Fisher's Z-Distribution

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

Fisher's z
Probability density function
Fisher's Z-Distribution
Parameters deg. of freedom
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Fisher's Z-Distribution
Ronald Fisher

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

  • If Fisher's Z-Distribution  then Fisher's Z-Distribution  (F-distribution)
  • If Fisher's Z-Distribution  then Fisher's Z-Distribution 

References

Tags:

F-distributionLogarithmStatistical distributionVariate

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