An application of the Perron-Frobenius theorem to a Damage Model Problem

Abstract

Using the Perron-Frobenius theorem, it is established that if (X, Y) is a random vector of non-negative integer-valued components such that Y≤X almost surely and two modified Rao-Rubin conditions hold, then under some mild assumptions the distribution of (X, Y) is uniquely determined by the conditional distribution of Y given X. this result extends the recent unpublished work of Shanbag and Taillie (1979) on damage models.