Certain characterizations with linearity of regression in additive damage models

This paper investigates the characterizations of certain discrete distributions within the framework of a multivariate additive damage model. The univariate case for such a model appeared in an article by [2]. In this model a p-dimensional observation is subjected to damage according to a specified probability law represented by a joint survival distribution. Here, it is shown that the linearity of regression of the damaged part on the undamaged ones leads to the characterizations of the multivariate binomial, and multiple inverse hypergeometric distribution as survival distributions.