Beta-hypergeometric probability distribution on symmetric matrices

In this paper, we first give some properties based on independence relations between matrix beta random variables of the first kind and of the second kind which are satisfied under a condition on the parameters of the distributions. We then show that with the matrix beta-hypergeometric distribution, the properties established for the beta distribution are satisfied without any condition on the parameters. The results involve many remarkable properties of the zonal polynomials with matrix arguments and the use of random matrix continued fractions. As a particular case, we get the results established for the real beta-hypergeometric distributions by Asci, Letac and Piccioni [1].