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

Common notation





Kendall’s rank correlation coefficient (for bivariate case)

Coefficient of upper tail dependence,

Coefficient of lower tail dependence,

Archimedean generator function,

Other comments

If  we obtain the independence copula and as  we approach the comonotonicity copula.


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.


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