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Fisher's z-distribution : ウィキペディア英語版
Fisher's z-distribution

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Fisher's z-distribution is the statistical distribution of half the logarithm of an F distribution variate:
: z = \frac \log F
It was first described by Ronald Fisher in a paper delivered at the International Mathematical Congress of 1924 in Toronto, titled "On a distribution yielding the error functions of several well-known statistics" (Proceedings of the International Congress of Mathematics, Toronto, 2: 805-813 (1924). Nowadays one usually uses the F distribution instead.
The probability density function and cumulative distribution function can be found by using the F-distribution at the value of x' = e^ \, . However, the mean and variance do not follow the same transformation.
The probability density function is
: f(x; d_1, d_2) = \frac} \frac + d_2\right)^},
where ''B'' is the beta function.
When the degrees of freedom becomes large (d_1, d_2 \rightarrow \infty) the distribution approach normality with mean〔
: \bar = (1/d_2 - 1/d_1)/2
and variance
: \sigma^2_x = (1/d_1 + 1/d_2)/2.
==Related Distribution==

*If X \sim \operatorname(n,m) then e^ \sim \operatorname(n,m) \, (F-distribution)
*If X \sim \operatorname(n,m) then \tfrac \sim \operatorname(n,m)

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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