Characterization of count data distributions involving additivity and binomial subsampling
Open Access
- 1 May 2007
- journal article
- Published by Bernoulli Society for Mathematical Statistics and Probability in Bernoulli
- Vol. 13 (2) , 544-555
- https://doi.org/10.3150/07-bej6021
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
All Related Versions
This publication has 14 references indexed in Scilit:
- Count Data DistributionsJournal of the American Statistical Association, 2006
- Binomial subsamplingProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2006
- Characterizing Additively Closed Discrete Models by a Property of Their Maximum Likelihood Estimators, With an Application to Generalized Hermite DistributionsJournal of the American Statistical Association, 2003
- On the Asymptotics of Constrained $M$-EstimationThe Annals of Statistics, 1994
- Generalized multivariate Hermite distributions and related point processesAnnals of the Institute of Statistical Mathematics, 1993
- Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests Under Nonstandard ConditionsJournal of the American Statistical Association, 1987
- Some Characterizations Involving Additivity and Infinite Divisibility and Their Applications to Poisson Mixtures and Poisson SumsPublished by Springer Nature ,1975
- A Generalized Hermite Distribution and Its PropertiesSIAM Journal on Applied Mathematics, 1974
- An alternative derivation of the Hermite distributionBiometrika, 1966
- On the Convolution of DistributionsThe Annals of Mathematical Statistics, 1954