混合幂级数分布及其应用
Mixture Power Series Distribution and Its Application

幂级数分布是一类广泛的概率分布，包括了常用的二项分布、Poisson分布等多种离散型概率分布。由若干个幂级数分布构成的混合幂级数分布，能够灵活地拟合如零膨胀、0~k膨胀以及其他多种膨胀类型的计数数据。本文基于EM算法给出了混合幂级数分布的参数估计，并对混合幂级数分布的特例0~1膨胀Poisson分布进行了说明，通过实例分析，说明混合幂级数分布及估计方法是适用的。
Power series distribution is a kind of extensive probability distribution, including the commonly used binomial distribution, Poisson distribution and other many discrete distributions. The mixed power series distribution, which is composed of multiple power series distributions, can flexibly fit the counting data of zero inflated, 0~k inflated and other many of inflated types. In this paper, the parameter estimation of mixed power series distribution is given based on EM algorithm, and the special case of mixed power series distribution 0~1 inflated Poisson distribution is explained. Through case analysis, the mixed power series distribution and estimation method are proved to be applicable.