F分布

F-distribution Fisher-Snedecor distribution
$F \sim F (n_{1}, n_{2})$

$F = \frac{X / n_{1}}{Y / n_{2}} \sim F (n_{1}, n_{2})$

$\frac{1}{F} = \frac{Y / n_{2}}{X / n_{1}} \sim F (n_{2}, n_{1})$

$X \sim χ^{2} (n_{1}) Y \sim χ^{2} (n_{2})$

$F_{1 - α} (n_{1}, n_{2}) = \frac{1}{F_{α} (n_{2}, n_{1})}$

\begin{aligned} P {F > F_{α} (n_{1}, n_{2})} = α \\ 1 - α & = P {F > F_{1 - α} (n_{1}, n_{2})} \\ = P {\frac{1}{F} < \frac{1}{F_{1 - α} (n_{1}, n_{2})}} \\ = 1 - P {\frac{1}{F} \geq \frac{1}{F_{1 - α} (n_{1}, n_{2})}} \\ α & = P {\frac{1}{F} \geq \frac{1}{F_{1 - α} (n_{1}, n_{2})}} \end{aligned}

主要用于方差分析和回归分析中的
转化表述，对立事件