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In this note we deduce several properties of the compound and generalized Poisson distributions; in particular their closure and divisibility properties. An infinite class of functions whose members are both compound and generalized Poisson distributions is exhibited, and several of the distributions of Neyman, Polya, etc. are identified. The present note stems from a paper by Feller 2.
E. Cansado Maceda (1948) studied this question.
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