The Generalised Clayton copula
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The Generalised Clayton copula is a copula that
allows any specific (non-zero) level of (lower) tail dependency between
individual variables. It is an Archimedean copula
and exchangeable.
Copula name
|
Generalised Clayton
copula
|
Common notation
|
![](I/GeneralisedClaytonCopula_files/image001.png)
|
Parameters
|
,
![](I/GeneralisedClaytonCopula_files/image003.png)
|
Domain
|
![](I/GeneralisedClaytonCopula_files/image004.png)
|
Copula
|
![](I/GeneralisedClaytonCopula_files/image005.png)
Or if we use the limit![](I/GeneralisedClaytonCopula_files/image007.png)
|
Kendall’s rank
correlation coefficient (for bivariate case), ![](I/GeneralisedClaytonCopula_files/image008.png)
|
![](I/GeneralisedClaytonCopula_files/image009.png)
|
Coefficient of upper
tail dependence, ![](I/GeneralisedClaytonCopula_files/image010.png)
|
![](I/GeneralisedClaytonCopula_files/image011.png)
|
Coefficient of lower
tail dependence, ![](I/GeneralisedClaytonCopula_files/image012.png)
|
![](I/GeneralisedClaytonCopula_files/image013.png)
|
Archimedean generator
function, ![](I/GeneralisedClaytonCopula_files/image014.png)
|
![](I/GeneralisedClaytonCopula_files/image015.png)
Or if we use the limit
|
Other comments
|
When the generalised
Clayton copula becomes the Clayton copula.
|
Nematrian web functions
Functions relating to the above distribution may be accessed
via the Nematrian
web function library by using a DistributionName of “Generalised Clayton
Copula”. For details of other supported probability distributions see here.
NAVIGATION LINKS
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