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

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

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.

Suggested Citation

  • Changyong Feng & Hongyue Wang & Yu Han & Yinglin Xia & Naiji Lu & Xin M. Tu, 2015. "Some Theoretical Comparisons of Negative Binomial and Zero-Inflated Poisson Distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(15), pages 3266-3277, August.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:15:p:3266-3277
    DOI: 10.1080/03610926.2013.823203
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