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, improvements on the best invariant UMVUE of reciprocals of scale parameter, component wise, are also obtained, when ordered scale parameters of two Gamma distributions is given, under entropy loss. Finally, the numerical results are given to illustrate the efficiency of MLE compare to UB, and improvements on the best invariant UMVUE of reciprocals of scale parameter. Key words and phrases: MLE, unbiased estimator, admissible estimator, entropy loss, reciprocal of scale parameter.