Mason's gain formula

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Template:Distinguish Template:Probability distribution

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, entitled "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 . However, the mean and variance do not follow the same transformation.

The probability density function is[1][2]

where B is the beta function.

When the degrees of freedom becomes large () the distribution approach normality with mean[1]

and variance

Related Distribution

References

  • Fisher, R.A. (1924) On a Distribution Yielding the Error Functions of Several Well Known Statistics Proceedings of the International Congress of Mathematics, Toronto, 2: 805-813 pdf copy

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