F Distribution
The F distribution
(for x > 0) has density function (for n = 1, 2, ...; w
= 1, 2, ...):
f(x) = {G[(n+w)/2]} / [G(n/2)*G(w/2)]*(n/w)n/2 *
x(n/2)-1 * {1+[(n/w)*x]} -(n+w)/2
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.