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贝叶斯和非贝叶斯估计的二变逆韦布尔分布参数使用排序集采样与并发变量的贝叶斯和非贝叶斯估计
Hiba Z Muhammed1, Mostafa Shaaban2
1Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt.
Scientific reports
|November 7, 2025
概括
排列采集采样 (RSS) 显著改善了比简单随机采样 (SRS) 的双变量分布参数估计. 使用RSS的贝叶斯方法提供更高的效率和更低的偏差可靠性和寿命分析.
科学领域:
- 统计 统计 统计 统计
- 可能性理论概率理论.
- 可靠性工程可靠性工程
背景情况:
- 估计双变量分布参数对于配对变量依赖关系至关重要.
- 简单的随机抽样 (SRS) 对变量或资源密集型数据可能是低效的.
- 排序集采样 (RSS) 通过对测量的子集进行排序来提高效率.
研究的目的:
- 用贝叶斯式和非贝叶斯式方法估计二变逆韦布尔 (BIW) 分布参数.
- 在不同的估计技术下比较RSS和SRS的性能.
- 为了评估贝叶斯估计的有效性与结合的马先验.
主要方法:
- 使用贝叶斯式和非贝叶斯式 (最大概率估计 - MLE) 技术.
- 在二次错误损失下使用联的马先验的衍生贝叶斯估计器.
- 由于非线性概率方程,使用牛顿-拉普森技术对数值MLE解决方案.
- 在四个参数设置中进行了广泛的蒙特卡洛模拟 (1万次复制).
主要成果:
- 在平均平方误差 (MSE) 和效率 (EFF) 方面,RSS 始终优于 SRS.
- 根据RSS的贝叶斯估计表明,与MLE相比,MSE和偏差较低.
- 对于含有RSS的大型样本,MSE减少了多达50%,EFF超过10个.
- 预先选择对贝叶斯表现产生了重大影响,特别是在小参数方面.
结论:
- 对于估计BIW分布参数,RSS是一种比SRS更有效的采样技术.
- 对于可靠性和寿命分析,建议使用贝叶斯估计,特别是RSS和适当的先验值.
- 这项研究使用对男性体脂肪和胸围的真实数据集来验证这些发现.
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