Applied Sciences, Vol. 14, Pages 3308: Reliability Estimation for Burr XII Distribution under the Weighted Q-Symmetric Entropy Loss Function

Applied Sciences, Vol. 14, Pages 3308: Reliability Estimation for Burr XII Distribution under the Weighted Q-Symmetric Entropy Loss Function

Applied Sciences doi: 10.3390/app14083308

Authors: Kexin He Wenhao Gui

Considering that the choice of loss function plays a significant role in the derivation of Bayesian estimators, we propose a novel asymmetric loss function named the weighted Q-symmetric entropy loss for computing the estimates of the parameter and reliability function of the Burr XII distribution. This paper covers the classical maximum-likelihood, uniformly minimum-variance unbiased, and Bayesian estimation methods under the squared error loss, general entropy loss, Q-symmetric entropy loss, and new loss functions. Through Monte Carlo simulation, the respective performances of the considered estimators for the reliability function are evaluated, indicating that the Bayesian estimator under the new loss function is more efficient than those under other loss functions. Finally, a real data set is used to demonstrate the practicality of the presented estimators.