Power Series Distribution With Expansion Model

Counting data is a kind of important data type,which has always been the focus and hotspot in statistics.Widely exists in the engineering,medicine,actuarial insurance,population,transportation and other fields,the commonly Poisson distribution and negative binomial distribution models are used to fit this data,Power series distribution,including the common binomial distribution,Poisson distribution,negative binomial distribution,geometric distribution and other distributions,belongs to a wide range of discrete probability distribution family,widely is generalized to or correction of power series of general distribution,such as generalized Poisson distribution and generalized negative binomial distribution and so on all belong to this type of distribution of power series distribution and the related contents of research on it is of great significance.On the basis of power series distribution some properties of zero expansion power series distribution are discussed in this paper,and the moment estimation method and maximum likelihood estimation of distribution,some special cases of zero expansion distribution are discussed and an application example of population migration is given.In recent years,on the basis of the zero inflated model,in order to better fit the data,the counting model of 0-k inflated and the multi-point inflated model are proposed,0-1 inflated count data has been mostly studied as an example.The mixed power series distribution composed of multiple power series distributions can flexibly fit various types of expansion data,including 0-k inflated and counting data of multi-point inflated.In this paper,the parameter estimation of the mixed power series distribution is studied,the EM algorithm is given,and the 0-1 inflated Poisson distribution is taken as a special case of the mixed power series distribution for parameter estimation.