Open Access
2016 Large deviations for homozygosity
Donald A. Dawson, Shui Feng
Electron. Commun. Probab. 21: 1-8 (2016). DOI: 10.1214/16-ECP34


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.


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Donald A. Dawson. Shui Feng. "Large deviations for homozygosity." Electron. Commun. Probab. 21 1 - 8, 2016.


Received: 17 August 2016; Accepted: 29 November 2016; Published: 2016
First available in Project Euclid: 8 December 2016

zbMATH: 1352.60037
MathSciNet: MR3592205
Digital Object Identifier: 10.1214/16-ECP34

Primary: 65G17 , 65G60

Keywords: Dirichlet process , homozygosity , large deviation , Poisson-Dirichlet distribution

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