ABSTRACT
This chapter reviews the literature related to finite mixture models designed specifically for discrete data. It provides a broad overview over a wide range of models for these data types and discusses both univariate and multivariate models. The chapter presents many of the existing models and discusses the problems and challenges that arise in generalizing them. It also reviews of mixture models that have been suggested for each of these data types. The chapter considers data sets that consist of counts, that is, they describe the number of occurrences of some event in some unit of time or space. The Poisson distribution is perhaps the simplest choice for modelling such data. A very common extension of a finite mixture model for count data is the zero-inflated model. Multivariate count data appear in a wide range of fields where incidences of several related events are counted, as in epidemiology, marketing and environmetrics.
