The Clayton copula
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The 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
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Clayton copula
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Common notation
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![](I/ClaytonCopula_files/image001.png)
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Parameters
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(can be
extended to )
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Domain
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![](I/ClaytonCopula_files/image004.png)
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Copula
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![](I/ClaytonCopula_files/image005.png)
Or if we use the limit![](I/ClaytonCopula_files/image007.png)
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Kendall’s rank
correlation coefficient (for bivariate case)
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![](I/ClaytonCopula_files/image008.png)
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Coefficient of upper
tail dependence, ![](I/ClaytonCopula_files/image009.png)
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![](I/ClaytonCopula_files/image010.png)
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Coefficient of lower
tail dependence, ![](I/ClaytonCopula_files/image011.png)
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![](I/ClaytonCopula_files/image012.png)
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Archimedean generator
function, ![](I/ClaytonCopula_files/image013.png)
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![](I/ClaytonCopula_files/image014.png)
Or if we use the limit .
If then a simpler version, which
does not alter the copula itself, is .
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Other comments
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If we obtain the independence copula.
The Clayton copula (like the Frank copula) is a
comprehensive copula in that it interpolates between a lower limit of the countermonotonicity
copula ( ) and an upper limit of the comonotonicity
copula ( )..
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Nematrian web functions
Functions relating to the above distribution may be accessed
via the Nematrian
web function library by using a DistributionName of “Clayton Copula”.
For details of other probability distributions see here.
NAVIGATION LINKS
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