F分布
g ( x ) = 1 B ( d 1 / 2 , d 2 / 2 ) ( d 1 x d 1 x + d 2 ) d 1 / 2 ( 1 − d 1 x d 1 x + d 2 ) d 2 / 2 x − 1 {\displaystyle g(x)={\frac {1}{\mathrm {B} (d_{1}/2,d_{2}/2)}}\;\left({\frac {d_{1}\,x}{d_{1}\,x+d_{2}}}\right)^{d_{1}/2}\;\left(1-{\frac {d_{1}\,x}{d_{1}\,x+d_{2}}}\right)^{d_{2}/2}\;x^{-1}}
(ここで実数 x ≥ 0 に対し d1 と d2 は正の整数で、B はベータ関数を表す)
累積分布関数は
G ( x ) = I d 1 x d 1 x + d 2 ( d 1 / 2 , d 2 / 2 ) {\displaystyle G(x)=I_{\frac {d_{1}x}{d_{1}x+d_{2}}}(d_{1}/2,d_{2}/2)}
(ここでI は正規化不完全ベータ関数)