Bayesian Estimation for Lomax Distribution: A Comparison of Loss Functions Using Jeffreys Priors

Abstract

This study investigates the estimation of the shape parameter for the Lomax distribution using complete data. We compare the performance of the classical Maximum Likelihood Estimation (MLE) method against the Bayesian framework. Within the Bayesian approach, three distinct loss functions were utilized: the linear exponential (LINEX), general entropy, and weighted general entropy loss functions. The precision of these estimators was assessed through Mean Squared Error (MSE) and bias metrics. Monte Carlo simulation results demonstrate that the LINEX loss function consistently provides the most accurate parameter estimates, yielding the lowest MSE and bias values.