Bayesian Estimation of Common Scale Parameter of Two Exponential Populations with Order Restricted Locations

SYNOPTIC ABSTRACT

The problem of estimating the common scale parameter of two exponential populations is considered when it is known a priori that the location parameters follow a certain ordering. The loss function is taken as quadratic or a weighted squared error. Assuming order restrictions on the location parameters, we propose Bayes estimators (exact expressions have been obtained) using a vague prior as well as a conditional inverse gamma prior. The proposed estimators are compared with the estimators obtained by Madi and Leonard (1996). It has been noticed from our numerical study that the proposed Bayes estimators outperform the existing estimators when it is known a priori that the location parameters are ordered. The percentage of relative risk improvements have been tabulated for illustration purposes.

KEY WORDS AND PHRASES:

• Bayes estimator
• best affine equivariant estimator (BAEE)
• maximum likelihood estimator (MLE)
• ordered parameters
• quadratic loss function
• relative risk improvements