BAYESIAN-ESTIMATION OF MEAN AND SQUARE OF MEAN OF NORMAL-DISTRIBUTION USING LINEX LOSS FUNCTION

In this paper, the Bayes estimators for mean and square of mean of a normal distribution with mean mu and variance sigma2 (known), relative to LINEX loss function are obtained. Comparisions in terms of risk functions and Bayes risks of those under LINEX loss and squared error loss functions with their respective alternative estimators viz. UMVUE and Bayes estimators relative to squared error loss function, are made. It is found that Bayes estimators relative to LINEX loss function dominate the alternative estimators in terms of risk function and Bayes risk. It is also found that if sigma2 is unknown the Bayes estimators are still preferable over alternative estimators.