On Double Stage Shrinkage-Bayesian Estimator for the Scale Parameter of Exponential Distribution

Abstract

  This paper is concerned with Double Stage Shrinkage Bayesian (DSSB) Estimator for lowering the mean squared error of classical estimator ˆ q for the scale parameter (q) of an exponential distribution in a region (R) around available prior knowledge (q0) about the actual value (q) as initial estimate as well as to reduce the cost of experimentations.         In situation where the experimentations are time consuming or very costly, a Double Stage procedure can be used to reduce the expected sample size needed to obtain the estimator. This estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y( ) and for acceptance region R. Expression for Bias, Mean Square Error (MSE), Expected sample size [E(n/q,R)], Expected sample size proportion [E(n/q,R)/n], probability for avoiding the second sample 1 ˆ [p( R)] qË› and percentage of overall sample saved 2 1 n ˆ [ p[ R) 100] n q Ë› * for the proposed estimator are derived.         Numerical results and conclusions are established when the consider estimator (DSSB) are testimator of level of significance a. Comparisons with the classical estimator as well as with some existing studies were made to show the usefulness of the proposed estimator