Characterization of count data distributions involving additivity and binomial subsampling

Pedro Puig; Jordi Valero

doi:10.3150/07-bej6021

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arXiv · 0708.4177

Characterization of count data distributions involving additivity and binomial subsampling

Pedro Puig·Jordi Valero

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Abstract

In this paper we characterize all the $r$-parameter families of count distributions (satisfying mild conditions) that are closed under addition and under binomial subsampling. Surprisingly, few families satisfy both properties and the resulting models consist of the $r$th-order univariate Hermite distributions. Among these, we find the Poisson ($r=1$) and the ordinary Hermite distributions ($r=2$).

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Pedro Puig, Jordi Valero. 2007-08-30. Characterization of count data distributions involving additivity and binomial subsampling. https://doi.org/10.3150/07-bej6021

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