The generalised gamma distribution
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The generalised gamma (or generalized gamma) distribution is
a generalisation of the gamma distribution that includes several of the
parametric distributions typically used in survival analysis.
![[SmartChart]](I/GeneralisedGammaDistribution_files/image001.gif)
![[SmartChart]](I/GeneralisedGammaDistribution_files/image002.gif)
![[SmartChart]](I/GeneralisedGammaDistribution_files/image003.gif)
Distribution name
|
Generalised
gamma distribution
|
Common notation
|
![](I/GeneralisedGammaDistribution_files/image004.png)
|
Parameters
|
=
shape parameter ( )
=
shape parameter ( )
=
scale parameter ( )
|
Domain
|
![](I/GeneralisedGammaDistribution_files/image011.png)
|
Probability density
function
|
![](I/GeneralisedGammaDistribution_files/image012.png)
|
Cumulative distribution
function
|
![](I/GeneralisedGammaDistribution_files/image013.png)
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Mean
|
![](I/GeneralisedGammaDistribution_files/image014.png)
|
Variance
|
![](I/GeneralisedGammaDistribution_files/image015.png)
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Skewness
|
![](I/GeneralisedGammaDistribution_files/image016.png)
|
(Excess) kurtosis
|
![](I/GeneralisedGammaDistribution_files/image017.png)
where:
![](I/GeneralisedGammaDistribution_files/image018.png)
![](I/GeneralisedGammaDistribution_files/image019.png)
![](I/GeneralisedGammaDistribution_files/image020.png)
![](I/GeneralisedGammaDistribution_files/image021.png)
|
Other comments
|
Its non-central moments are:
![](I/GeneralisedGammaDistribution_files/image022.png)
The Weibull
distribution is a special case with . The gamma distribution
is a special case with .
|
Nematrian web functions
Functions relating to the above distribution may be accessed
via the Nematrian
web function library by using a DistributionName of “generalised
gamma”. 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 “generalised gamma4”, see also including
additional shift and scale parameters. For details of other supported
probability distributions see here.
NAVIGATION LINKS
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