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<p>This study addresses the estimation of stress–strength reliability <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R=\Pr (X&gt;Y)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mo>=</mo> <mo>Pr</mo> <mo stretchy="false">(</mo> <mi>X</mi> <mo>&gt;</mo> <mi>Y</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> for Gompertz lifetime models with a common shape parameter using left-truncated data. We derive the maximum likelihood estimator (MLE) and the exact confidence interval for <i>R</i> when the shape parameter is known. Conversely, when the shape parameter is unknown, we develop the MLE and an asymptotic confidence interval. We conduct simulation studies to assess the performance of the proposed estimation methods, comparing various confidence intervals in terms of expected length (EL) and coverage probability (CP). Additionally, we apply our estimation methods to a real dataset to demonstrate their practical utility.</p>

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Statistical Inference on Strength–Stress Reliability for Gompertz Distribution Based on Left Truncated Data

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月6日

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  • Abouzar Hemmati,
  • Zahra Khodadadi,
  • Mohammad Reza Mahmudi,
  • Karim Zare

摘要

This study addresses the estimation of stress–strength reliability \(R=\Pr (X>Y)\) R = Pr ( X > Y ) for Gompertz lifetime models with a common shape parameter using left-truncated data. We derive the maximum likelihood estimator (MLE) and the exact confidence interval for R when the shape parameter is known. Conversely, when the shape parameter is unknown, we develop the MLE and an asymptotic confidence interval. We conduct simulation studies to assess the performance of the proposed estimation methods, comparing various confidence intervals in terms of expected length (EL) and coverage probability (CP). Additionally, we apply our estimation methods to a real dataset to demonstrate their practical utility.