Fisher's z-distribution is the statistical distribution of half the logarithm of an F-distribution variate:
Probability density function
deg. of freedom|
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