The Beta distribution
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The beta distribution describes a distribution in which
outcomes are limited to a specific range, the probability density function
within this range being characterised by two shape parameters.
![[SmartChart]](I/BetaDistribution_files/image001.gif)
![[SmartChart]](I/BetaDistribution_files/image002.gif)
![[SmartChart]](I/BetaDistribution_files/image003.gif)
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Distribution name
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Beta
distribution
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Common notation
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Parameters
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 = shape
parameter (
 = shape
parameter (
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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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Other comments
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The beta distribution is also known as a beta distribution
of the first kind. Its mode is  .
There is no simple closed form solution for its median.
The beta distribution parameters are sometimes taken to
include boundary parameters  ( ) in
which case its domain is  , and its pdf and cdf are  and
 where
 ,
its mean is  ,
its mode is  for
 and
its variance is 
If  and
 then
 .
If then
 and
if  then
 (if
 and
 ).
The  ’th order statistic of a
sample of size  from the uniform distribution
has a beta distribution,  .
If  then
 ,
i.e. the Pert distribution is a special case of the beta distribution.
Its non-central moments are  .
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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 “beta”.
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 “beta4”, see also including
additional shift and scale parameters. For details of other supported
probability distributions see here.
NAVIGATION LINKS
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