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October 2007 Large deviations associated with Poisson–Dirichlet distribution and Ewens sampling formula
Shui Feng
Ann. Appl. Probab. 17(5-6): 1570-1595 (October 2007). DOI: 10.1214/105051607000000230

Abstract

Several results of large deviations are obtained for distributions that are associated with the Poisson–Dirichlet distribution and the Ewens sampling formula when the parameter θ approaches infinity. The motivation for these results comes from a desire of understanding the exact meaning of θ going to infinity. In terms of the law of large numbers and the central limit theorem, the limiting procedure of θ going to infinity in a Poisson–Dirichlet distribution corresponds to a finite allele model where the mutation rate per individual is fixed and the number of alleles going to infinity. We call this the finite allele approximation. The first main result of this article is concerned with the relation between this finite allele approximation and the Poisson–Dirichlet distribution in terms of large deviations. Large θ can also be viewed as a limiting procedure of the effective population size going to infinity. In the second result a comparison is done between the sample size and the effective population size based on the Ewens sampling formula.

Citation

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Shui Feng. "Large deviations associated with Poisson–Dirichlet distribution and Ewens sampling formula." Ann. Appl. Probab. 17 (5-6) 1570 - 1595, October 2007. https://doi.org/10.1214/105051607000000230

Information

Published: October 2007
First available in Project Euclid: 3 October 2007

zbMATH: 1145.92025
MathSciNet: MR2358634
Digital Object Identifier: 10.1214/105051607000000230

Subjects:
Primary: 60F10
Secondary: 92D10

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.17 • No. 5-6 • October 2007
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