SYSTEMS OF FREQUENCY CURVES GENERATED BY METHODS OF TRANSLATION
SYSTEMS OF FREQUENCY CURVES GENERATED BY METHODS OF TRANSLATION
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DOI：
10.1093/biomet/36.1-2.149
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发表时间：
1949-01-01
期刊：
影响因子：
2.7
通讯作者：
JOHNSON, NL
中科院分区：
文献类型：
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作者：
JOHNSON, NL
变量x被变换为z=f(X)，使得z是单位正态变量。如果变换f(X)依赖于几个参数，则生成一组频率曲线。具体地说，取z=[IMAGE]，参数VA/‘[Gamma]和[Delta]确定x的分布形状，而[lambda]和[xi]是比例和位置参数。讨论了三个系统，对应于变换z=[Gamma]+[Delta]log(x-[xi])的Sl，具有变换z=[Gamma]+[Delta]log[Image]的Sb和对应于z=[Gamma]+[Delta]log[Image]的SU，并根据可能的值[beta]1和[beta]2来表示构成单个曲线系。系统S1是对数正态函数，并且充当其他两个之间的过渡函数。给出了三个数值算例。附录给出了系统SB中的分布矩。
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.