Estimation of ordered scale parameters of two exponential distributions with a common guarantee time

Abstract

This paper deals with the estimation of the scale parameters of two exponential distributions having a common location parameter. It is assumed that the failure rates are unknown, but an ordering among the failure rates is known a priori. We derive the UMVUE. The restricted MLE is shown to be better than the MLE. We also derive admissible classes of estimators of scale parameters. Improved estimators are derived in classes of scale and affine equivariant estimators. A Monte Carlo simulation study is then performed to compare new estimators to the existing estimators. The percentage risk improvements over the UMVUE are presented to show the performance of new estimators.