# F-distribution

In

statistics, the

*F*-distribution is the

probability distribution of a random variable of the form

where

*U*_{1} and *U*_{2} have chi-square distributions with *d*_{1} and *d*_{2} degrees of freedom respectively, and

*U*_{1} and *U*_{2} are independent.

The

*F*-distribution arises frequently as the null distribution of a test statistic, especially in likelihood-ratio tests, perhaps most notably in the

analysis of variance.