About: Poisson-Dirichlet distribution

In probability theory, a branch of mathematics Poisson-Dirichlet distributions are probability distributions on the set of nonnegative, non-decreasing sequences with sum 1, depending on two parameters and . It can be defined as follows. One considers independent random variables such that follows the beta distribution of parameters and . Then, the Poisson-Dirichlet distribution of parameters and is the law of the random decreasing sequence containing and the products . This definition is due to and Marc Yor. It generalizes Kingman's law, which corresponds to the particular case .