F-distribution
E212217
continuous probability distribution
probability distribution
ratio distribution
univariate distribution
The F-distribution is a continuous probability distribution widely used in statistics, especially for comparing variances and conducting analysis of variance (ANOVA) tests.
All labels observed (1)
| Label | Occurrences |
|---|---|
| F-distribution canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T1908293 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: F-distribution Context triple: [Ronald A. Fisher, knownFor, F-distribution]
-
A.
Hotelling’s T-squared distribution
Hotelling’s T-squared distribution is a multivariate generalization of Student’s t-distribution used primarily for hypothesis testing and constructing confidence regions for mean vectors in multivariate statistics.
-
B.
Gaussian distribution
The Gaussian distribution, also known as the normal distribution, is a fundamental continuous probability distribution characterized by its symmetric bell-shaped curve and central role in statistics and the natural sciences.
-
C.
Gamma function
The Gamma function is a fundamental extension of the factorial function to complex and real non-integer arguments, widely used in analysis, probability, and mathematical physics.
-
D.
Gumbel
Gumbel is a surname most notably associated with American sportscaster Greg Gumbel.
-
E.
Boltzmann distribution
The Boltzmann distribution is a fundamental probability distribution in statistical mechanics that describes how particles or states are populated over different energy levels at thermal equilibrium.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: F-distribution Target entity description: The F-distribution is a continuous probability distribution widely used in statistics, especially for comparing variances and conducting analysis of variance (ANOVA) tests.
-
A.
Hotelling’s T-squared distribution
Hotelling’s T-squared distribution is a multivariate generalization of Student’s t-distribution used primarily for hypothesis testing and constructing confidence regions for mean vectors in multivariate statistics.
-
B.
Gaussian distribution
The Gaussian distribution, also known as the normal distribution, is a fundamental continuous probability distribution characterized by its symmetric bell-shaped curve and central role in statistics and the natural sciences.
-
C.
Gamma function
The Gamma function is a fundamental extension of the factorial function to complex and real non-integer arguments, widely used in analysis, probability, and mathematical physics.
-
D.
Gumbel
Gumbel is a surname most notably associated with American sportscaster Greg Gumbel.
-
E.
Boltzmann distribution
The Boltzmann distribution is a fundamental probability distribution in statistical mechanics that describes how particles or states are populated over different energy levels at thermal equilibrium.
- F. None of above. chosen
Statements (52)
| Predicate | Object |
|---|---|
| instanceOf |
continuous probability distribution
ⓘ
probability distribution ⓘ ratio distribution ⓘ univariate distribution ⓘ |
| application |
construction of confidence intervals for variance ratios
ⓘ
experimental design analysis ⓘ model comparison in econometrics ⓘ |
| assumes |
homoscedasticity under null hypothesis in ANOVA
ⓘ
independent observations in classical ANOVA ⓘ normally distributed errors in classical ANOVA ⓘ |
| cdfExpression | F(x; d1, d2) = I_{d1 x / (d1 x + d2)}(d1/2, d2/2) ⓘ |
| definedAs |
(U1/df1) / (U2/df2) where U1 and U2 are independent chi-squared variables
ⓘ
distribution of ratio of two scaled chi-squared variables ⓘ |
| hasProperty |
as degrees of freedom increase, approaches normality after transformation
ⓘ
non-negative ⓘ right-skewed ⓘ |
| kurtosisExcess | 12 (d1 (5 d2 - 22) (d1 + d2 - 2) + (d2 - 4)^2 (d2 - 2)) / ( d1 (d2 - 6) (d2 - 8) (d1 + d2 - 2) ) for d2 > 8 ⓘ |
| limitingBehavior |
as both degrees of freedom go to infinity, distribution becomes concentrated near 1
ⓘ
as d2 -> infinity, d2 X / d1 converges to chi-squared(d1) ⓘ |
| mean | d2 / (d2 - 2) for d2 > 2 ⓘ |
| mode | (d1 - 2) d2 / (d1 (d2 + 2)) for d1 > 2 ⓘ |
| namedAfter |
Ronald A. Fisher
ⓘ
surface form:
Ronald Fisher
|
| parameter |
denominator degrees of freedom
ⓘ
numerator degrees of freedom ⓘ |
| pdfExpression | f(x; d1, d2) = sqrt(((d1 x)^{d1} d2^{d2}) / ((d1 x + d2)^{d1 + d2})) / (x B(d1/2, d2/2)) for x > 0 ⓘ |
| relatedDistribution |
Student’s t-distribution
ⓘ
surface form:
Student's t-distribution
beta distribution ⓘ chi-square distribution ⓘ
surface form:
chi-squared distribution
normal distribution ⓘ |
| skewness | ( (2 d1 + d2 - 2) sqrt(8 (d2 - 4)) ) / ( (d2 - 6) sqrt(d1 (d1 + d2 - 2)) ) for d2 > 6 ⓘ |
| specialCaseOf | beta prime distribution ⓘ |
| support |
x > 0
ⓘ
x in (0, infinity) ⓘ |
| symbol | F ⓘ |
| transformationRelation |
if T ~ t(d2) then T^2 ~ F(1, d2)
ⓘ
if X ~ F(d1, d2) then d1 X / (d1 X + d2) ~ Beta(d1/2, d2/2) ⓘ |
| usedFor |
ANOVA
ⓘ
analysis of variance ⓘ comparing variances of two normal populations ⓘ overall F-test in linear regression ⓘ regression model significance testing ⓘ testing equality of variances ⓘ testing multiple linear restrictions ⓘ testing nested linear models ⓘ variance ratio tests ⓘ |
| usedIn |
MANOVA via related statistics
ⓘ
general linear models ⓘ one-way ANOVA ⓘ random effects models ⓘ two-way ANOVA ⓘ variance components analysis ⓘ |
| variance | 2 d2^2 (d1 + d2 - 2) / (d1 (d2 - 2)^2 (d2 - 4)) for d2 > 4 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: F-distribution Description of subject: The F-distribution is a continuous probability distribution widely used in statistics, especially for comparing variances and conducting analysis of variance (ANOVA) tests.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.