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F Distribution

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Definition Background Example See Also

Definition

The pdf for the F distribution is

where Γ( · ) is the Gamma function.

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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.

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.

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Example

The most common application of the F distribution is in standard tests of hypotheses in analysis of variance and regression.

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

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

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See Also

Continuous Distributions (Statistics)

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Extreme Value Distribution

Gamma Distribution

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