Mixtures of discrete distributions

Abstract

In this chapter, mixtures of certain discrete distributions will be considered. As with mixtures of normals, Pearson (1915) appears to have been the first to study such distributions in any detail, deriving moment estimators for the parameters in a mixture of binomial density functions. A large part of this chapter will involve mixtures in which the components are binomial or Poisson distributions, since these have been extensively studied in the literature. However, mixtures of other discrete distributions will be considered briefly, in particular the multivariate Bernoulli distribution which, as noted by Wolfe (1969), may be used as the basis of latent class analysis (see Lazarsfeld, 1968). We begin by considering mixtures of binomial distributions.