Information and mixtures of two normal distributions

Abstract

The information available for estimating the parameters of a mixture of two normal distributions is examined for five different types of sample. The information in these samples is compared through the asymptotic relative efficiencies of the maximum likelihood estimates using both generalized and total variances. The efficiency of the maximum likelihood estimates is increased substantially if the component of origin of a small proportion of the sample is known. Guidelines are suggested for choosing the best type of sample.