English

Characterization of count data distributions involving additivity and binomial subsampling

Statistics Theory 2011-11-10 v1 Statistics Theory

Abstract

In this paper we characterize all the rr-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 rrth-order univariate Hermite distributions. Among these, we find the Poisson (r=1r=1) and the ordinary Hermite distributions (r=2r=2).

Keywords

Cite

@article{arxiv.0708.4177,
  title  = {Characterization of count data distributions involving additivity and binomial subsampling},
  author = {Pedro Puig and Jordi Valero},
  journal= {arXiv preprint arXiv:0708.4177},
  year   = {2011}
}

Comments

Published at http://dx.doi.org/10.3150/07-BEJ6021 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

R2 v1 2026-06-21T09:12:23.514Z