Maximum $$\log _q$$ likelihood estimation for parameters of Weibull distribution and properties: Monte Carlo simulation

The maximum $${\log }_q$$ likelihood estimation method is a generalization of the known $$\log $$ to overcome problem for modeling non-identical observations (inliers and outliers). parameter q tuning constant manage capability. Weibull flexible popular distribution problems in engineering. In this study, used estimate parameters when exist. Since main idea based on capability objective function $$\rho (x;\varvec{\theta })=\log _q\big [f(x;\varvec{\theta })\big ]$$ , we observe that finiteness score functions cannot play role robust inliers. properties are examined. numerical experiment, estimated by _q$$ its special form, methods if different designs contamination into underlying applied. optimization performed via genetic algorithm. competence })$$ insensitiveness observed Monte Carlo simulation. value can be chosen use mean squared error simulation p Kolmogorov–Smirnov test statistic evaluation fitting competence. Thus, about determining real data sets.