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).

REFERENCES:

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 536, 1987.