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

Clayton copula

Common notation


 (can be extended to )



Or if  we use the limit

Kendall’s rank correlation coefficient (for bivariate case)

Coefficient of upper tail dependence,

Coefficient of lower tail dependence,

Archimedean generator function,

Or if  we use the limit. If  then a simpler version, which does not alter the copula itself, is .

Other comments

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 ()..


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.


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