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.