Application Of Hypergeometric Series In The Inverse Moments Of Special Discrete Distribution

In this paper,we obtain the inverse moments expressions for some discrete distri-bution using the method of generalized hypergeometric series,including generalized ge-ometric distribution,generalized Polya Eggenberger of the first kind distribution,Katz distribution,Lagrangian Katz distribution.At the same time,extension of generalized hy-pergeometric series to obtain a new generalized hypergeometric,and the inverse moments and factorial moments of some discrete distribution are obtained,mainly the generalized Polya Eggenberger of the second kind distribution,the linear function negative binomial distribution,the Lagrangian Katz distribution.It shows an important role of the hyper-geometric series in the calculation of the inverse moments.Chapter 1,we briefly introduce the research background of combinatorics,probability theory,the inverse moment of probability distribution and the research status at home and abroad.Chapter 2:Based on the generalized hypergeometric series to obtain the inverse moments and factorial moments for some discrete distribution,mainly the generalized geometric distribution,generalized Polya Eggenberger of the first kind distribution,Katz distribution,Lagrangian Katz distribution.Chapter 3:The extension of generalized hypergeometric series to obtain a new gen-eralized hypergeometric,and the inverse moments and factorial moments of some discrete distribution are obtained,mainly the generalized Polya Eggenberger of the second kind distribution,the linear function negative binomial distribution,the Lagrangian Katz dis-tribution.