PDF (with 0.0 for x < 0)

Parameters:

x - query value

dof - Degrees of freedom.

Returns:

probability density

quantile

@Reference(authors="D. J. Best, D. E. Roberts",
           title="Algorithm AS 91: The percentage points of the \u03c7\u00b2 distribution",
           booktitle="Journal of the Royal Statistical Society. Series C (Applied Statistics)",
           url="https://doi.org/10.2307/2347113",
           bibkey="doi:10.2307/2347113")
public static double quantile(double x,
                                                                                                                                                                                                                                                                                                                                                                     double dof)

Return the quantile function for this distribution

Reference:

D. J. Best, D. E. Roberts
Algorithm AS 91: The percentage points of the χ² distribution
Journal of the Royal Statistical Society. Series C (Applied Statistics)

Parameters:

x - Quantile

dof - Degrees of freedom

Returns:

quantile position

toString

public java.lang.String toString()

Description copied from class: GammaDistribution

Simple toString explaining the distribution parameters. Used in producing a model description.

Specified by:

toString in interface Distribution

Overrides:

toString in class GammaDistribution

Returns:

description