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

Part of: Combinatorial probability Limit theorems

Published online by Cambridge University Press:  01 July 2016

Fang Xu
Fang Xu*
Affiliation:
McMaster University
*
∗ Postal address: Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada. Email address: xuf23@math.mcmaster.ca
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Abstract

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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.

Keywords

Poisson-Dirichlet distributiontwo-parameter Poisson-Dirichlet distributionsampling formulaLaplace transform

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 60F05: Central limit and other weak theorems
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 4 , December 2011 , pp. 1066 - 1085
Copyright
Copyright © Applied Probability Trust 2011 

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