  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.
