文章基本信息

标题：Large deviations for homozygosity
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作者：Donald A. Dawson ; Shui Feng
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2016
卷号：21
DOI：10.1214/16-ECP34
语种：English
出版社：Electronic Communications in Probability
摘要：For any $m \geq 2$, the homozygosity of order $m$ of a population is the probability that a sample of size $m$ from the population consists of the same type individuals. Assume that the type proportions follow Kingman’s Poisson-Dirichlet distribution with parameter $\theta $. In this paper we establish the large deviation principle for the naturally scaled homozygosity as $\theta $ tends to infinity. The key step in the proof is a new representation of the homozygosity. This settles an open problem raised in [1]. The result is then generalized to the two-parameter Poisson-Dirichlet distribution.
关键词：Dirichlet process;Poisson-Dirichlet distribution;homozygosity;large deviation