E-Bayesian and Hierarchical Bayesian Estimation for the Shape Parameter and Reversed Hazard Rate of Power Function Distribution Under Different Loss Functions

Abstract

This paper presents the E-Bayesian and hierarchical Bayesian estimation of the shape parameter and reversed hazard rate of Power function distribution under the condition that scale parameter is known, based on the different loss functions. We also study some important properties of the proposed estimators. Based on Monte Carlo Simulation study and using a real dataset comparisons are made between the proposed estimators and existing Bayesian estimators. Confidence intervals and coverage probability of the estimators are also computed. From the numerical studies it can be seen that the proposed E-Bayesian and hierarchical Bayesian estimators have better performance when compared to the existing Bayesian estimators in terms of bias and MSE respectively.