In statistics and probability, 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*(*d*_{1}, *d*_{2}) distributed random variable is given by -
for real *x* ≥ 0, where *d*_{1} and *d*_{2} are positive integers, and B is the beta function. The cumulative distribution function is where *I* is the regularized incomplete beta function. An *F*(*d*_{1}, *d*_{2}) random variable has the following properties: - mode
- provided
*d*_{1} > 2 - mean
- provided
*d*_{2} > 2 - variance
- provided
*d*_{2} > 4 - skewness
- provided
*d*_{2} > 6 ## Generalization
A generalization of the (central) F-distribution is the noncentral F-distribution.
## External links - Table of critical values of the
*F*-distribution (*http://www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm*) - Online significance testing with the F-distribution (
*http://home.clara.net/sisa/signhlp.htm*) - Distribution Calculator (
*http://www.vias.org/simulations/simusoft_distcalc.html*) Calculates probabilities and critical values for normal, t-, chi2- and F-distribution |