F-distribution

URI: https://gptkb.org/entity/F-distribution

GPTKB entity

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