A Novel Exact Inference Approach for Log-Logistic Reliability Functions with Applications to Time-to-Event Data

TL;DR

This paper introduces a new inference method for log-logistic distribution parameters and reliability functions, especially effective with small samples, using least squares estimator-based generalized pivotal quantities.

Contribution

It proposes a novel LSE-GPQ framework that improves reliability inference for log-logistic distributions over traditional methods.

Findings

LSE-GPQ provides better coverage in small samples.

Simulation studies show improved accuracy over MLE.

Real data applications validate the method's effectiveness.

Abstract

Log-logistic distribution is a flexible distribution that can model a wide range of failure patterns in the field of electrical, electronic and mechanical engineering and is often used in reliability inference. However, the inference of the parameters and reliability function of the log-logistic distribution can be challenging, especially in small sample scenarios. In this paper, we propose a new inference framework based on the least squares estimator-based generalized pivotal quantities (LSE-GPQ) for the parameters and reliability functions of the log-logistic distribution, which can provide better coverage in small sample scenarios. We will compare the performance of our proposed method with traditional methods such as the MLE and parametric bootstrapping through simulation studies and real data applications.