On the improved estimation of a function of the scale parameter of an exponential distribution based on doubly censored sample.

In the present article, we have studied the estimation of entropy, that is, a function of scale parameter of an exponential distribution based on doubly censored sample when the location parameter is restricted to positive real line. The estimation problem is studied under a general class of bowl-shaped non monotone location invariant loss functions. It is established that the best affine equivariant estimator (BAEE) is inadmissible by deriving an improved estimator.