Exact simulation of two-parameter Poisson-Dirichlet random variables

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