SYSTEMS OF FREQUENCY CURVES GENERATED BY METHODS OF TRANSLATION
SYSTEMS OF FREQUENCY CURVES GENERATED BY METHODS OF TRANSLATION
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DOI：
10.2307/2332539
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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：
--
作者：
JOHNSON, NL
变量x通过z = f（x）变换，使得z是单位正规变量。如果变换f（x）取决于几个参数，则生成频率曲线系统。特别地，取z = [image]，参数[lambda][gamma]和[delta]确定x的分布的形状，而[lambda]和[xi]是尺度和位置参数。讨论了三个系统，即对应于变换z = [gamma] + [delta] log（x - [xi]）的S1、具有变换z = [gamma] + [delta] log [image]的SB和对应于z = [gamma] + [delta] log [image]的Su，并且示出了根据可能值[beta]1和[beta]2构成单个曲线系统。系统S1是对数正态函数，并且用作两个其它函数之间的过渡函数。给出了三个数值例子。附录给出了系统SB中的分布时刻。
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.