Exact simulation of two-parameter Poisson-Dirichlet random variables

Consider a random vector (V1, . . . , Vn) where {Vk}k=1,...,n are the first n components of a two-parameter Poisson-Dirichlet distribution P D(α, θ). In this paper, we derive a decomposition for the components of the random vector, and propose an exact simulation algorithm to sample from the random vector. Moreover, a special case arises when θ/α is a positive integer, for which we present a very fast modified simulation algorithm using a compound geometric representation of the decomposition. Numerical examples are provided to illustrate the accuracy and effectiveness of our algorithms.