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Characterization of the Compound Poisson Distribution

By Evdokia Xekalaki and John Panaretos

Abstract

Consider two non-negative integer-valued r.v.'s X,Y with X=>Y. Suppose that the conditional distribution of Y|X is binomial with parameters (n,p), n=0,1,2,...; 0 < p < 1 and p independent of n. It is known, and can be checked easily, that under the above assumption the distribution of Y is Poisson with parameter λp, λ>0 (Poisson(λp)) if and only if (iff) X is Poisson (λ). This model has been extensively used in the literature under different names in many practical situations.

Topics: C01 - Econometrics
Year: 1979
DOI identifier: 10.1080/03461238.1983.10408688
OAI identifier: oai:mpra.ub.uni-muenchen.de:6221

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