389: Separating Mixtures of Normal Distributions

Suppose a set of data is believed to have been drawn from a population that consists of a known number of k-variate normal distributions, with the same, unknown, dispersion matrix but different means. It is desired to estimate the parameters of the distributions, and assign the data points to them with minimum probability of misclassification. This is a well-known problem in cluster analysis. Recently, two solutions have been proposed, by Day 1969 and Scott and Symons 1971. Both are based on ML estimation, but they are not, in general, the same. In this note, the two solutions will be compared, discussion being restricted, for simplicity, to the case of two groups.