Large deviation analysis for a Poisson model on thecoverage problem

GAO Fu-qing; ZHAO Xin-qiu

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Large deviation analysis for a Poisson model on thecoverage problem

GAO Fu-qing 1 * #,ZHAO Xin-qiu 2

1.School of Mathematics and Statistics, Wuhan University, Wuhan 430072

2.Department of Applied Mathematics, The Hong Kong PolytechnicUniversity, Hong Kong

*Correspondence author

#Submitted by

Subject:

Funding: Specialized Research Fund for the Doctoral Program of Higher Education of China （No.20130141110076）, National Natural Science Foundation of China（No.11571262）

Opened online:23 May 2017

Accepted by: none

Citation: GAO Fu-qing,ZHAO Xin-qiu.Large deviation analysis for a Poisson model on thecoverage problem[OL]. [23 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4735015

Mao and Lindsay proposed a Poisson model for the coverageproblem and studied the Good-Turing estimators associated with themodel. The Poisson model provides a simplified framework forinferring any general abundance-$mathcal K$ coverage. In thispaper, we prove that the Good-Turing estimators satisfy largedeviation principle and moderate deviation principle, which yieldrates of convergence and a useful method for constructing asymptoticconfidence intervals.

Keywords:Large deviation principle; Moderate deviation principle; Poisson mixture; Sample coverage

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