# Fisher-Snedecor distribution

The Fisher-Snedecor distribution (also known as F-distribution) is a probability distribution defined on the range $[0, \infty]$. The Fisher-Snedecor distribution with parameters $p_{1}$  and $p_{2}$  arises as the ratio of two Chi-square variables with resp. $p_{1}$  and $p_{2}$  degrees of freedom.

$\begin{matrix} &f(x) = \dfrac{\sqrt{\dfrac{(p_1\,x)^{p_1}\,\,p_2^{p_2}} {(p_1\,x+p_2)^{p_1+p_2}}}} {x\,\mathrm{B}\!\left(\dfrac{p_1}{2},\dfrac{p_2}{2}\right)}\ \\ &F(x)=I_{\dfrac{p_1 x}{p_1 x + p_2}}(p_1/2, p_2/2) \\ \end{matrix}$

where $I$  is the regularised incomplete beta function.

$\mu = \frac{p_2}{p_2-2}$ for $p_2 > 2$

$\sigma = \sqrt{\dfrac{2\,p_2^2\,(p_1+p_2-2)}{p_1 (p_2-2)^2 (p_2-4)}}$ for $p_2 > 4$