BAYES ESTIMATION AND PREDICTION OF A THREE COMPONENT MIXTURE OF RAYLEIGH DISTRIBUTION UNDER TYPE-I CENSORING

Abstract

This paper considers maximum likelihood estimation, Bayes estimation and prediction of a three component mixture of Rayleigh distribution under type-I censoring. By assuming independent priors for the unknown parameters of the Rayleigh mixture model, Bayes estimates are computed under the squared error loss, quadratic loss and general entropy loss functions. Mathematical expressions for the joint posterior, marginal posterior-distribution, Bayes estimators, posterior predictive distribution and Bayes point predictors are given in explicit forms. Detailed Monte Carlo simulations are used to study the performances of the maximum likelihood and Bayes estimators in terms of simulated risks. It is observed that the Bayes estimates under the considered loss functions are more precise than the maximum likelihood estimates. Moreover, the Bayes point predictive estimates of the future observation are also obtained under the squared error loss and general entropy loss functions.