More About the F-distribution

The F-distribution is one of the most fundamental distributions in Statistics, along with the normal distribution and the Chi-Square distribution. Technically, the F-distribution is obtained by constructing the ratio between two properly scaled variables that have a Chi-Squared distribution

Indeed if $U_1$ and $U_2$ are two independent random variables that have a Chi-Square distribution, and $U_1$ has $df_1$ degrees of freedom and $U_2$ has $df_2$ degrees of freedom, then the variable $F$ defined as

$$F = \displaystyle \frac{U_1/df_1}{U_2/df_2}$$

has an F-distribution, with degrees of freedom $df_1$ and $df_2$.

The F-distribution is one of the crucial continuous distributions in Statistics. You can use other probability calculators for continuous distributions, such as our normal probability calculator , Chi-Square distribution calculator or our uniform probability calculator , among many others.