Comparison of Robust and Bayesian Methods for Estimating the Burr Type XII Distribution

Abstract

This paper compares the robust and E-Bayesian estimations of the shape parameter for Burr XII distribution. BurrXII distribution was already reviewed by many researchers, as this distribution has gained special attention in recent times due to its complete applications, including the reliability field and failure time modeling. Burr distributions include 12 types of functions that produce a variety of probability density forms. We used two loss functions, quadratic, and LINEX with the E-Bayes method. The comparison conducted by simulation technique, and the absolute mean square error was measured to test the estimation methods' preference. In this study, many familiar distributions methods such as Weibull distribution, exponential logistic distribution, generalized logistic distribution, extreme value, and uniform distribution have been discussed accordingly by employing special cases and belonging to Burr distribution family. The current is dealing with the Bayesian method by depending on the parameter c that must be chosen to be close or not far from parameter b to ensure the robustness of the Bayesian estimator. Then the Bayesian expected of the parameter β under a quadratic loss function. It has been compared estimation for Burr-XII distribution by using the mentioned methods. We found many essential points, such as Robust estimates, in all cases, tend to be more efficient than the Bayes estimates. Also, by increasing the sample size, the robust estimates are still better than other estimation methods. When increasing the sample size, we notice a decrease in MAPE, which supports the statistical theory. We recommend using non-parametric methods to estimate Burr XII parameters. Thus, the main conclusion is that the robust process was the best.