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<p>This article introduces the auto-relevated log-logistic distribution, a new lifetime model obtained by applying the auto-relevation transform to the classical log-logistic distribution. A comprehensive reliability analysis of the proposed distribution, with a specific focus on its non-monotonic hazard rate behavior, is conducted. The tail properties of the distribution are also rigorously investigated. The practical efficacy of the ARLL distribution is demonstrated through a detailed real-data application. In addition, important risk assessment measures, including value-at-risk and tail-value-at-risk, mean of order <i>P</i> and peak over relative threshold-VaR are analyzed.</p>

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Reliability Properties and Applications of Auto-Relevated Log-Logistic Model

  • 期刊论文

  • 发表日期：

    2026年7月3日

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  • Anand R,
  • Dileepkumar M,
  • Greeshma Chandran

摘要

This article introduces the auto-relevated log-logistic distribution, a new lifetime model obtained by applying the auto-relevation transform to the classical log-logistic distribution. A comprehensive reliability analysis of the proposed distribution, with a specific focus on its non-monotonic hazard rate behavior, is conducted. The tail properties of the distribution are also rigorously investigated. The practical efficacy of the ARLL distribution is demonstrated through a detailed real-data application. In addition, important risk assessment measures, including value-at-risk and tail-value-at-risk, mean of order P and peak over relative threshold-VaR are analyzed.