F-distribution
Notation:
$X \sim F(d_1,d_2)$
Probability Density Function:
$ff(x)=\frac{\sqrt{\frac{(d_1 x)^{d_1} {d_2}^{d_2}}{(d_1 x
+ d_2)^{d_1+d_2}} }} {x \mathcal{B}\left(\frac{d_1}{2}, \frac{d_2}{2} \right)}$
where:
- $d_1 > 0$
- $d_2 > 0$
- $x > 0$
- $\mathcal{B}$ is the beta function
Mean:
$\mathrm{E}[X]=\mu=\frac{d_2}{d_2-2}$ for $d_2>2$
Variance:
$\mathrm{Var}[X]=\sigma^2=\frac{2d_2^2 (d_1+d_2-2)}{d_1(d_2-2)^2(d_2-4)}$ for
$d_2 > 4$
References:
-
F-distribution - Wikipedia
-
F-distribution - Wolfram MathWorld