Improved estimators of the entropy in scale mixture of exponential distributions

Abstract

In the present communication, the problem of estimating entropy of a scale mixture of exponential distributions is considered under the squared error loss. Inadmissibility of the best affine equivariant estimator(BAEE) is established by deriving an improved estimator which is not smooth. Using the integral expression of risk difference (IERD) approach of Kubokawa (The Annals of Statistics 22 (1994) 290–299), classes of estimators are obtained which improve upon the BAEE. The boundary estimator of this class is the Brewster and Zidek-type estimator and this estimator is smooth. We have shown that the Brewster and Zidek-type estimator is a generalized Bayes estimator. As an application of these results, we have obtained improved estimators for the entropy of a multivariate Lomax distribution. Finally, percentage risk reduction of the improved estimators for the entropy of a multivariate Lomax distribution is plotted to compare the risk performance of the improved estimators.