Empirical Bayes Estimators for Mean Parameter of Exponential Distribution with Conjugate Inverse Gamma Prior Under Stein’s Loss

A Bayes estimator for a mean parameter of an exponential distribution is calculated using Stein’s loss, which equally penalizes gross overestimation and underestimation. A corresponding Posterior Expected Stein’s Loss (PESL) is also determined. Additionally, a Bayes estimator for a mean parameter is obtained under a squared error loss along with its corresponding PESL. Furthermore, two methods are used to derive empirical Bayes estimators for the mean parameter of the exponential distribution with an inverse gamma prior. Numerical simulations are conducted to illustrate five aspects. Finally, theoretical studies are illustrated using Static Fatigue 90% Stress Level data.