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.
"The sampling formula and Laplace transform associated with the two-parameter Poisson-Dirichlet distribution." Adv. in Appl. Probab. 43 (4) 1066 - 1085, Decemmber 2011. https://doi.org/10.1239/aap/1324045699