F-distribution
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| Probability density function None uploaded yet. | |
| Cumulative distribution function None uploaded yet. | |
| Parameters |  deg. of freedom
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| Support | 
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| cdf | 
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| Mean |  for 
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| Median | |
| Mode |  for 
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| Variance |  for 
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| Skewness |  for 
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| Entropy | |
| mgf | see text for raw moments |
| Char. func. | |
In probability theory and statistics, the F-distribution is a continuous probability distribution. It is also known as Snedecor's F distribution or the Fisher-Snedecor distribution (after Ronald Fisher and George W. Snedecor).
A random variate of the F-distribution arises as the ratio of two chi-squared variates:
where
- U1 and U2 have chi-square distributions with d1 and d2 degrees of freedom respectively, and
- U1 and U2 are independent (see Cochran's theorem for an application).
The F-distribution arises frequently as the null distribution of a test statistic, especially in likelihood-ratio tests, perhaps most notably in the analysis of variance; see F-test.
The probability density function of an F(d1, d2) distributed random variable is given by
for real x ≥ 0, where d1 and d2 are positive integers, and B is the beta function.
The cumulative distribution function is
where I is the regularized incomplete beta function.
Contents |
[edit] Generalization
A generalization of the (central) F-distribution is the noncentral F-distribution.
[edit] Related distributions
is a chi-square distribution as 
for 
.
[edit] See also
[edit] References & Bibliography
[edit] Key texts
[edit] Books
[edit] Papers
[edit] Additional material
[edit] Books
[edit] Papers
[edit] External links
- Table of critical values of the F-distribution
- Online significance testing with the F-distribution
- Distribution Calculator Calculates probabilities and critical values for normal, t-, chi2- and F-distributionde:F-Verteilung
es:Distribución Fnl:F-verdeling
