Reliability Engineering

Appendix F:Percentage Points for the F-Distribution

Let W and Y be independent chi-square random variables with u and v degrees of freedom, respectively. Then the ratio

has the probability density function

This is the probability density for the F distribution with u degrees of freedom for the numerator and v degrees of freedom for the denominator and is denoted by F_{u, v}.

The percentage points of the F distribution are given in the following table. If be the percentage point of the F distribution with the numerator degrees of freedom of ν₁ and the denominator degrees of freedom of ν₂, then

The lower tail percentage points f_{1−a, u, v} can be found using the following equation