The F distribution (for x > 0) has density function (for n = 1, 2, ...; w = 1, 2, ...):

f(x) = {

where

n, w |
are the degrees of freedom |

G |
(gamma) is the Gamma function. |

The animation above shows various tail areas (p-values) for an F distribution with both degrees of freedom equal to 10. Note that F represents the critical value from the F distribution displayed in the animation. For a complete listing of all distribution functions, see Distributions and Their Functions.