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Comparing Several Methods to Fit Finite Mixture Models to Grouped Data by the EM Algorithm

The EM algorithm is a standard tool for maximum likelihood estimation in finite mixture models. Common approaches assume continuous data for its application. Frequently in practice, data is only available in grouped form, i.e. the frequencies of observations in fixed intervals are reported. The fitting of two-component Gaussian mixture to such data is considered in this paper. The aim is to compare several methods for fitting mixtures to grouped data via the EM algorithm, as well as to propose some new methods based on modifications of existing ones. Furthermore, the influence of different widths of intervals on the estimation is investigated. Finally, an example is presented.