Robust inferential methods based on divergences measures have shown an appealing trade-off between efficiency and robustness in many different statistical models. In this paper, minimum density power divergence estimators (MDPDEs) for the scale and shape parameters of the log-logistic distribution are considered. The log-logistic is a versatile distribution modeling lifetime data which is commonly adopted in survival analysis and reliability engineering studies when the hazard rate is initially increasing but then it decreases after some point. Further, it is shown that the classical estimators based on maximum likelihood (MLE) are included as a particular case of the MDPDE family. Moreover, the corresponding influence function of the MDPDE is obtained, and its boundlessness is proved, thus leading to robust estimators. A simulation study is carried out to illustrate the slight loss in efficiency of MDPDE with respect to MLE and, at besides, the considerable gain in robustness.

翻译：基于散度度量的鲁棒推断方法已在多种统计模型中展现出效率与鲁棒性之间的理想权衡。本文考虑了对数逻辑分布尺度参数与形状参数的最小密度功率散度估计量（MDPDE）。对数逻辑分布是一种适用于寿命数据建模的通用分布，在风险率呈现先增后减特征时，常用于生存分析与可靠性工程研究。进一步证明，基于极大似然估计（MLE）的经典估计量是MDPDE族的一个特例。与此同时，推导了MDPDE对应的影响函数并证明其有界性，从而得到鲁棒估计量。通过模拟研究展示了MDPDE相对于MLE在效率上的轻微损失以及鲁棒性上的显著提升。