Associative n -dimensional copulas

Andrea Stupňanová; Anna Kolesárová

Kybernetika (2011)

  • Volume: 47, Issue: 1, page 93-99
  • ISSN: 0023-5954

Abstract

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The associativity of n -dimensional copulas in the sense of Post is studied. These copulas are shown to be just n -ary extensions of associative 2-dimensional copulas with special constraints, thus they solve an open problem of R. Mesiar posed during the International Conference FSTA 2010 in Liptovský Ján, Slovakia.

How to cite

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Stupňanová, Andrea, and Kolesárová, Anna. "Associative $n$-dimensional copulas." Kybernetika 47.1 (2011): 93-99. <http://eudml.org/doc/196948>.

@article{Stupňanová2011,
abstract = {The associativity of $n$-dimensional copulas in the sense of Post is studied. These copulas are shown to be just $n$-ary extensions of associative 2-dimensional copulas with special constraints, thus they solve an open problem of R. Mesiar posed during the International Conference FSTA 2010 in Liptovský Ján, Slovakia.},
author = {Stupňanová, Andrea, Kolesárová, Anna},
journal = {Kybernetika},
keywords = {Archimedean copula; associativity in the sense of Post; $n$-dimensional copula; associativity of -ary functions; Archimedean copula; -dimensional copula},
language = {eng},
number = {1},
pages = {93-99},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Associative $n$-dimensional copulas},
url = {http://eudml.org/doc/196948},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Stupňanová, Andrea
AU - Kolesárová, Anna
TI - Associative $n$-dimensional copulas
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 1
SP - 93
EP - 99
AB - The associativity of $n$-dimensional copulas in the sense of Post is studied. These copulas are shown to be just $n$-ary extensions of associative 2-dimensional copulas with special constraints, thus they solve an open problem of R. Mesiar posed during the International Conference FSTA 2010 in Liptovský Ján, Slovakia.
LA - eng
KW - Archimedean copula; associativity in the sense of Post; $n$-dimensional copula; associativity of -ary functions; Archimedean copula; -dimensional copula
UR - http://eudml.org/doc/196948
ER -

References

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  1. Couceiro, M., On two generalizations of associativity, In: Abstracts of FSTA 2010 (E. P. Klement et. al., eds.), Liptovský Ján 2010, p. 47. (2010) 
  2. Fodor, J., Yager, R., Rybalov, A., 10.1142/S0218488597000312, Internat. J. Uncertainty, Fuzziness Knowledge-Based Systems 5 (1997), 411–427. (1997) MR1471619DOI10.1142/S0218488597000312
  3. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E., Aggregation Functions, Cambridge University Press, Cambridge 2009. (2009) Zbl1196.00002MR2538324
  4. Joe, H., Multivariable Models and Dependence Concepts, Chapman & Hall, London 1997. (1997) MR1462613
  5. Klement, E.-P., Mesiar, R., Pap, E., Triangular Norms, Kluwer Academic Publishers, Dortrecht 2000. (2000) Zbl1010.03046MR1790096
  6. Ling, C. H., Representation of associative functions, Publicationes Mathematicae Debrecen 12 (1965), 189–212. (1965) MR0190575
  7. McNeil, A.-J., Nešlehová, J., 10.1214/07-AOS556, Annals Statist. 37 (2009), 3059–3097. (2009) MR2541455DOI10.1214/07-AOS556
  8. Mesiar, R., Sarkoci, P., Open problems posed at the 10th International Conference on Fuzzy Set Theory and Appl, (FSTA 2010), Liptovský Ján. Kybernetika 46 (2010), 585–598. (2010) MR2722089
  9. Mesiar, R., Sempi, C., 10.1007/s00010-010-0013-6, Aequationes Math. 79 (2010), 1–2, 39–52. (2010) Zbl1205.62063MR2640277DOI10.1007/s00010-010-0013-6
  10. Moynihan, R., 10.1017/S1446788700011721, J. Austral. Math. Soc. Ser. A 26 (1978), 227–240. (1978) MR0511607DOI10.1017/S1446788700011721
  11. Nelsen, R.-B., An Introduction to Copulas, Second edition. Springer Science and Business Media, New York 2006. (2006) Zbl1152.62030MR2197664
  12. Post, E.-L., 10.1090/S0002-9947-1940-0002894-7, Trans. Amer. Math. Soc. 48 (1940), 208–350. (1940) Zbl0025.01201MR0002894DOI10.1090/S0002-9947-1940-0002894-7
  13. Sklar, A., Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231. (1959) MR0125600

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