jdistlib

Class Wishart

java.lang.Object

jdistlib.Wishart

public class Wishart
extends java.lang.Object

Wishart distribution By: Roby Joehanes

Constructor Summary

Constructors

Constructor and Description
Wishart()

Method Summary

Modifier and Type	Method and Description
static double[][]	random(double n, double[][] L, RandomEngine rand) Sample Wishart distribution with n degree of freedom and LL' scale parameter.

Methods inherited from class java.lang.Object

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

Constructor Detail

Wishart

public Wishart()

Method Detail

random

public static final double[][] random(double n,
                                      double[][] L,
                                      RandomEngine rand)

Sample Wishart distribution with n degree of freedom and LL' scale parameter. Wishart distribution is multivariate generalization of Gamma distribution. Remember that Gamma distribution is a generalization of both Chi-square and exponential distribution.

I use L instead of the usual V to denote the scale parameter. Note that V = LL'. Compute L using Cholesky decomposition. L is a lower triangular matrix.

The algorithm described here is due to:
Smith, W. B. and Hocking, R. R.; Algorithm AS 53: Wishart Variate Generator, Applied Statistician, v.21(341--345), 1972 http://www.jstor.org/stable/2346290

See also: Gentle, J. E., Random Number Generation and Monte Carlo Methods, 2nd ed., Springer-Verlag, 2003, pp. 199

Note: If you want to generate an inverse-wishart distribution, simply generate a matrix from Wishart distribution and invert it.

Parameters:

n - degree of freedom

L - square matrix of d x d, lower triangular Cholesky factor of sigma matrix

rand - Randomizer

Returns:

square matrix of d x d