E‐Bayesian estimation and associated properties of simple step–stress model for exponential distribution based on type‐II censoring

Abstract

Abstract In this paper, expected Bayesian (E‐Bayesian) estimation for the simple step–stress model based on type‐II censoring scheme is considered. The case of exponential distribution for the underlying lifetimes is considered assuming a cumulative exposure model. The E‐Bayesian estimation is discussed by considering three different prior distributions for the hyperparameters. The E‐Bayesian estimators as well as the corresponding E‐posterior risks are obtained by using squared error and linear‐exponential (LINEX) loss functions. Some properties of the E‐Bayesian estimators are also derived. We conduct a simulation study to compare the various estimators and a simulated and real data sets are analyzed to show the applicability of the different estimators. The numerical results show that the E‐Bayesian estimators perform better than the classical and Bayesian estimators.