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The Probability Function of the Compound Poisson Distribution Using Integer Partitions and Ferrer’s Graph

Gamze Ozel, Ceyhan İnal

Abstract


Obtaining the probability function is a problem in a compound Poisson distribution. In this study, the explicit probability function of the compound Poisson distribution is derived via integer partitions and a direct and straightforward proof for this function is given. By means of written macros some numerical examples are also given to illustrate the usage of the probability function.

Keywords


Compound Poisson distribution, Pólya-Aeppli distribution, Neyman Type A and B distributions, Integer partitions, Ferrer’s graph

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