Snedecor,s F-Distribution
المؤلف:
Beyer, W. H.
المصدر:
CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press
الجزء والصفحة:
p. 536
14-4-2021
1766
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
so the first few central moments are given by
and the mean, variance, skewness, and kurtosis excess are
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.
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