Versions of de Finetti’s Theorem with applications to damage models

Abstract

Alzaid et al., An application of the Perron-Frobenius theorem to a damage model problem, and Rao et al., Damage models: A Martin boundary connection. Basu Memorial Volume, have shown that several of the results on damage models have links with certain results on nonnegative matrices. In the present article, we deal with integral equations met in damage model studies via specialized versions of de Finetti’s theorem and extend further the theorems of Rao and Rubin, On a characterization of the Poisson distribution, and Shanbhag , An extension of the Rao-Rubin characterization of the Poisson distribution, on damage models.