发表机构
Department of Mathematics, Saitsohpen, Sohra, East Khasi Hills District, Meghalaya, India（印度梅加拉亚邦东卡西丘陵县索拉赛特索彭数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对带逐次I型区间删失数据的Power Lindley模型，采用贝叶斯与频率论方法估计相对变异性，经模拟和实际数据验证，贝叶斯框架在点与区间估计中性能更优。
AI 中文摘要
针对Power Lindley分布，利用逐次I型区间删失数据对变异系数等相对变异性度量进行估计。采用贝叶斯和频率论两种方法，包括中点近似、极大似然估计、矩估计、自助法和非线性最小二乘法。由于参数无闭式表达式，采用数值近似方法进行参数估计。在似然框架内构造渐近置信区间，还提出了百分位自助区间和学生t自助区间。在贝叶斯范式中，假设参数的独立有信息先验和无信息先验，通过切片采样算法完成后验点和区间推断，同时重点讨论了最优监测区间的选择。开展了综合模拟研究，以评估所提估计量在不同删失方案和样本量下的性能，实际数据应用也验证了所提方法的实用性。结果表明，贝叶斯框架在点估计和区间估计中通常表现更优。
英文摘要
The measures of relative variability, such as the coefficient of variation, are highly utilized tools of inference in several interdisciplinary fields such as reliability, finance, quality control, and biological sciences. Inferential studies of these measures are highly limited for lifetime models, such as the flexible power Lindley distribution, particularly under progressive type-I interval censoring. In this article, frequentist approaches including the midpoint approximation, maximum likelihood estimation, method of moments, bootstrap, and nonlinear least squares methods, and Bayesian inference using slice sampling are applied for estimation of these measures of relative variability for the power Lindley distribution under progressive type-I interval censoring. Confidence intervals are also constructed based on asymptotic theory, bootstrap and Bayesian paradigm. A discussion on choosing optimal monitoring intervals is also highlighted. A comprehensive simulation study is conducted to evaluate the performance of the proposed estimators across various censoring plans and sample sizes. A real data application illustrates the practical utility of the proposed methodologies. The results indicate that the Bayesian framework generally exhibits superior performance in both point and interval estimation.
Comments20 pages
