Fischer's distribution is the general distribution defined by
(1)

(Kenney and Keeping 1951) which includes the chisquared distribution and Student's tdistribution as special cases.
Let and be independent unbiased estimators of the variance of a normally distributed variate. Define
(2)

Then let
(3)

so that is a ratio of chisquared variates
(4)

which makes it a ratio of gamma distribution variates, which is itself a beta prime distribution variate,
(5)

giving
(6)

The mean is
(7)

and the mode is
(8)
