On numerical evaluation of maximum-likelihood estimates for finite mixtures of distributions

The paper deals with estimation of finite distribution mixtures which are practically important in cluster analysis, pattern recognition and other fields. After a brief survey of existing methods attention is confined to maximum-likelihood estimates, especially to an iterative procedure frequently discussed in the recent literature. It is shown that this procedure in a general form converges monotonly to a possibly local maximum of likelihood function. Application of the general iterative procedure to a particular type of mixture is simplified and illustrated by several examples.