\(\normalsize F-distribution\ F(x,\nu_1,\nu_2)\\
(1) probability\ density\\
\hspace{30px}f(x,\nu_1,\nu_2)={\large\frac{\nu_1^{\frac{\nu_1}{2}}\ \nu_2^{\frac{\nu_2}{2}}}{B(\frac{\nu_1}{2},\frac{\nu_2}{2})}} {\large\frac{x^{\frac{\nu_1}{2}-1}} {\ (\nu_2+\nu_1x)^{\frac{\nu_1+\nu_2}{2}}}}\\
(2) lower\ cumulative\ distribution\\
\hspace{30px}P(x,\nu_1,\nu_2)={\large\int_{\small 0}^{\small x}}f(t,\nu_1,\nu_2)dt\\
(3) upper\ cumulative\ distribution\\
\hspace{30px}Q(x,\nu_1,\nu_2)={\large\int_{\small x}^{\small\infty}}f(t,\nu_1,\nu_2)dt\\\) |
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