Characterization of the Compound Poisson Distribution
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 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.
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- J. Panaretos, 1982. "An extension of the damage model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 29(1), pages 189-194, December.
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