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

F
distribution

Common notation


Parameters

=
degrees of freedom (first) (positive integer)
=
degrees of freedom (second) (positive integer)

Domain


Probability density
function


Cumulative distribution
function


Mean


Variance


Skewness


(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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