The Beta prime distribution

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Distribution name

Beta prime distribution

Common notation


 = shape parameter (

 = shape parameter (


Probability density function

Cumulative distribution function



Other comments

The beta prime distribution is also called the inverted beta or the beta distribution of the second kind or the Pearson Type 6 distribution. The mode of the beta prime distribution is . There is no simple closed form expression for its median.


Its non-central moments (for integral ) are:


Nematrian web functions


Functions relating to the above distribution may be accessed via the Nematrian web function library by using a DistributionName of “beta prime”. 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 “beta prime4”, see also including additional shift and scale parameters. For details of other supported probability distributions see here.


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