In statistics, the

**is the probability distribution of a random variable of the form**

*F*-distribution

*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.

*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.