Application of the Perron-Frobenius Theorem to a Damage Model Problem

摘要

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 < or = 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of (X,Y) is uniquely determined by the conditional distribution of Y given X. This result extends the recent unpublished work of Shanbhag and Taillie (1979) on damage models.