 | ||
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