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.
![[SmartChart]](I/FDistribution_files/image001.gif)
![[SmartChart]](I/FDistribution_files/image002.gif)
![[SmartChart]](I/FDistribution_files/image003.gif)
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Distribution name
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F
distribution
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Common notation
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Parameters
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 =
degrees of freedom (first) (positive integer)
 =
degrees of freedom (second) (positive integer)
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Domain
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Probability density
function
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Cumulative distribution
function
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Mean
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Variance
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Skewness
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(Excess) kurtosis
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Characteristic function
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Where  is
the confluent hypergeometric function of the second kind
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Other comments
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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.
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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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