On Pearson–Kotz Dirichlet distributions

In this paper, we discuss some basic distributional and asymptotic properties of the Pearson–Kotz Dirichlet multivariate distributions. These distributions, which appear as the limit of conditional Dirichlet random vectors, possess many appealing properties and are interesting from theoretical as well as applied points of view. We illustrate an application concerning the approximation of the joint conditional excess distribution of elliptically symmetric random vectors.