The Dagum distribution
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![[SmartChart]](I/DagumDistribution_files/image001.gif)
![[SmartChart]](I/DagumDistribution_files/image002.gif)
![[SmartChart]](I/DagumDistribution_files/image003.gif)
Distribution name
|
Dagum
distribution
|
Common notation
|
![](I/DagumDistribution_files/image004.png)
|
Parameters
|
= shape
parameter ( )
= shape
parameter ( )
= scale
parameter ( )
|
Domain
|
![](I/DagumDistribution_files/image011.png)
|
Probability density
function
|
![](I/DagumDistribution_files/image012.png)
|
Cumulative distribution
function
|
![](I/DagumDistribution_files/image013.png)
|
Mean
|
![](I/DagumDistribution_files/image014.png)
|
Variance
|
![](I/DagumDistribution_files/image015.png)
where
![](I/DagumDistribution_files/image016.png)
![](I/DagumDistribution_files/image017.png)
|
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:
![](I/DagumDistribution_files/image020.png)
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.
NAVIGATION LINKS
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