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F-distribution

{(d_1\,x+d_2)^{d_1+d_2}}}} {x\,\mathrm{B}\!\left(\frac{d_1}{2},\frac{d_2}{2}\right)}\!|

cdf =$I_{\frac{d_1 x}{d_1 x + d_2}} \left(\tfrac{d_1}{2}, \tfrac{d_2}{2} \right)$|
mean =$\frac{d_2}{d_2-2}\!$
for d > 2|
median =|
mode =$\frac{d_1-2}{d_1}\;\frac{d_2}{d_2+2}$
for d > 2|
variance =$\frac{2\,d_2^2\,(d_1+d_2-2)}{d_1 (d_2-2)^2 (d_2-4)}\!$
for d > 4|
skewness =$\frac{(2 d_1 + d_2 - 2) \sqrt{8 (d_2-4)}}{(d_2-6) \sqrt{d_1 (d_1 + d_2 -2)}}\!$
for d > 6|
kurtosis =see text|
entropy =|
mgf =''does not exist, raw moments defined in text and in ''|
char =see text|}}

The F-distribution, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor) is, in probability theory and statistics, a continuous probability distribution.

The F-distribution arises frequently as the null distribution of a test statistic, most notably in the analysis of variance; see F-test.