# Characterizations of generalized multivariate discrete distributions by a regression point

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## Abstract

Given that the conditional distribution of Yi given Xi = xi is an xi-fdd convolution of a nonnegative integer-valued r.v. [nu]i for every si = P [[nu]i = 0] > 0 and I = 1, ..., k, or that the conditional distribution of Y = (Yl,...,Yk given X = x is an x-fold convolution of a random discrete vector [xi] for every s = P[[xi] = 0] > 0, distribution of X = (Xl,...,Xk) or X, hence also of Y, is characterized by the regression point m(0; s) = E(Y/Y = 0) = m(0; s) or E[X/Y = 0] - m(0; s), respectively ((s = (s1,...,sk)).

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