Characterization Theorems Involving the Generalized Markov-Polya Damage Model.

Abstract : In the present paper, certain random damage models are examined, such as the Generalized Markov-Polya and the Quasi-Binomial, in which an integer-valued random variable N is reduced to N(A). If N(B) is the missing part, where N = N(A) + N(B), the covariance between N(A) and N(B) is obtained for some general classes of distributions, such as the G.P.S.D. and M.P.S.D. for the random variable N. A characterization theorem is proved that under the generalized Markov-Polya damage model, the random variables N(A) and N(B) are independent if, and only if, N has the Generalized Polya-Eggenberger distribution. This generalizes the corresponding result for the Quasi-Binomial damage model and the generalized Poisson distribution. Finally, some interesting identities are obtained using the independence property and the covariance formulas between the numbers N(A) and N(B). (Author)