THE GENERALIZATION OF STUDENTS PROBLEM WHEN SEVERAL DIFFERENT POPULATION VARIANCES ARE INVOLVED
成果类型：
Article
署名作者：
WELCH, BL
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/34.1-2.28
发表日期：
1947
页码：
2835
关键词：
摘要：
A population parameter [eta] is estimated by a statistic [gamma], normally distributed about [eta] with variance [image], where the [sigma]i are positive numbers and the [sigma]2 are unknown variances. If independent estimates of these variances are provided by the observed data, it is possible to make probability statements about [gamma] similar to those Student gave for the mean of a single sample. The form of the exact solution is given and a series solution is developed. The series converges rapidly for large samples and thus may be useful in constructing tables for this situation. An approximate solution is also given, indicating that [gamma] is approximately distributed as Student''s t. Comparison with the exact solution shows excellent agreement for large and substantial agreement for small samples.
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