Exact simulation of two-parameter Poisson-Dirichlet random variables

Consider a random vector $(V_{1}, \dots , V_{n})$ where $\{V_{k}\}_{k=1, \dots , n}$ are the first $n$ components of a two-parameter Poisson-Dirichlet distribution $PD(\alpha , \theta )$. 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 $\theta /\alpha $ 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.