Fast MCD-Augmented Rank Regression for Robust Estimation of Weibull Parameters

Outliers hurt the accuracy of life distribution parameters, including the Weibull distribution. Therefore, we suggest employing the fast minimum covariance determinant method in rank regression estimators (Although rank regression provides robust estimates for the shape and scale parameters of the Weibull distribution, it tends to lack efficiency compared to other estimation methods, particularly under ideal model conditions.) to obtain robust estimators for the shape and scale parameters of the Weibull distribution. The proposed method is based on the robust means vector and the robust covariance matrix obtained from the fast minimum covariance determinant method and employed in the rank regression estimation method that depends on the ordinary least squares estimators of the simple linear regression model. The estimated parameters of the Weibull distribution obtained using the proposed technique have been compared with those derived from the conventional maximum likelihood estimation and rank regression, utilizing mean square error as the comparison metric via both simulation and real data. The study's results confirmed the effectiveness of the proposed approach in managing outliers and delivering highly efficient estimators for the shape and scale parameters of the Weibull distribution.