Copula name

Clayton copula

Common notation

Parameters

 (can be extended to )

Domain

Copula

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 ()..