A comparison of some estimators of the mixture proportion of mixed normal distributions

Fisher's method of maximum likelihood breaks down when applied to the problem of estimating the five parameters of a mixture of two normal densities from a continuous random sample of size n. Alternative methods based on minimum-distance estimation by grouping the underlying variable are proposed. Simulation results compare the efficiency as well as the robustness under symmetric departures from component normality of these estimators. Our results indicate that the estimator based on Rao's divergence is better than other classic ones.