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.


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Distribution name

Kumaraswamy distribution

Common notation


 = shape parameter (

 = shape parameter (


Probability density function

Cumulative distribution function



Other comments

A standard Kumaraswamy distribution has  and . Its non-central moments are given by:

and its median is  and its mode is  (for ,, .


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.


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