
(1) 
(Kenney and Keeping 1951). This general distribution 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) 
See also Beta Distribution, Beta Prime Distribution, ChiSquared Distribution, Gamma Distribution,
Normal Distribution, Student's tDistribution
References
Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, pp. 180181, 1951.
© 19969 Eric W. Weisstein
19990526