Some characterizations based on a multivariate splitting model

Abstract

The paper deals with a splitting model where a discrete random variable 'Z is decomposed into k parts, Z=Z₁+...+Z_k. The distribution of Z is characterized using the properties of ₁=r|Z₂=0) for r=0,1,... uniquely determines the distrubution of Z when the splitting distribution is multinomial, that is, the distribution of Z₁,...,Z_k given Z is multinomial, This extends a theorem of Rao and Rubin for K=2. Other splitting distributions are also considered.