SYSTEMS OF FREQUENCY CURVES GENERATED BY METHODS OF TRANSLATION
成果类型：
Article
署名作者：
JOHNSON, NL
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.2307/2332539
发表日期：
1949
页码：
149176
关键词：
摘要：
A variable x is transformed by z = f(x) so that z is a unit normal variable. If the transformation, f(x), depends on a few parameters, a system of frequency curves is generated. In particular, taking z = [image] the parametersV A /'' [gamma] and [delta] determine the shape of the distributions of x while [lambda]and [xi] are scale and location parameters. The three systems, Sl corresponding to the transformation z = [gamma] + [delta] log (x - [xi]), SB with transformation z = [gamma] + [delta] log [image] and Su corresponding to z = [gamma] + [delta] log [image] are discussed and shown to constitute a single system of curves in terms of possible values [beta]1 and [beta]2. The system Sl is the logarithmic normal function and serves as a transition function between the two others. Three numerical examples are given. An appendix gives moments of distributions in the system SB.
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