Characterization of generalized markov-polya and generalized polya-eggenberger distributions |
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Authors: | KG Janardan B Raja Rao |
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Institution: | 1. Mathematical Systems , Sangamon State University , Springfield, IL, 62708;2. Department of Blostatistics , University of Pittsburgh , Pittsburgh, PA, 15261 |
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Abstract: | 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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Keywords: | Generalized Markov-Polya distribution Generalized Polya-Eggenberger distribution damage model Rao-Rubin Condition Characterizations |
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