@article {18235,
	title = {COM-negative binomial distribution: modeling overdispersion and ultrahigh zero-inflated count data},
	journal = {Frontiers of Mathematics in China},
	volume = {13},
	year = {2018},
	pages = { 967{\textendash}998},
	abstract = {We focus on the COM-type negative binomial distribution with three parameters, which belongs to COM-type (a,\&nbsp;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{\textquoteright}s identity are given for theoretical properties. COM-negative binomial distribution was applied to overdispersion and ultrahigh zero-inflated data sets. With the aid of ratio regression, we employ maximum likelihood method to estimate the parameters and the goodness-of-fit are evaluated by the discrete Kolmogorov-Smirnov test.},
	url = {https://link.springer.com/article/10.1007\%2Fs11464-018-0714-z},
	author = {Huiming Zhang and Kai Tan and Li Bo}
}
