Why does the IWISHRND function in the Statistics Toolbox 5.0.2 (R14SP2) return unexpected results?

When I enter the following commands:

s = [2 1 0.5;1 2 1;0.5 1 2];

for k=1:5000

    d(:,:,k) = iwishrnd(s*96,100);

end

m = mean(d,3)

sd = std(d,0,3)

I receive the following output:

 m =

     2.6236    1.0813    0.4332

     1.0813    1.8743    0.7485

     0.4332    0.7485    1.5013

 sd =

     0.3864    0.2524    0.2072

     0.2524    0.2703    0.1903

     0.2072    0.1903    0.2206

The expected value of the draws should be the same as "s." Also, the variance of the draws should be the same for each element along the diagonal.

Answer 1

[MathWorks Support Team]

This bug has been fixed in Release 14 Service Pack 3 (R14SP3). For previous product releases, read below for any possible workarounds:

We have verified that there is a bug in the Statistics Toolbox 5.0.2 (R14SP2) when using the IWISHRND function to generate an inverse Wishart distribution.

To work around this issue, use:

inv(wishrnd(inv(S),100));           % if you do it just once

D = chol(inv(S)); iwishrnd(S,100,D) % for repeated calls re-using D