Bayesian analysis of the two component mixture of inverted exponential distribution under quadratic loss function

Abstract

The inverted exponential distribution is studied as a prospective life distribution. A two component mixture of inverted exponential distribution is considered in this paper. The Bayes estimators and Bayes posterior risk for the unknown parameters, and mixing weight of the mixture model are derived under quadratic loss function. For comparative study of these Bayes estimates uniform, improper and informative priors are considered. The Bayes and maximum likelihood estimators and Bayes posterior risks are viewed as a function of the test termination time. As a special case, the limiting expressions for these estimates are derived under the condition of infinite test termination time. Finally, a mixture data is simulated and numerical study is given to illustrate the results. Key words: Inverted exponential distribution, mixture models, Bayes estimates, quadratic loss function, fixed test termination time.