Derivation of probabilities and moments os ceria1n generalized discrete distributions via urn models

Abstract

Considering a supply of balls randomly distributed in n distinguishable urns and assuming that qr, r=;0,l,2,…and u r(K) k=1,2 …are the probability function and the factorial moments of the number of balls allocated in any specific urn, the probability function and the factorial moments of certain occupancy distributions are expressed as partition polynomials of qr r=0,l,2,…and u(k), k=l,2,… respectively. In addition the probability function and the factorial moments of these occupancy distributions are given in terms of finite differences of the u-fold convolutions of qr,r=0,l,2,… and u(k), k=1,2,…,respectively. Illustrating these results the probability function and the factorial moments of the n-fold convolution of a zero-truncated discrete distribution and the number of positive random variables given their sum are concluded.. Further This work was completed while the author was visiting lemple University, on leave from the University of Athens