M Kolossiatis, JE Griffin and MFJ Steel
Modelling overdispersion with the Normalized Tempered Stable distribution
Abstract: This paper discusses a multivariate distribution which generalizes the Dirichlet distribution and demonstrates its usefulness for modelling overdispersion in count data. The distribution is constructed by normalizing a vector of independent Tempered Stable random variables. General formulae for all moments and cross-moments of the distribution are derived and they are found to have similar forms to those for the Dirichlet distribution. The univariate version of the distribution can be used as a mixing distribution for the success probability of a Binomial distribution to define an alternative to the well-studied Beta-Binomial distribution. Examples of fitting this model to simulated and real data are presented.
Keywords: Mice Fetal Mortality; Normalized Random Measures; Overdispersion.