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

Class BetaDistribution

java.lang.Object

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

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

All Implemented Interfaces:

Distribution

public class BetaDistribution
extends AbstractDistribution

Beta Distribution with implementation of the regularized incomplete beta function

Author:

Jan Brusis, Erich Schubert

Nested Class Summary

Nested Classes

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

Field Summary

Fields

Modifier and Type	Field and 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

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

random

Constructor Summary

Constructors

Constructor and Description
BetaDistribution(double a, double b) Constructor.
BetaDistribution(double a, double b, Random random) Constructor.
BetaDistribution(double a, double b, RandomFactory random) Constructor.

Method Summary

Methods

Modifier and Type	Method and 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)
static double	logpdf(double val, double alpha, double beta) Static version of the PDF of the beta distribution
double	nextRandom() 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	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".
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

BetaDistribution

public BetaDistribution(double a,
                double b,
                Random random)

Constructor.

Parameters:

a - shape Parameter a

b - shape Parameter b

random - Random generator

BetaDistribution

public BetaDistribution(double a,
                double b,
                RandomFactory random)

Constructor.

Parameters:

a - shape Parameter a

b - shape Parameter b

random - Random generator

Method Detail

pdf

public double pdf(double val)

Description copied from interface: Distribution

Return the density of an existing value

Parameters:

val - existing value

Returns:

distribution density

cdf

public double cdf(double x)

Description copied from interface: Distribution

Return the cumulative density function at the given value.

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.

Parameters:

x - Quantile to find

Returns:

Quantile position

nextRandom

public double nextRandom()

Description copied from interface: Distribution

Generate a new random value

Specified by:

nextRandom in interface Distribution

Overrides:

nextRandom in class AbstractDistribution

Returns:

new random value

toString

public String toString()

Description copied from interface: Distribution

Describe the distribution

Specified by:

toString in interface Distribution

Overrides:

toString in class 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

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