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Asymptotic Results for the Two-parameter Poisson-Dirichlet Distribution

Abstract

The two-parameter Poisson-Dirichlet distribution is the law of a sequence of decreasing nonnegative random variables with total sum one. It can be constructed from stable and Gamma subordinators with the two-parameters, α\alpha and θ\theta, corresponding to the stable component and Gamma component respectively. The moderate deviation principles are established for the two-parameter Poisson-Dirichlet distribution and the corresponding homozygosity when θ\theta approaches infinity, and the large deviation principle is established for the two-parameter Poisson-Dirichlet distribution when both α\alpha and θ\theta approach zero.

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