Characterization of count data distributions involving additivity and binomial subsampling

Preprint

30 August 2007

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.0708.4177

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 ($r=2$).

Keywords

DISTRIBUTIONS INVOLVING
HERMITE DISTRIBUTIONS
BINOMIAL SUBSAMPLING
INVOLVING ADDITIVITY
DATA DISTRIBUTIONS
SUBSAMPLING
COUNT DATA

All Related Versions

Version 1, 2007-08-30, ArXiv
Published version: Bernoulli, 13 (2), 544.

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