An R Introduction to Statistics

F Distribution

If V 1 and V 2 are two independent random variables having the Chi-Squared distribution with m1 and m2 degrees of freedom respectively, then the following quantity follows an F distribution with m1 numerator degrees of freedom and m2 denominator degrees of freedom, i.e., (m1,m2) degrees of freedom.

F = V1∕m1-~ F (m ,m ) V2∕m2 1 2

Here is a graph of the F distribution with (5, 2) degrees of freedom.

PIC

Problem

Find the 95th percentile of the F distribution with (5, 2) degrees of freedom.

Solution

We apply the quantile function qf of the F distribution against the decimal value 0.95.

> qf(.95, df1=5, df2=2) 
[1] 19.296

Answer

The 95th percentile of the F distribution with (5, 2) degrees of freedom is 19.296.

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