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Fisher's z-distribution

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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:

Quick Facts z, Parameters ...
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Ronald Fisher

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

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  • If then (F-distribution)
  • If then
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References

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