Soft Computing, vol.27, no.11, pp.6903-6926, 2023 (SCI-Expanded)
The maximum log q likelihood estimation method is a generalization of the known maximum log likelihood method to overcome the problem for modeling non-identical observations (inliers and outliers). The parameter q is a tuning constant to manage the modeling capability. Weibull is a flexible and popular distribution for problems in engineering. In this study, this method is used to estimate the parameters of Weibull distribution when non-identical observations exist. Since the main idea is based on modeling capability of objective function ρ(x; θ) = log q[f(x; θ)] , we observe that the finiteness of score functions cannot play a role in the robust estimation for inliers. The properties of Weibull distribution are examined. In the numerical experiment, the parameters of Weibull distribution are estimated by log q and its special form, log , likelihood methods if the different designs of contamination into underlying Weibull distribution are applied. The optimization is performed via genetic algorithm. The modeling competence of ρ(x; θ) and insensitiveness to non-identical observations are observed by Monte Carlo simulation. The value of q can be chosen by use of the mean squared error in simulation and the p value of Kolmogorov–Smirnov test statistic used for evaluation of fitting competence. Thus, we can overcome the problem about determining of the value of q for real data sets.