F Distribution
The F distribution (for x > 0) has density function (for

= 1, 2, ...;

= 1,2, ...):

where

,

are the degrees of freedom

(gamma) is the Gamma function.
F Distribution (animation)The animation above shows various tail areas (p-values) for an F distribution with both degrees of freedom equal to 10.
A continuous probability distribution of the ratio of two independent random variables, each having a Chi-squared distribution, divided by their respective degrees of freedom. The commonest use is to assign p values to mean square ratios (variance ratios) in ANOVA. In regression analysis, the F-test can be used to test the joint significance of all variables of a model.