The Kumaraswamy distribution
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The Kumaraswamy 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. It is
similar to the beta
distribution but possibly easier to use because it has simpler analytical
expressions for its probability density function and cumulative distribution
function.
![[SmartChart]](I/KumaraswamyDistribution_files/image001.gif)
![[SmartChart]](I/KumaraswamyDistribution_files/image002.gif)
![[SmartChart]](I/KumaraswamyDistribution_files/image003.gif)
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Distribution name
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Kumaraswamy
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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Other comments
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A standard Kumaraswamy distribution has  and
 . Its non-central
moments are given by:
and its median is  and its mode is  (for  , ,  .
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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 “kumaraswamy”.
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 “kumaraswamy4” ”, see also including
additional shift and scale parameters. For details of other supported
probability distributions see here.
NAVIGATION LINKS
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