Open Access
May 2007 Characterization of count data distributions involving additivity and binomial subsampling
Pedro Puig, Jordi Valero
Bernoulli 13(2): 544-555 (May 2007). DOI: 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 $(r=2)$.


Download Citation

Pedro Puig. Jordi Valero. "Characterization of count data distributions involving additivity and binomial subsampling." Bernoulli 13 (2) 544 - 555, May 2007.


Published: May 2007
First available in Project Euclid: 18 May 2007

zbMATH: 1127.62009
MathSciNet: MR2331263
Digital Object Identifier: 10.3150/07-BEJ6021

Keywords: closed under addition , Hermite distribution , independent p-thinning , Mixed Poisson distribution , overdispersion , top inverse

Rights: Copyright © 2007 Bernoulli Society for Mathematical Statistics and Probability

Vol.13 • No. 2 • May 2007
Back to Top