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 -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 th-order univariate Hermite distributions. Among these, we find the Poisson () and the ordinary Hermite distributions ().
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)