Estimation of Linear Functions of Ordered Scale Parameters of Two Gamma Distributions under Entropy Loss

Abstract

The problem of estimating linear functions of ordered scale parameters of two Gamma distributions is considered under entropy loss. A necessary and sufficient condition for the maximum likelihood estimator (MLE) to dominate the crude unbiased estimator (UE) is given on two non-negative coefficients. Furthermore, improvement on the UE of the reciprocal of each scale parameter is also obtained under entropy loss. Some numerical results are given to illustrate how much improvement is obtained over the UE.