Package elki.math.statistics.distribution

Class BetaDistribution

java.lang.Object

elki.math.statistics.distribution.BetaDistribution

All Implemented Interfaces:

Distribution

public class BetaDistribution
extends java.lang.Object
implements Distribution

Beta Distribution with implementation of the regularized incomplete beta function

Since:

0.5.0

Author:

Jan Brusis, Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	BetaDistribution.Par	Parameterization class

Nested classes/interfaces inherited from interface elki.math.statistics.distribution.Distribution

Distribution.Parameterizer

Field Summary

Fields

Modifier and Type	Field	Description
private double	alpha	Shape parameter of beta distribution
private double	beta	Shape parameter of beta distribution
(package private) static double[]	GAUSSLEGENDRE_W	Weights for Gauss-Legendre quadrature
(package private) static double[]	GAUSSLEGENDRE_Y	Abscissas for Gauss-Legendre quadrature
private double	logbab	Log beta(a, b) cache
(package private) static double	NUM_PRECISION	Numerical precision to use
(package private) static double	SWITCH	Limit of when to switch to quadrature method

Constructor Summary

Constructors

Constructor	Description
BetaDistribution(double a, double b)	Constructor.

Method Summary

Modifier and Type	Method	Description
double	cdf(double x)	Return the cumulative density function at the given value.
static double	cdf(double val, double alpha, double beta)	Static version of the CDF of the beta distribution
static double	logBeta(double alpha, double beta)	Compute log beta(a,b)
double	logpdf(double val)	Return the log density of an existing value
static double	logpdf(double val, double alpha, double beta)	Static version of the PDF of the beta distribution
double	nextRandom(java.util.Random random)	Generate a new random value
double	pdf(double val)	Return the density of an existing value
static double	pdf(double val, double alpha, double beta)	Static version of the PDF of the beta distribution
double	quantile(double x)	Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.
static double	quantile(double p, double alpha, double beta)	Compute quantile (inverse cdf) for Beta distributions.
protected static double	rawQuantile(double p, double alpha, double beta, double logbeta)	Raw quantile function
static double	regularizedIncBeta(double x, double alpha, double beta)	Computes the regularized incomplete beta function I_x(a, b) which is also the CDF of the beta distribution.
protected static double	regularizedIncBeta(double x, double alpha, double beta, double logbab)	Computes the regularized incomplete beta function I_x(a, b) which is also the CDF of the beta distribution.
protected static double	regularizedIncBetaCF(double alpha, double beta, double x)	Returns the regularized incomplete beta function I_x(a, b) Includes the continued fraction way of computing, based on the book "Numerical Recipes".
protected static double	regularizedIncBetaQuadrature(double alpha, double beta, double x)	Returns the regularized incomplete beta function I_x(a, b) by quadrature, based on the book "Numerical Recipes".
java.lang.String	toString()	Describe the distribution

Methods inherited from class java.lang.Object

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

Field Detail

NUM_PRECISION

static final double NUM_PRECISION

Numerical precision to use

See Also:

Constant Field Values

SWITCH

static final double SWITCH

Limit of when to switch to quadrature method

See Also:

Constant Field Values

GAUSSLEGENDRE_Y

static final double[] GAUSSLEGENDRE_Y

Abscissas for Gauss-Legendre quadrature

GAUSSLEGENDRE_W

static final double[] GAUSSLEGENDRE_W

Weights for Gauss-Legendre quadrature

alpha

private final double alpha

Shape parameter of beta distribution

beta

private final double beta

Shape parameter of beta distribution

logbab

private double logbab

Log beta(a, b) cache

Constructor Detail

BetaDistribution

public BetaDistribution(double a,
                        double b)

Constructor.

Parameters:

a - shape Parameter a

b - shape Parameter b

Method Detail

pdf

public double pdf(double val)

Description copied from interface: Distribution

Return the density of an existing value

Specified by:

pdf in interface Distribution

Parameters:

val - existing value

Returns:

distribution density

logpdf

public double logpdf(double val)

Description copied from interface: Distribution

Return the log density of an existing value

Specified by:

logpdf in interface Distribution

Parameters:

val - existing value

Returns:

log distribution density

cdf

public double cdf(double x)

Description copied from interface: Distribution

Return the cumulative density function at the given value.

Specified by:

cdf in interface Distribution

Parameters:

x - existing value

Returns:

cumulative density

quantile

public double quantile(double x)

Description copied from interface: Distribution

Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.

Specified by:

quantile in interface Distribution

Parameters:

x - Quantile to find

Returns:

Quantile position

nextRandom

public double nextRandom(java.util.Random random)

Description copied from interface: Distribution

Generate a new random value

Specified by:

nextRandom in interface Distribution

Parameters:

random - Random number generator

Returns:

new random value

toString

public java.lang.String toString()

Description copied from interface: Distribution

Describe the distribution

Specified by:

toString in interface Distribution

Overrides:

toString in class java.lang.Object

Returns:

description

cdf

public static double cdf(double val,
                         double alpha,
                         double beta)

Static version of the CDF of the beta distribution

Parameters:

val - Value

alpha - Shape parameter a

beta - Shape parameter b

Returns:

cumulative density

pdf

public static double pdf(double val,
                         double alpha,
                         double beta)

Static version of the PDF of the beta distribution

Parameters:

val - Value

alpha - Shape parameter a

beta - Shape parameter b

Returns:

probability density

logpdf

public static double logpdf(double val,
                            double alpha,
                            double beta)

Static version of the PDF of the beta distribution

Parameters:

val - Value

alpha - Shape parameter a

beta - Shape parameter b

Returns:

probability density

logBeta

public static double logBeta(double alpha,
                             double beta)

Compute log beta(a,b)

Parameters:

alpha - Shape parameter a

beta - Shape parameter b

Returns:

Logarithm of result

regularizedIncBeta

public static double regularizedIncBeta(double x,
                                        double alpha,
                                        double beta)

Computes the regularized incomplete beta function I_x(a, b) which is also the CDF of the beta distribution. Based on the book "Numerical Recipes"

Parameters:

alpha - Parameter a

beta - Parameter b

x - Parameter x

Returns:

Value of the regularized incomplete beta function

regularizedIncBeta

protected static double regularizedIncBeta(double x,
                                           double alpha,
                                           double beta,
                                           double logbab)

Computes the regularized incomplete beta function I_x(a, b) which is also the CDF of the beta distribution. Based on the book "Numerical Recipes"

Parameters:

x - Parameter x

alpha - Parameter a

beta - Parameter b

logbab - Cached logBeta(alpha, beta)

Returns:

Value of the regularized incomplete beta function

regularizedIncBetaCF

protected static double regularizedIncBetaCF(double alpha,
                                             double beta,
                                             double x)

Returns the regularized incomplete beta function I_x(a, b) Includes the continued fraction way of computing, based on the book "Numerical Recipes".

Parameters:

alpha - Parameter a

beta - Parameter b

x - Parameter x

Returns:

result

regularizedIncBetaQuadrature

protected static double regularizedIncBetaQuadrature(double alpha,
                                                     double beta,
                                                     double x)

Returns the regularized incomplete beta function I_x(a, b) by quadrature, based on the book "Numerical Recipes".

Parameters:

alpha - Parameter a

beta - Parameter b

x - Parameter x

Returns:

result

quantile

public static double quantile(double p,
                              double alpha,
                              double beta)

Compute quantile (inverse cdf) for Beta distributions.

Parameters:

p - Probability

alpha - Shape parameter a

beta - Shape parameter b

Returns:

Probit for Beta distribution

rawQuantile

protected static double rawQuantile(double p,
                                    double alpha,
                                    double beta,
                                    double logbeta)

Raw quantile function

Parameters:

p - P, must be 0 < p <= .5

alpha - Alpha

beta - Beta

logbeta - log Beta(alpha, beta)

Returns:

Position