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International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems

IPMU 2012: Advances in Computational Intelligence pp 186–193Cite as

How Many Archimedean Copulæ Are There?

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 298))

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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Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Fisica ‘‘Ennio De Giorgi’’, Università del Salento, 73100, Lecce, Italy

    Carlo Sempi

Authors
  1. Carlo Sempi
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Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco  & Benedetto Matarazzo  & 

  2. Université Pierre et Marie Curie - Paris6, CNRS UMR 7606, DAPA, LIP6 8, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute, IONA College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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© 2012 Springer-Verlag Berlin Heidelberg

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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

  • Print ISBN: 978-3-642-31714-9

  • Online ISBN: 978-3-642-31715-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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