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October 2008 Moderate deviations for Poisson–Dirichlet distribution
Shui Feng, Fuqing Gao
Ann. Appl. Probab. 18(5): 1794-1824 (October 2008). DOI: 10.1214/07-AAP501


The Poisson–Dirichlet distribution arises in many different areas. The parameter θ in the distribution is the scaled mutation rate of a population in the context of population genetics. The limiting case of θ approaching infinity is practically motivated and has led to new, interesting mathematical structures. Laws of large numbers, fluctuation theorems and large-deviation results have been established. In this paper, moderate-deviation principles are established for the Poisson–Dirichlet distribution, the GEM distribution, the homozygosity, and the Dirichlet process when the parameter θ approaches infinity. These results, combined with earlier work, not only provide a relatively complete picture of the asymptotic behavior of the Poisson–Dirichlet distribution for large θ, but also lead to a better understanding of the large deviation problem associated with the scaled homozygosity. They also reveal some new structures that are not observed in existing large-deviation results.


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Shui Feng. Fuqing Gao. "Moderate deviations for Poisson–Dirichlet distribution." Ann. Appl. Probab. 18 (5) 1794 - 1824, October 2008.


Published: October 2008
First available in Project Euclid: 30 October 2008

zbMATH: 1156.60018
MathSciNet: MR2462549
Digital Object Identifier: 10.1214/07-AAP501

Primary: 60F10
Secondary: 92D10

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.18 • No. 5 • October 2008
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