Linear characterizations of the Poisson distribution

Ed. McKenzie

Statistics & Probability Letters, 1991, vol. 11, issue 5, 459-461

Abstract: Some new distribution theoretic results are presented for non negative integer random variables using an alternative and more sutiable form of linear combination. In particular, characterizations based on the behaviour of such linear combinations are considered. Discrete analogues of the Cramer-Wold and Skitovich-Darmois theorems are derived. They both yield characterizations of the Poisson distribution. In addition, constancy of regression of such linear combinations of independent variates on each other is also shown to characterize the Poisson distribution.

Date: 1991
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