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On Some Bivariate Discrete Distributions with Multivariate Components

Panaretos, John (1983): On Some Bivariate Discrete Distributions with Multivariate Components. Published in: Publicationes Mathematicae (Hungary) , Vol. 30, No. 1-2 (1983): pp. 177-184.

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Abstract

Consider a random vector (X,Y) where X=(X1,X2, ...., Xs,) and Y=(Y1,Y2, ...., Ys) with Xi, Yi, i=1,2,..., s independent non-negative, integer-valued random variables with finite support and such that X>=Y. We show that in the case where the distribution of (YlX=n) is of a certain structural form then there exists a relationship between the distributions of Y and of Y|(X=Y) which uniquely determines the distribution of X. The relationship in question is less stringent that the condition of independence between Y and X-Y usually involved in pro¬blems of this nature. Examples are given to illustrate the result. The case where X,Y have infinite support has been examined earlier by the author.

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