The F distribution

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The F distribution is also known as Snedecor’s F or the Fisher-Snedecor distribution. It commonly arises in statistical tests linked to analysis of variance.




Distribution name

F distribution

Common notation


 = degrees of freedom (first) (positive integer)

 = degrees of freedom (second) (positive integer)


Probability density function

Cumulative distribution function




(Excess) kurtosis

Characteristic function

Where  is the confluent hypergeometric function of the second kind

Other comments

The F distribution is a special case of the Pearson type 6 distribution. It is also a particular example of the beta prime distribution.


If  and  are independent random variables then



Its mode is . There is no simple closed form for the median.


Nematrian web functions


Functions relating to the above distribution may be accessed via the Nematrian web function library by using a DistributionName of “f”. Functions relating to a generalised version of this distribution including additional location (i.e. shift) and scale parameters may be accessed by using a DistributionName of “f4”, see also including additional shift and scale parameters. For details of other supported probability distributions see here.


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