Fisher's z-distribution

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
Probability density function
Parameters deg. of freedom
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Ronald Fisher

Fisher's z-distribution is the statistical distribution of half the logarithm of an F-distribution variate:

It was first described by Ronald Fisher in a paper delivered at the International Mathematical Congress of 1924 in Toronto. 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

where B is the beta function.

When the degrees of freedom becomes large (), the distribution approaches normality with mean

and variance

Related distribution