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 Π2, if it is strict, or to the lower Fréchet–Hoeffding bound W 2, if it is nilpotent.
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Sempi, C. (2012). How Many Archimedean Copulæ Are There?. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31715-6_21
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DOI: https://doi.org/10.1007/978-3-642-31715-6_21
Publisher Name: Springer, Berlin, Heidelberg
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