AI 中文总结
本文针对逐步II型删失下多个Weibull总体的公共形状参数与变异系数，采用多种统计方法开展区间估计比较研究，提出最优删失方案，经模拟与实例验证推荐贝叶斯及方差估计恢复类区间估计方法。
AI 中文摘要
Weibull分布是可靠性工程、工业、气象研究及癌症研究中用于建模各类失效率和偏态数据的最灵活连续概率分布之一。在统计推断中，多个Weibull总体共享同一形状参数是常见场景，这也意味着它们具有相同的变异系数。尽管针对完整样本的公共形状参数推断研究常被考虑，但删失数据的存在需要单独研究，而现有文献对此关注不足。因此，本文的重点是基于大样本理论、方差估计恢复、广义枢轴量和贝叶斯推断的频率论方法，对逐步II型删失下公共形状参数和公共变异系数的区间估计进行比较研究，还提出了一种最优删失方案以提升区间估计的稳健性。通过模拟研究和真实碳纤维强度数据实例开展数值分析用于比较，结果表明基于贝叶斯方法和方差估计恢复方法的区间估计表现令人满意。
英文摘要
The Weibull distribution is one of the most flexible continuous probability distributions used to model various failure rates and skewed data in reliability engineering, industry, weather studies and cancer studies. It is a common scenario in statistical inference that several Weibull populations share the same shape parameter, which also implies that they have the same coefficient of variation. While the inferential study of the common shape parameter is often considered for complete samples, the presence of censored data requires a separate investigation that has not received enough attention in the existing literature. Therefore, the focus of this article is on a comparative study of interval estimators for the common shape parameter and the common coefficient of variation under progressive type-II censoring using frequentist methods based on large-sample theory, variance estimates recovery, generalized pivots, and Bayesian inference. An optimal censoring scheme is also proposed to enhance the robustness of interval estimation. Numerical data analyses using a simulation study and a real carbon fiber strength data example are carried out for comparison, and the results recommend the intervals based on Bayesian and variance estimates recovery methods for their satisfactory performance.
Comments23 pages
