Robust explicit estimation of the log-logistic distribution with applications

TL;DR

This paper introduces robust, closed-form estimators for the log-logistic distribution parameters that outperform traditional methods like maximum likelihood in contaminated data scenarios, validated through simulations and real data.

Contribution

The paper proposes new robust estimators with closed-form expressions for the log-logistic distribution, improving estimation accuracy under data contamination.

Findings

Proposed estimators are comparable to MLE on clean data.

They outperform MLE when data contain outliers.

Estimators have high breakdown points, indicating robustness.

Abstract

The parameters of the log-logistic distribution are generally estimated based on classical methods such as maximum likelihood estimation, whereas these methods usually result in severe biased estimates when the data contain outliers. In this paper, we consider several alternative estimators, which not only have closed-form expressions, but also are quite robust to a certain level of data contamination. We investigate the robustness property of each estimator in terms of the breakdown point. The finite sample performance and effectiveness of these estimators are evaluated through Monte Carlo simulations and a real-data application. Numerical results demonstrate that the proposed estimators perform favorably in a manner that they are comparable with the maximum likelihood estimator for the data without contamination and that they provide superior performance in the presence of data contamination.