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Asymptotic Results for the Twoparameter PoissonDirichlet Distribution
, 906
"... The twoparameter PoissonDirichlet 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 twoparameters, α and θ, corresponding to the stable component and Gamma component respectively. ..."
Abstract

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The twoparameter PoissonDirichlet 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 twoparameters, α and θ, corresponding to the stable component and Gamma component respectively. The moderate deviation principles are established for the twoparameter PoissonDirichlet distribution and the corresponding homozygosity when θ approaches infinity, and the large deviation principle is established for the twoparameter PoissonDirichlet distribution when both α and θ approach zero.
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, 2008
"... The behavior of the PoissonDirichlet distribution with small mutation rate is studied through large deviations. The structure of the rate function indicates that the number of alleles is finite at the instant when mutation appears. The large deviation results are then used to study the asymptotic b ..."
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The behavior of the PoissonDirichlet distribution with small mutation rate is studied through large deviations. The structure of the rate function indicates that the number of alleles is finite at the instant when mutation appears. The large deviation results are then used to study the asymptotic behavior of the homozygosity, and the PoissonDirichlet distribution with symmetric selection. The latter shows that several alleles can coexist when selection intensity goes to infinity in a particular way as the mutation rate approaches zero.