The Dagum distribution

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Distribution name

Dagum distribution

Common notation


 = shape parameter ()

 = shape parameter ()

 = scale parameter ()


Probability density function

Cumulative distribution function




Other comments

Also known as the Dagum type 1 distribution. Is used in modelling income distributions. The cdf of a Dagum type 2 distribution adds a point mass at the origin and then follows a Dagum type 1 distribution over the positive halfline.


Its median is  and its mode is .


Its non-central moments are:


If  then .


Nematrian web functions


Functions relating to the above distribution may be accessed via the Nematrian web function library by using a DistributionName of “dagum”. Functions relating to a generalised version of this distribution including an additional location (i.e. shift) parameter may be accessed by using a DistributionName of “dagum4” ”, see also including additional shift and scale parameters. For details of other supported probability distributions see here.


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