Optimal B-Robust Estimation for the Parameters of the Marshall-Olkin Extended Burr XII Distribution with an Application to Pharmacokinetics

Abstract

Parameters of Marshall–Olkin Extended Burr XII (MOEBXII) distribution are usually estimated using maximum likelihood (ML) and least squares (LS) estimation methods. However, these estimators are not robust to the outliers which are often encountered in practice. The purpose of this paper is to obtain robust estimators for the parameters of MOEBXII distribution using optimal B-robust estimation method. A simulation study is provided to show the performance of the proposed estimators over ML, LS and robust M estimators. Further, a real data example from a pharmacokinetics study is also given to illustrate the modeling capacity of the MOEBXII distribution when the parameters are properly estimated.

Keywords

• least squares estimator
• Marshall–Olkin extended Burr XII (MOEBXII) distribution
• maximum likelihood estimator
• optimal B-robust estimator