A Comparison of Restricted and Unrestricted Estimators in Estimating the Linear Functions of Two Ordered Scale Parameters of Gamma Distributions under Entropy Loss

Abstract

The problem of estimating linear function of ordered scale parameters of two Gamma distributions under entropy loss is considered. A necessary and sufficient condition on two non-negative coefficients is given for maximum likelihood estimator (MLE) to dominate the crude unbiased estimator (UE). Furthermore, improvements on the best invariant UMVUE of inversed scale parameter, component wise, are also obtained, when ordered scale parameters of two Gamma distributions is given.