F distribution

An F Distribution is a kind of Sampling Distribution formed by combining two independent Chi Squared Distributions in the following fasion

$$F\equiv \frac{{\chi }_{(n)}^2/n}{{\chi }_{(m)}^2/m}\sim F(n,m)$$

• F shows up when we want to find Confidence Intervals or conduct Hypothesis Tests

F Quantiles

If $F\sim F(n,m)$ then the $(1-\alpha )$ quantile is denoted $F_{\alpha ,n,m}$

• where $P(F>F_{\alpha ,n,m})=\alpha$
• where the CDF does not have a simple closed form, and the PDF is a mess
• where $\alpha$ is type I error
• where $n,m$ are separate Degree of Freedoms
• where $F_{1-\alpha ,n,m}=1/F_{\alpha ,n,m}$