Two algebraic notions, power of an associative binary function and nilpotency, are used in order to show that every bivariate Archimedean copula $C$ is isomorphic to either the independence copula $\Pi_2$, if it is strict, or to the lower Fr\'{e}chet--Hoeffding bound $W_2$, if it is nilpotent.
How many Archimedean copulas are there?
SEMPI, Carlo
2012-01-01
Abstract
Two algebraic notions, power of an associative binary function and nilpotency, are used in order to show that every bivariate Archimedean copula $C$ is isomorphic to either the independence copula $\Pi_2$, if it is strict, or to the lower Fr\'{e}chet--Hoeffding bound $W_2$, if it is nilpotent.File in questo prodotto:
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