The Gumbel copula
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The Gumbel copula is a copula that allows any
specific level of (upper) tail dependency between individual variables. It is
an Archimedean
copula, and exchangeable.
Copula name
|
Gumbel copula
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Common notation
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![](I/GumbelCopula_files/image001.png)
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Parameters
|
|
Domain
|
![](I/GumbelCopula_files/image003.png)
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Copula
|
![](I/GumbelCopula_files/image004.png)
|
Kendall’s rank
correlation coefficient (for bivariate case)
|
![](I/GumbelCopula_files/image005.png)
|
Coefficient of upper
tail dependence, ![](I/GumbelCopula_files/image006.png)
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![](I/GumbelCopula_files/image007.png)
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Coefficient of lower
tail dependence, ![](I/GumbelCopula_files/image008.png)
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![](I/GumbelCopula_files/image009.png)
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Archimedean generator
function, ![](I/GumbelCopula_files/image010.png)
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![](I/GumbelCopula_files/image011.png)
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Other comments
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If we obtain the independence copula
and as we approach 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 “Gumbel Copula”.
For details of other supported probability distributions see here.
NAVIGATION LINKS
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