Characterization of count data distributions involving additivity and binomial subsampling

Details Characterization of count data distributions involving additivity and binomial subsampling Characterization of count data distributions involving additivity and binomial subsampling

2007-08-30

arxiv.org/abs/0708.4177v1

Bernoulli 2007, Vol. 13, No. 2, 544-555

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.3150/07-BEJ6021 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ6021

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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