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

2026-05-01

AI Summary

This study addresses the challenges of inferring parameters and reliability functions of the log-logistic distribution under small-sample settings, where conventional methods often yield confidence intervals with inadequate coverage probabilities. To overcome this limitation, the authors propose a novel inference framework based on generalized pivotal quantities derived from least squares estimation (LSE-GPQ). This work represents the first application of the LSE-GPQ approach to reliability analysis for the log-logistic distribution, constructing accurate confidence intervals by integrating least squares estimates with generalized pivotal quantities. Extensive simulations and real-data analyses demonstrate that, compared to maximum likelihood estimation and parametric bootstrap methods, the proposed LSE-GPQ method achieves substantially higher coverage rates in small samples, offering superior inferential accuracy and robustness.

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.

Problem

• log-logistic distribution
• reliability inference
• small sample
• parameter estimation
• time-to-event data

Innovation

• log-logistic distribution
• generalized pivotal quantities
• least squares estimator
• reliability inference
• small sample inference