Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 2 , pp. 335--346

CHARACTERIZATIONS OF SOME WELL-KNOWN DISCRETE DISTRIBUTIONS BASED ON VARIANTS OF THE RAO-RUBIN CONDITION

By

T. SAPATINAS and M. A. H. ALY, University of Sheffield

SUMMARY. The present note investigates characterizations of some well-known discrete distributions based on variants of the Rao-Rubin condition. Shanbhg and Clark (1972), and Patil and Ratnaparkhi (1977), have given characterizations for the Poisson, and for the binomial and negative binomial distributions, respectively replacing the Rao-Rubin condition by conditional expectations of the distributions of the r.v.ís X and Y. Our work focuses on unification and generalizations well as some extensions of these results. A result relating to this Srivastava and Singh (1975) conjecture and modified versions of the results of Shanbag (1977) and Alzaid (1986) are also given.

AMS (1992) subject classification. 62E10.

Key words and phrases. Damage model, Rao-Rubin condition, power series distributions, Poisson, binomial, negative binomial, Markov-Polya and polya-Eggenberger distributions, factorial moments.

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