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

Abstract: In this paper we introduce a new family of estimators for the parameters of shape and scale of the log-logistic distribution being robust when rank set sample method is used to select the data. Rank set sampling arises as a way to reduce the impact of extremal data. Log-logistic distribution is an important distribution suitable for modeling many different situations ranging from Economy to Engineering and Hydrology. This new family of estimators is based on density power divergences. The choice of this family of divergence measures is motivated by the fact that they have shown a very good behavior in terms of robustness at a reduced cost in efficiency. This new family recovers the classical maximum likelihood estimator as a special case. We have developed the form of these estimators and derived their corresponding asymptotic distribution. A simulation study is carried out, suggesting that these new estimators are very robust when contamination arises and are competitive with classical estimators in terms of efficiency.