Hypergeometric Series Applying In Probability Distributions

In this paper, we obtain the inverse moments and their recursive relations for some generalized discrete distributions using the method of generalized geometric series and properties. While taking advantage of iterative method obtains the accurate values on in-verse moments for some generalized discrete distributions, including generalized negative binomial distribution, generalized Poisson distribution, generalized logarithmic distribu-tion. Showing an important role of hyper-geometric series on inverse matrix calculation.Chapter2:we use the generalized hyper-geometric series to obtain the inverse mo-ments and factorial moments for some generalized discrete distributions, mainly the gener-alized negative binomial distribution, the generalized Poisson distribution, the generalized logarithmic distribution and so on. It shows an important role of the hyper-geometric series in the calculation of the inverse moments.Chapter3:we use the properties of generalized hyper-geometric series functions to get the recurrence relations for inverse moments and inverse factorial moments of some generalized discrete distributions. Meanwhile, we obtain the accurate values for inverse moment of generalized discrete distributions using the recurrence relations.