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Fisher-Snedecor
Probability density function
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Parameters deg. of freedom
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Mean for
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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

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.

Generalization

A generalization of the (central) F-distribution is the noncentral F-distribution.

Related distributions

  • is a chi-square distribution as for .

External links

de:F-Verteilung es:Distribución F nl:F-verdeling

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