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. Beside...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 zeroinflated 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.展开更多
基金The proposed COM-negative binomial distribution of this work was as early as conceptualized in December, 2014 when the authors saw the online version of [15]. The authors want to thank Prof. R. KShler for mailing the valuable encyclopedia of discrete univariate distributions [39] to them. This work was partly supported by the National Natural Science Foundation of China （Grant No. 11201165）.
文摘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 zeroinflated 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.
