Limitations of the Welch-Satterthwaite approximation for measurement uncertainty calculations
Limitations of the Welch-Satterthwaite approximation for measurement uncertainty calculations
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DOI：
10.1088/0026-1394/37/1/8
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发表时间：
2000-01-01
期刊：
影响因子：
2.4
通讯作者：
Ballico, M
中科院分区：
文献类型：
--
作者：
Ballico, M
Welch-Satterthwaite 近似用于估计由几个独立正态分布形成的概率分布的“有效自由度”，其中仅已知方差估计。国际标准化组织 (ISO) 测量不确定度表达指南建议使用它来计算由多个分布形成的不确定度的扩展不确定度（置信区间的 ISO 术语）。尽管众所周知该公式是一个近似值，但当主分布的方差估计具有少量自由度时，可能会获得反直觉的结果；有时会发现计算出的置信限会随着贡献不确定性的增加而减少。
The Welch-Satterthwaite approximation is used to estimate an "effective degrees of freedom" for a probability distribution formed from several independent normal distributions for which only estimates of the variance are known. The International Organization for Standardization (ISO) Guide to the Expression of Uncertainty in Measurement recommends its use for the calculation of expanded uncertainties (the ISO term for confidence intervals) for uncertainties formed from several distributions. Although it is well recognized that this formula is an approximation, counter-intuitive results may be obtained when a variance estimate of the dominant distribution has a small number of degrees of freedom; the calculated confidence limits are sometimes found to decrease with increases in the contributing uncertainties.