Remarks on Two Product-like Constructions for Copulas

Fabrizio Durante; Erich Peter Klement; José Quesada-Molina; Peter Sarkoci

Kybernetika (2007)

  • Volume: 43, Issue: 2, page 235-244
  • ISSN: 0023-5954

Abstract

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We investigate two constructions that, starting with two bivariate copulas, give rise to a new bivariate and trivariate copula, respectively. In particular, these constructions are generalizations of the * -product and the ☆ -product for copulas introduced by Darsow, Nguyen and Olsen in 1992. Some properties of these constructions are studied, especially their relationships with ordinal sums and shuffles of Min.

How to cite

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Durante, Fabrizio, et al. "Remarks on Two Product-like Constructions for Copulas." Kybernetika 43.2 (2007): 235-244. <http://eudml.org/doc/33854>.

@article{Durante2007,
abstract = {We investigate two constructions that, starting with two bivariate copulas, give rise to a new bivariate and trivariate copula, respectively. In particular, these constructions are generalizations of the $\ast $-product and the $\star $-product for copulas introduced by Darsow, Nguyen and Olsen in 1992. Some properties of these constructions are studied, especially their relationships with ordinal sums and shuffles of Min.},
author = {Durante, Fabrizio, Klement, Erich Peter, Quesada-Molina, José, Sarkoci, Peter},
journal = {Kybernetika},
keywords = {copula; ordinal sum; shuffle of Min; concordance; copula; ordinal sum; shuffle of Min; concordance},
language = {eng},
number = {2},
pages = {235-244},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Remarks on Two Product-like Constructions for Copulas},
url = {http://eudml.org/doc/33854},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Durante, Fabrizio
AU - Klement, Erich Peter
AU - Quesada-Molina, José
AU - Sarkoci, Peter
TI - Remarks on Two Product-like Constructions for Copulas
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 2
SP - 235
EP - 244
AB - We investigate two constructions that, starting with two bivariate copulas, give rise to a new bivariate and trivariate copula, respectively. In particular, these constructions are generalizations of the $\ast $-product and the $\star $-product for copulas introduced by Darsow, Nguyen and Olsen in 1992. Some properties of these constructions are studied, especially their relationships with ordinal sums and shuffles of Min.
LA - eng
KW - copula; ordinal sum; shuffle of Min; concordance; copula; ordinal sum; shuffle of Min; concordance
UR - http://eudml.org/doc/33854
ER -

References

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  1. Darsow W. F., Nguyen, B., Olsen E. T., Copulas and Markov processes, Illinois J. Math. 36 (1992), 600–642 (1992) Zbl0770.60019MR1215798
  2. Baets B. De, Meyer H. De, Copulas and the pairwise probabilistic comparison of ordered lists, In: Proc. 10th International Conference IPMU, Perugia 2004, pp. 1091–1098 
  3. Durante F., Klement E. P., Quesada-Molina J. J., Copulas: compatibility and Fréchet classes, Submitted 
  4. Joe H., Multivariate Models and Dependence Concepts, Chapman & Hall, London 1997 Zbl0990.62517MR1462613
  5. Kolesárová A., Mesiar, R., Sempi C., Three copulas and compatibility, In: Proc. IPMU 2006 (B. Bouchon-Meunier and R. Yager, eds.), Vol. 1, Éditions E.D.K., Paris 2006, pp. 658–663 
  6. Mesiar R., Szolgay J., W-ordinal sums of copulas and quasi-copulas, In: Proc. MAGIA 2004 Conference, Kočovce, Slovak Republic 2004, pp. 78–83 
  7. Mikusiński P., Sherwood, H., Taylor M. D., Shuffles of Min, Stochastica 13 (1992), 61–74 (1992) Zbl0768.60017MR1197328
  8. Nelsen R. B., An Introduction to Copulas, Springer, New York 2006 Zbl1152.62030MR2197664
  9. Schweizer B., Sklar A., Probabilistic Metric Spaces, North–Holland, New York 1983. Second edition: Dover Publications, Mineola, New York 2005 (1983) Zbl0546.60010MR0790314
  10. 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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