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F Distribution

TOP/Statistical Functions/F-distribution
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Calculate the probability density function, lower cumulative probability, and upper cumulative probability of the F distribution.
Percentile Point x
x≧0
Number of degrees of freedom in the numerator ν1
ν1＞0
Degrees of freedom in the denominator ν2
ν2＞0
\(\normalsize F-distribution\ F(x,\nu_1,\nu_2)\\ (1) probability\ density\\ \hspace{30px}f(x,\nu_1,\nu_2)={\large\frac{\nu_1^{\frac{\nu_1}{2}}\ \nu_2^{\frac{\nu_2}{2}}}{B(\frac{\nu_1}{2},\frac{\nu_2}{2})}} {\large\frac{x^{\frac{\nu_1}{2}-1}} {\ (\nu_2+\nu_1x)^{\frac{\nu_1+\nu_2}{2}}}}\\ (2) lower\ cumulative\ distribution\\ \hspace{30px}P(x,\nu_1,\nu_2)={\large\int_{\small 0}^{\small x}}f(t,\nu_1,\nu_2)dt\\ (3) upper\ cumulative\ distribution\\ \hspace{30px}Q(x,\nu_1,\nu_2)={\large\int_{\small x}^{\small\infty}}f(t,\nu_1,\nu_2)dt\\\)

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