Some Theoretical Comparisons of Negative Binomial and Zero-Inflated Poisson Distributions

Changyong Feng, Hongyue Wang, Yu Han, Yinglin Xia, Naiji Lu and Xin M. Tu

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 15, 3266-3277

Abstract: In this article, we compare the zero-inflated Poisson (ZIP) and negative binomial (NB) distributions based on three most important criteria: the probability of zero, the mean value, and the variance. Our results show that with same mean value and variance, the ZIP distribution always has a larger probability of zeros; with same mean value and probability of zeros, the NB distribution always has a larger variance; and with same variance and probability of zeros, the ZIP distribution always has a larger mean value. We also study the properties of Vuong test in model selection in three cases by simulations.

Date: 2015
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DOI: 10.1080/03610926.2013.823203

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