Snedecor's F-Distribution

If a random variable has a chi-squared distribution with degrees of freedom () and a random variable has a chi-squared distribution with degrees of freedom (), and and are independent, then

(1)

is distributed as Snedecor's -distribution with and degrees of freedom

(2)

for . The raw moments are

			(3)
			(4)
			(5)
			(6)

so the first few central moments are given by

			(7)
			(8)
			(9)

and the mean, variance, skewness, and kurtosis excess are

			(10)
			(11)
			(12)
			(13)

The characteristic function can be computed, but it is rather messy and involves the generalized hypergeometric function .

Letting

(14)

gives a beta distribution (Beyer 1987, p. 536).