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gptkbp:instanceOf
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Probability distribution
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gptkbp:alsoKnownAs
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gptkb:Fisher–Snedecor_distribution
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gptkbp:application
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Comparing variances
Model comparison
Testing equality of means
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gptkbp:category
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Continuous probability distributions
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gptkbp:cumulativeDistributionFunction
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I_{d1 x/(d1 x + d2)}(d1/2, d2/2)
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gptkbp:field
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gptkb:Probability_theory
Statistics
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gptkbp:firstDescribed
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1924
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https://www.w3.org/2000/01/rdf-schema#label
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F-distribution
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gptkbp:kurtosis
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Defined for d2 > 8
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gptkbp:limitation
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As d2 → ∞, F-distribution approaches chi-squared/d1
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gptkbp:meaning
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d2/(d2-2) for d2 > 2
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gptkbp:mode
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[(d1-2)d2]/[d1(d2+2)] for d1 > 2
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gptkbp:namedAfter
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gptkb:Ronald_Fisher
gptkb:George_W._Snedecor
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gptkbp:parameter
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Degrees of freedom denominator
Degrees of freedom numerator
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gptkbp:pdf
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f(x; d1, d2) = [d1^{d1/2} d2^{d2/2} x^{(d1/2)-1}]/[B(d1/2, d2/2) (d1 x + d2)^{(d1+d2)/2}]
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gptkbp:relatedTo
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gptkb:Student's_t-distribution
gptkb:Beta_distribution
gptkb:Chi-squared_distribution
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gptkbp:skewness
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Defined for d2 > 6
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gptkbp:supports
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x > 0
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gptkbp:usedFor
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F-test
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gptkbp:usedIn
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gptkb:Analysis_of_variance
gptkb:Hypothesis_testing
gptkb:Regression_analysis
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gptkbp:variant
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[2 d2^2 (d1 + d2 - 2)]/[d1 (d2 - 2)^2 (d2 - 4)] for d2 > 4
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gptkbp:bfsParent
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gptkb:Ronald_Fisher
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gptkbp:bfsLayer
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4
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