# F-distribution (chart) Calculator

## Calculates a table of the probability density function, or lower or upper cumulative distribution function of the F-distribution, and draws the chart.

 select function probability density f lower cumulative distribution P upper cumulative distribution Q degree of freedom ν1 ν1＞0 degree of freedom ν2 ν2＞0 [ initial percentile x x≧0 increment repetition ]
 $\normal F-distribution\ F(x,\nu_1,\nu_2)\\[10](1)\qquad probability\ density\\\hspace{30}f(x,\nu_1,\nu_2)={\large\frac{\nu_1^{\frac{\nu_1}{2}}\ \nu_2^{\frac{\nu_2}{2}}}{B(\frac{\nu_1}{2},\frac{\nu_2}{2})}} {\large\frac{x^{\frac{\nu_1}{2}-1}} {\ (\nu_2+\nu_1x)^{\frac{\nu_1+\nu_2}{2}}}}\\(2)\qquad lower\ cumulative\ distribution\\\hspace{30}P(x,\nu_1,\nu_2)={\large\int_{\small 0}^{\hspace{25}\small x}}f(t,\nu_1,\nu_2)dt\\(3)\qquad upper\ cumulative\ distribution\\\hspace{30}Q(x,\nu_1,\nu_2)={\large\int_{\small x}^{\hspace{25}\small\infty}}f(t,\nu_1,\nu_2)dt\\$

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