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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1981
- Accession Number
- ADA098073
Entities
People
- B. Raja Rao
- K. G. Janardan
Organizations
- University of Pittsburgh