RESEARCH ARTICLE

COM-negative binomial distribution: modeling overdispersion and ultrahigh zero-inated count data

  • Huiming ZHANG , 1 ,
  • Kai TAN 2 ,
  • Bo LI 3
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  • 1. School of Mathematical Sciences and Center for Statistical Science, Peking University, Beijing 100871, China
  • 2. Department of Statistics, University of Kentucky, Lexington, KY 40508, USA
  • 3. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received date: 20 Jun 2017

Accepted date: 05 Jul 2018

Published date: 14 Aug 2018

Copyright

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature

Abstract

We focus on the COM-type negative binomial distribution with three parameters, which belongs to COM-type (a, b, 0) class distributions and family of equilibrium distributions of arbitrary birth-death process. Besides, we show abundant distributional properties such as overdispersion and underdispersion, log-concavity, log-convexity (infinite divisibility), pseudo compound Poisson, stochastic ordering, and asymptotic approximation. Some characterizations including sum of equicorrelated geometrically distributed random variables, conditional distribution, limit distribution of COM-negative hypergeometric distribution, and Stein's identity are given for theoretical properties. COM-negative binomial distribution was applied to overdispersion and ultrahigh zero-inated data sets. With the aid of ratio regression, we employ maximum likeli-hood method to estimate the parameters and the goodness-of-fit are evaluated by the discrete Kolmogorov-Smirnov test.

Cite this article

Huiming ZHANG , Kai TAN , Bo LI . COM-negative binomial distribution: modeling overdispersion and ultrahigh zero-inated count data[J]. Frontiers of Mathematics in China, 2018 , 13(4) : 967 -998 . DOI: 10.1007/s11464-018-0714-z

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