An Efficient Bayesian Estimation of Ordered Parameters of Two Exponential Distributions

The situations where several population parameters need to be estimated simultaneously arise frequently in wide areas of applications, including reliability modeling. survival analysis and biological study. In this paper, we propose Bayesian methods of estimation of the ordered parameters of the two exponential populations, which incorporate the prior information about the simple order restriction, but sometimes breaks the order restriction. A simulation study shows that the proposed estimators are more efficient (in terms of mean square errors) than the isotonic regression of the maximum likelihood estimators with equal weights. An illustrative example is finally presented.