Robust estimators for the log-logistic model based on ranked set sampling

Abstract

In this paper, we introduce a novel family of estimators for the shape and scale parameters of the log-logistic distribution being robust when rank set sample method for data selection is used. Rank set sampling effectively reduces the influence of extreme data points. The log-logistic distribution is a versatile model, suitable in various fields such as Economics, Engineering, and Hydrology. Our proposed family of estimators is based on the density power divergence, chosen for its demonstrated robustness and efficiency. Notably, this family includes the classical maximum likelihood estimator as a special case. Besides explicit forms of the estimators, their asymptotic distribution is derived, proving the consistency of the estimators. Finally, a comprehensive simulation study illustrates the significant robustness of the proposed estimators in the presence of data contamination, while also performing competitively with traditional estimators, including the maximum likelihood estimator in terms of efficiency.