F分布

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

$X \sim χ^{2} (n_{1}) Y \sim χ^{2} (n_{2})$ 服从[卡方分布]]，则 F 分布定义为：

\begin{array}{r} F = \frac{X / n_{1}}{Y / n_{2}} \sim F (n_{1}, n_{2}) \Leftrightarrow \frac{1}{F} = \frac{Y / n_{2}}{X / n_{1}} \sim F (n_{2}, n_{1}) \end{array}

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

\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