 | ||
Parameters d 1 > 0 , d 2 > 0 {displaystyle d_{1}>0, d_{2}>0} deg. of freedom Support x ∈ ( − ∞ ; + ∞ ) {displaystyle xin (-infty ;+infty )!} PDF 2 d 1 d 1 / 2 d 2 d 2 / 2 B ( d 1 / 2 , d 2 / 2 ) e d 1 z ( d 1 e 2 z + d 2 ) ( d 1 + d 2 ) / 2 {displaystyle { rac {2d_{1}^{d_{1}/2}d_{2}^{d_{2}/2}}{B(d_{1}/2,d_{2}/2)}}{ rac {e^{d_{1}z}}{left(d_{1}e^{2z}+d_{2}ight)^{left(d_{1}+d_{2}ight)/2}}}!} Mode 0 {displaystyle 0} | ||
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
The probability density function is
where B is the beta function.
When the degrees of freedom becomes large (
and variance