Fisher's z-distribution
Statistical distribution / From Wikipedia, the free encyclopedia
Not to be confused with Fisher z-transformation.
"z-distribution" redirects here. For the distribution related to z-scores, see Normal distribution § Standard normal distribution.
Fisher's z-distribution is the statistical distribution of half the logarithm of an F-distribution variate:
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It was first described by Ronald Fisher in a paper delivered at the International Mathematical Congress of 1924 in Toronto.[1] 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 . However, the mean and variance do not follow the same transformation.
The probability density function is[2][3]
where B is the beta function.
When the degrees of freedom becomes large (), the distribution approaches normality with mean[2]
and variance