Dispersion statistics in overdispersed mixture models

Abstract

Samples are often found to be too heterogeneous to be explained by a one-parameter family of models in the sense that the implicit mean-variance relationship in such a family is violated by the data. This phenomenon is often called over-dispersion. The most frequently used method in dealing with over-dispersion is to mix a one-parameter family creating a two parameter marginal mixture family for the data. In this paper, we investigate performance of estimators such as maximum likelihood estiamtor, method of moment estimator, and maximum quasi-likelihood estimator in negative binomial and beta-binomial distribution. Numerical results are obtained for various mean parameter and dispersion parameter in both distributions, and we conclude that the moment estimators are very superior in the sense of bias and asymptotic relative efficiency. Two real data sets are used for applications.