Bayesian Shrinkage Estimator for the Scale Parameter of Exponential Distribution under Improper Prior Distribution

This paper deals with preliminary test single stage Bayesian Shrinkage estimator for the scale parameter (θ) of an exponential distribution when a guess value (θ0) for (θ) available from the past studies under the improper prior distribution and the quadratic loss function. The proposed estimators are shown to be a more efficient than the usual estimators θ when θ is close to θ0 in the sense of mean squared error (MSE). In which the expression for bias and mean squared error of the proposed estimator are derived. Numerical results for the bias and MSE are using different constants were involved in it which had been given as well as comparisons.