Fisher-Snedecor distribution

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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


Fpdf.png
Fcdf.png

External link

Fisher-Snedecor distribution