Syntax Supported by the IML Procedure and the iml Action

RANDDIRICHLET (N, Shape) ;

This function is supported by the IML procedure and the iml action.

The RANDDIRICHLET function is part of the IMLMLIB library. The RANDDIRICHLET function generates a random sample from a Dirichlet distribution, which is a multivariate generalization of the beta distribution.

The input parameters are as follows:

The RANDDIRICHLET function returns an matrix that contains N random draws from the Dirichlet distribution.

If with and follows a Dirichlet distribution with shape parameter , then

The following example generates 1,000 samples from a two-dimensional Dirichlet distribution. Each row of the returned matrix x is a row vector sampled from the Dirichlet distribution. The following example computes the sample mean and covariance and compares them with the expected values:

call randseed(1);
n = 1000;
Shape = {2, 1, 1};
x = RandDirichlet(n,Shape);
d = nrow(Shape)-1;
s = Shape[1:d];
Shape0 = sum(Shape);
Mean = s`/Shape0;
Cov = -s*s` / (Shape0##2*(Shape0+1));
/* replace diagonal elements with variance */
Variance = s#(Shape0-s) / (Shape0##2*(Shape0+1));
do i = 1 to d;
   Cov[i,i] = Variance[i];
end;

SampleMean = mean(x);
SampleCov = cov(x);
print SampleMean Mean, SampleCov Cov;

For further details about sampling from the Dirichlet distribution, see Kotz, Balakrishnan, and Johnson (2000); Gentle (2003); or Devroye (1986).