If Wishart samples are generated by taking the sample covariance from Gaussian-distributed data and the degrees of freedom parameter is estimated by maximum likelihood, the maximum likelihood estimate is within the range expected. For instance, if p=10, N=1e5 and nu=15, then the ML estimate of nu is within 0.01 of 15.
By contrast, when using distributions.wishart.rnd to generate samples, the ML estimate of nu is ~17.
The sampler in distributions.wishart.rnd (as described in section 3: http://www.math.wustl.edu/~sawyer/hmhandouts/Wishart.pdf) is incorrectly implemented.
If Wishart samples are generated by taking the sample covariance from Gaussian-distributed data and the degrees of freedom parameter is estimated by maximum likelihood, the maximum likelihood estimate is within the range expected. For instance, if p=10, N=1e5 and nu=15, then the ML estimate of nu is within 0.01 of 15.
By contrast, when using distributions.wishart.rnd to generate samples, the ML estimate of nu is ~17.