A few relations for sums of differences of discrete probability distributions

by Subrata Chakraborty.

Abstract: In this article some interesting relationship between sums of differences and different moments of discrete probability distributions with support {0,1,2,...} have been derived. The work has been motivated by the list of such relationships for Generalized Poisson distribution (GPD) presented in Consul (1989 page 66-67). Here some generalized relationships have been obtained between sums (() of differences [both forward (() and backward (()] of probabilities and moments for any discrete distribution having support {0,1,2,...}and all the corresponding results of Consul (1989) for GPD have been seen as particular cases of one of the general relations. Some new relations between different partial sums of probabilities with different moments for discrete distributions have also been stated.

Key Words: Generalized Poisson Distribution; Shift Operator; Forward and Backward Difference Operators; Discrete Probability Distribution; Stirling number of the 1st, 2nd, 3rd and 4th kind; Binomial coefficients

Subrata Chakraborty, subrata_arya@yahoo.co.in

Editor: Ravi Khattree,Khattree@oakland.edu

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