Estimation of Finite Mixtures of Distributions from the Exponential Family

Abstract General “successive substitutions” iteration equations are developed for obtaining estimates for finite mixtures of distributions from the exponential family. These, in general, correspond to relative maximums of the likelihood function. It is assumed that the number of distributions is known, and that the mixtures are from distributions of the same type, but with different parameter values. The particular equations for the Poisson, binomial, and exponential distributions are given, as well as examples of the results of the procedure for each distribution. From the examples tried, it was observed that the likelihood function increased at each iteration. Graphs of the asymptotic variances of the estimates are given, and two sampling experiments comparing estimates obtained by this scheme with moment estimates are also given.