E-Bayesian Estimation of the Weighted Power Function Distribution with Application to Medical Data

Abstract

This paper investigates E-Bayesian estimation for the Weighted Power Function Distribution (WPFD), a modified version of the Power Function distribution which is widely applied in biosciences and engineering. Three distinct priors for hyper-parameters are considered, and E-posterior risks are derived using squared error, entropy (measuring uncertainty), and precautionary loss functions (penalizing extreme deviations). Properties of the E-Bayesian estimators are analyzed, supplemented by a simulation study and real data application. Results indicate that E-Bayesian estimators outperform Bayesian counterparts in terms of E-posterior risk, as demonstrated in simulation studies.