A Comparison of Two Test Statistics for Poisson Overdispersion/Underdispersion

Hongyue Wang, Changyong Feng, Xinming Tu, Jeanne Kowalski

Department of Biostatistics & Bioinformatics, Rollins School of Public Health Winship Cancer Institute, Emory University 1365-B Clifton Rd. NE, Suite 4100, Room B4109, Atlanta, GA 30322.
Department of Biostatistics and Computational Biology, University of Rochester, 601 Elmwood Ave., Box 630, Rochester, NY 14642.

DOI: 10.4236/am.2012.37118                

Abstract

Within the family of zero-inflated Poisson distributions, the data has Poisson distribution if any only if the mean equals the variance. In this paper we compare two closely related test statistics constructed based on this idea. Our results show that although these two tests are asymptotically equivalent under the null hypothesis and are equally efficient, one test is always more efficient than the other one for small and medium sample sizes.

Keywords

Poisson Distribution; Over-Dispersion; Asymptotic Relative Efficiency

Conflicts of Interest

The authors declare no conflicts of interest.

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