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F-distribution

In probability theory and statistics, the F-distribution or F-ratio, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor), is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA) and…

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CDF
I d 1 x d 1 x + d 2 ( d 1 2 , d 2 2 ) {\displaystyle I_{\frac {d_{1}x}{d_{1}x+d_{2}}}\left({\tfrac {d_{1}}{2}},{\tfrac {d_{2}}{2}}\right)}
CF
see text
Entropy
ln ⁡ Γ ( d 1 2 ) + ln ⁡ Γ ( d 2 2 ) − ln ⁡ Γ ( d 1 + d 2 2 ) + ( 1 − d 1 2 ) ψ ( 1 + d 1 2 ) − ( 1 + d 2 2 ) ψ ( 1 + d 2 2 ) + ( d 1 + d 2 2 ) ψ ( d 1 + d 2 2 ) + ln ⁡ d 2 d 1 {…
Excess kurtosis
see text
Mean
d 2 d 2 − 2 {\displaystyle {\frac {d_{2}}{d_{2}-2}}} for d2 > 2
MGF
does not exist, raw moments defined in text and in

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F-distribution

Nodes43
Edges42
Triples40
Avg. degree1.95
Density0.046512
Components1

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F-distribution

Top relations

related to In general · 15
F-distribution → Beta, Chi, Equivalently, Fisher's, FisherZ, Gamma, Hotelling's T-squared, If, Laplace, Pearson, Student's, The, W-distribution, X/, Y/
related to External links · 6
F-distribution → F-distributionEarliest Uses, F-testing, Mathematics, Some, Table, Words
related to Relation to the chi-squared distribution · 3
F-distribution → Cochran's, Equivalently, In
is a · 2
F-distribution → particular parametrization of the beta prime distribution, special case of type 6 Pearson distribution.If X
CDF · 1
F-distribution → I d 1 x d 1 x + d 2 ( d 1 2 , d 2 2 ) {\displaystyle I_{\frac {d_{1}x}{d_{1}x+d_{2}}}\left({\tfrac {d_{1}}{2}},{\tfrac {d_{2}}{2}}\right)}
CF · 1
F-distribution → see text
Entropy · 1
F-distribution → ln ⁡ Γ ( d 1 2 ) + ln ⁡ Γ ( d 2 2 ) − ln ⁡ Γ ( d 1 + d 2 2 ) + ( 1 − d 1 2 ) ψ ( 1 + d 1 2 ) − ( 1 + d 2 2 ) ψ ( 1 + d 2 2 ) + ( d 1 + d 2 2 ) ψ ( d 1 + d 2 2 ) + ln ⁡ d 2 d 1 {…
Excess kurtosis · 1
F-distribution → see text
Mean · 1
F-distribution → d 2 d 2 − 2 {\displaystyle {\frac {d_{2}}{d_{2}-2}}} for d2 2
MGF · 1
F-distribution → does not exist, raw moments defined in text and in

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Important terminology

displaystyle distribution frac sim textstyle operatorname left right probability beta independent function tfrac gamma also variance mathrm see sigma snedecor

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
F-distributionCDFI d 1 x d 1 x + d 2 ( d 1 2 , d 2 2 ) {\displaystyle I_{\frac {d_{1}x}{d_{1}x+d_{2}}}\left({\tfrac {d_{1}}{2}},{\tfrac {d_{2}}{2}}\right)}1.00infobox
F-distributionCFsee text1.00infobox
F-distributionEntropyln ⁡ Γ ( d 1 2 ) + ln ⁡ Γ ( d 2 2 ) − ln ⁡ Γ ( d 1 + d 2 2 ) + ( 1 − d 1 2 ) ψ ( 1 + d 1 2 ) − ( 1 + d 2 2 ) ψ ( 1 + d 2 2 ) + ( d 1 + d 2 2 ) ψ ( d 1 + d 2 2 ) + ln ⁡ d 2 d 1 {…1.00infobox
F-distributionExcess kurtosissee text1.00infobox
F-distributionMeand 2 d 2 − 2 {\displaystyle {\frac {d_{2}}{d_{2}-2}}} for d2 > 21.00infobox
F-distributionMGFdoes not exist, raw moments defined in text and in1.00infobox
F-distributionModed 1 − 2 d 1 d 2 d 2 + 2 {\displaystyle {\frac {d_{1}-2}{d_{1}}}\;{\frac {d_{2}}{d_{2}+2}}} for d1 > 21.00infobox
F-distributionParametersd1, d2 > 0 deg. of freedom1.00infobox
F-distributionPDF( d 1 x ) d 1 d 2 d 2 ( d 1 x + d 2 ) d 1 + d 2 x B ( d 1 2 , d 2 2 ) {\displaystyle {\frac {\sqrt {\frac {(d_{1}x)^{d_{1}}d_{2}^{d_{2}}}{(d_{1}x+d_{2})^{d_{1}+d_{2}}}}}{x\,\mat…1.00infobox
F-distributionSkewness( 2 d 1 + d 2 − 2 ) 8 ( d 2 − 4 ) ( d 2 − 6 ) d 1 ( d 1 + d 2 − 2 ) {\displaystyle {\frac {(2d_{1}+d_{2}-2){\sqrt {8(d_{2}-4)}}}{(d_{2}-6){\sqrt {d_{1}(d_{1}+d_{2}-2)}}}}} for d…1.00infobox
F-distributionSupportx ∈ (0, +∞) if d1 = 1, otherwise x ∈ [0, +∞)1.00infobox
F-distributionVariance2 d 2 2 ( d 1 + d 2 − 2 ) d 1 ( d 2 − 2 ) 2 ( d 2 − 4 ) {\displaystyle {\frac {2\,d_{2}^{2}\,(d_{1}+d_{2}-2)}{d_{1}(d_{2}-2)^{2}(d_{2}-4)}}} for d2 > 41.00infobox
F-distributionis aparticular parametrization of the beta prime distribution0.90text
F-distributionis aspecial case of type 6 Pearson distribution.If X0.90text

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