The sampling formula and Laplace transform associated with the two-parameter Poisson-Dirichlet distribution

Abstract

In this paper we investigate the relationship between the sampling formula and Laplace transform associated with the two-parameter Poisson-Dirichlet distribution. We conclude that they are equivalent to determining the corresponding infinite-dimensional distribution. With these tools, a central limit theorem is established associated with the infinitely-many-neutral-alleles model at any fixed time. We also obtain the probability generating function of random sampling from a generalized two-parameter diffusion process. At the end of the paper a selection case is considered.