The countermonotonicity copula

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The Countermonotonicity copula is a special copula characterising perfect negative dependence, in the sense that  is almost surely a strictly decreasing function of  and vice-versa.


Copula name

countermonotonicity copula

Common notation





Kendall’s rank correlation coefficient

Coefficient of upper tail dependence

Coefficient of lower tail dependence

Other comments

Is the extreme case where dependency is as strongly “negative” as possible (i.e. achieves the Fréchet lower bound)


Nematrian web functions


Functions relating to the above distribution may be accessed via the Nematrian web function library by using a DistributionName of “Countermonotonicity Copula”. For details of other supported probability distributions see here.


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