Estimation of parameters for a mixture of normal distributions on the basis of the Cressie and Read divergence

Abstract

The estimation of the five parameters of the mixture of two normal components is studied, with emphasis on the estimation of mixing proportion. The method proposed is based on the power-divergence introduced by Cressie and Read (1984) and Read and Cressie (1988). Computational results compare the efficiency as well as the robustness under symmetric departures from component normality of different members of the family we study. Our results indicate that the member of the family corresponding to the parameter value 2/3 is, for almost all the cases, comparable to the well-known estimators.