## Bernoulli

• Bernoulli
• Volume 13, Number 2 (2007), 544-555.

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

#### 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 $(r=2)$.

#### Article information

Source
Bernoulli, Volume 13, Number 2 (2007), 544-555.

Dates
First available in Project Euclid: 18 May 2007

https://projecteuclid.org/euclid.bj/1179498760

Digital Object Identifier
doi:10.3150/07-BEJ6021

Mathematical Reviews number (MathSciNet)
MR2331263

Zentralblatt MATH identifier
1127.62009

#### Citation

Puig, Pedro; Valero, Jordi. Characterization of count data distributions involving additivity and binomial subsampling. Bernoulli 13 (2007), no. 2, 544--555. doi:10.3150/07-BEJ6021. https://projecteuclid.org/euclid.bj/1179498760

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