## The F - Distribution

The- distribution arises as the ratio of two chi-squared distributions:

where

• andhave chi-square distributions withanddegrees of freedom respectively, and

• andare independent.

• The mean, variance and skew areand respectively.

The probability density function of andistributed random variable is given by

for realwhereand are positive integers, andis the beta function.

The cumulative distribution function iswhereis the regularized incomplete beta function.