edu.northwestern.at.utils.math.distributions
Class Beta

java.lang.Object
  edu.northwestern.at.utils.math.distributions.Beta

public class Beta
extends java.lang.Object

Beta distribution functions.

Constructor Summary

protected

Beta() Make class non-instantiable but inheritable.

Method Summary

static double	beta(double a, double b) Beta function.
static double	incompleteBeta(double x, double alpha, double beta) Cumulative probability density function for the incomplete beta function.
static double	incompleteBeta(double x, double alpha, double beta, int dPrec) Cumulative probability density function for the incomplete beta function.
static double	incompleteBetaInverse(double p, double alpha, double beta) Compute value of inverse incomplete beta distribution.
static double	logBeta(double a, double b) Log of the Beta distribution.

Methods inherited from class java.lang.Object

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

Constructor Detail

Beta

protected Beta()

Make class non-instantiable but inheritable.

Method Detail

logBeta

public static double logBeta(double a,
                             double b)

Log of the Beta distribution.

Parameters:

a -

b -

Returns:

Log of the Beta distribution for specofied parameters.

The log of the beta distribution is calculated from the log of the gamma distribution using the following relationship:

logBeta(a,b) = logGamma(a) + logGamma(b) - logGamma( a + b )

beta

public static double beta(double a,
                          double b)
                   throws java.lang.ArithmeticException

Beta function.

Parameters:

a -

b -

Returns:

Beta distribution for specified arguments.

The beta distribution value is calculated from the gamma distribution using the following relationship:

Beta(a,b) = ( Gamma(a) * Gamma(b) ) / Gamma( a + b )

Throws:

java.lang.ArithmeticException

incompleteBeta

public static double incompleteBeta(double x,
                                    double alpha,
                                    double beta,
                                    int dPrec)
                             throws java.lang.IllegalArgumentException

Cumulative probability density function for the incomplete beta function.

Parameters:

x - Upper percentage point of incomplete beta probability density function

alpha - First shape parameter

beta - Second shape parameter

dPrec - Digits of precision desired (1 < dPrec < Constants.MAXPREC)

Returns:

Cumulative probability density function value.

Throws:

java.lang.IllegalArgumentException - if x <= 0 or a <= 0 or b <= 0 .

The continued fraction expansion as given by Abramowitz and Stegun (1964) is used. This method works well unless the minimum of (alpha, beta) exceeds about 70000. For most common values the result will be accurate to about 14 decimal digits.

incompleteBeta

public static double incompleteBeta(double x,
                                    double alpha,
                                    double beta)
                             throws java.lang.IllegalArgumentException

Cumulative probability density function for the incomplete beta function.

Parameters:

x - Upper percentage point of incomplete beta probability density function

alpha - First shape parameter

beta - Second shape parameter

Returns:

Cumulative probability density function value.

Throws:

java.lang.IllegalArgumentException - if x <= 0 or a <= 0 or b <= 0 .

The continued fraction expansion as given by Abramowitz and Stegun (1964) is used. This method works well unless the minimum of (alpha, beta) exceeds about 70000. For most common values the result will be accurate to about 14 decimal digits.

incompleteBetaInverse

public static double incompleteBetaInverse(double p,
                                           double alpha,
                                           double beta)
                                    throws java.lang.IllegalArgumentException

Compute value of inverse incomplete beta distribution.

Parameters:

p - Probability value.

alpha - First shape parameter.

beta - Second shape parameter.

Returns:

Percentage point of inverse beta distribution.

Throws:

java.lang.IllegalArgumentException - if alpha <= 0 or beta <= 0 or p <= 0 or p >= 1 .