Characterization of generalized markov-polya and generalized polya-eggenberger distributions
Titel:
Characterization of generalized markov-polya and generalized polya-eggenberger distributions
Auteur:
Janardan, K.G. Rao, B. Raja
Verschenen in:
Communications in statistics
Paginering:
Jaargang 11 (1982) nr. 18 pagina's 2113-2124
Jaar:
1982
Inhoud:
A discrete model is considered where the original observation is subjected to partial destruction according to the Generalized Markov-Polya (GMP) damage model. A characterization of the Generalized Polya-Eggenberger distribution (GPED) is given in the context of the Rao-Rubin condition. More specifically, if the probability that an observation n of a non-negative integer valued r.v.X is reduced to an integer k during a damage, process is given by the GMPD, and if the resulting r.v.Y is such thatrit satisfies the RR-conditlon, then X has a GPED. Secondly, if N = A + B, where B is the missing part and A is the recorded part such that the conditional distribution P(A= x|N=n) is the GMPD, then the r.v.'s A and B are independent if, and only if, N has a GPED. Several other characterizations are also given for these two distributions. The results of Rao-Rubin '1964', Patil-Ratnaparkhi (1977) and Consul (1975) follow as special cases.
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