Asymptotic Results for the Two-parameter Poisson-Dirichlet Distribution

Shui Feng; Fuqing Gao

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arXiv · 0906.2217

Asymptotic Results for the Two-parameter Poisson-Dirichlet Distribution

Shui Feng·Fuqing Gao

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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, $α$ and $θ$, 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 $θ$ approaches infinity, and the large deviation principle is established for the two-parameter Poisson-Dirichlet distribution when both $α$ and $θ$ approach zero.

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Shui Feng, Fuqing Gao. 2009-06-11. Asymptotic Results for the Two-parameter Poisson-Dirichlet Distribution. https://arxiv.org/abs/0906.2217

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