THE FREQUENCY DISTRIBUTION OF SQUARE-ROOT-B1 FOR SAMPLES OF ALL SIZES DRAWN AT RANDOM FROM A NORMAL POPULATION
成果类型：
Article
署名作者：
GEARY, RC
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.2307/2332513
发表日期：
1947
页码：
6897
关键词：
摘要：
A general integral relation is established between the frequency functions of [square root]b1 or a3, in samples of size n and (n[long dash]1) from a normal population. Using the known distribution for samples of size 3 given by Fisher and iterative methods, it is possible to obtain solutions to any desired degree of precision for the frequency functions for samples of 4, 5, 6, 7 and 8. At n = 8, it is shown that the frequency distribution is closely approximated by the Gram-Charlier series with the known moments up to [mu]8. Thus, for n > 8, empirical solutions accurate enough for practical purposes may be found by the Gram-Charlier curve.