F Distribution

Definition

The pdf for the F distribution is

y=f(x|ν1,ν2)=Γ[(ν1+ν2)2]Γ(ν12)Γ(ν22)(ν1ν2)ν12xν122[1+(ν1ν2)x]ν1+ν22

where Γ( · ) is the Gamma function.

Background

The F distribution has a natural relationship with the chi-square distribution. If χ1 and χ2 are both chi-square with ν1 and ν2 degrees of freedom respectively, then the statistic F below is F-distributed.

F(ν1,ν2)=χ1ν1χ2ν2

The two parameters, ν1 and ν2, are the numerator and denominator degrees of freedom. That is, ν1 and ν2 are the number of independent pieces of information used to calculate χ1 and χ2, respectively.

Examples

Compute the F Distribution pdf

Compute the pdf of an F distibution with 5 numerator degrees of freedom and 3 denominator degrees of freedom.

x = 0:0.01:10;
y = fpdf(x,5,3);

Plot the pdf.

figure;
plot(x,y)

The plot shows that the F distribution exists on positive real numbers and is skewed to the right.

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