F-distribution Fisher-Snedecor distribution
服从[卡方分布]]，则 F 分布定义为：
F=\dfrac{X / n_{1}}{Y / n_{2}}\sim F(n_{1},n_{2}) \quad {\color{red}\Leftrightarrow} \quad \dfrac{1}{F}=\dfrac{Y / n_{2}}{X / n_{1}}\sim F(n_{2},n_{1}) \end{align}$$ - $n_{1}$ 为第一自由度 - $n_{2}$ 为第二自由度 $F_{1-\alpha}(n_{1},n_{2})= \dfrac{1}{F_{\alpha}(n_{2},n_{1})}$ $$\begin{align} & P\left\{F>F_{\alpha}(n_{1},n_{2}) \right\}=\alpha \\ 1-\alpha &=P\left\{F> F_{1-\alpha}(n_{1},n_{2}) \right\} \\ &=P\left\{\dfrac{1}{F}< \dfrac{1}{F_{1-\alpha}(n_{1},n_{2})} \\ \right\} \\ &=1-P\left\{\dfrac{1}{F}\geq \dfrac{1}{F_{1-\alpha}(n_{1},n_{2})} \right\} \\ \alpha &=P\left\{\dfrac{1}{F}\geq \dfrac{1}{F_{1-\alpha}(n_{1},n_{2})} \right\} \end{align}$$ 主要用于[[方差分析\|方差分析]]和[[线性回归\|回归分析]]中的转化表述/对立事件