On a problem by Schweizer and Sklar

Fabrizio Durante

Kybernetika (2012)

  • Volume: 48, Issue: 2, page 287-293
  • ISSN: 0023-5954

Abstract

top
We give a representation of the class of all n -dimensional copulas such that, for a fixed m ∈ ℕ , 2 ≤ m < n , all their m -dimensional margins are equal to the independence copula. Such an investigation originated from an open problem posed by Schweizer and Sklar.

How to cite

top

Durante, Fabrizio. "On a problem by Schweizer and Sklar." Kybernetika 48.2 (2012): 287-293. <http://eudml.org/doc/246977>.

@article{Durante2012,
abstract = {We give a representation of the class of all $n$-dimensional copulas such that, for a fixed $m\in \mathbb \{N\}$, $2\le m < n$, all their $m$-dimensional margins are equal to the independence copula. Such an investigation originated from an open problem posed by Schweizer and Sklar.},
author = {Durante, Fabrizio},
journal = {Kybernetika},
keywords = {copulas; distributions with given marginals; Frèchet–Hoeffding bounds; partial mutual independence; copulas; distributions with given marginals; Fréchet–Hoeffding bounds; partial mutual independence},
language = {eng},
number = {2},
pages = {287-293},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On a problem by Schweizer and Sklar},
url = {http://eudml.org/doc/246977},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Durante, Fabrizio
TI - On a problem by Schweizer and Sklar
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 2
SP - 287
EP - 293
AB - We give a representation of the class of all $n$-dimensional copulas such that, for a fixed $m\in \mathbb {N}$, $2\le m < n$, all their $m$-dimensional margins are equal to the independence copula. Such an investigation originated from an open problem posed by Schweizer and Sklar.
LA - eng
KW - copulas; distributions with given marginals; Frèchet–Hoeffding bounds; partial mutual independence; copulas; distributions with given marginals; Fréchet–Hoeffding bounds; partial mutual independence
UR - http://eudml.org/doc/246977
ER -

References

top
  1. V. Beneš, J. Štěpán, eds., Distributions With Given Marginals and Moment Problems., Kluwer Academic Publishers, Dordrecht 1997. Zbl0885.00054MR1614650
  2. C. M. Cuadras, J. Fortiana, J. A. Rodriguez-Lallena, eds., Distributions With Given Marginals and Statistical Modelling., Kluwer Academic Publishers, Dordrecht 2002. Papers from the meeting held in Barcelona 2000. Zbl1054.62002MR2058972
  3. G. Dall'Aglio, S. Kotz, G. Salinetti, eds., Advances in Probability Distributions with Given Marginals., Mathematics and its Applications 67, Kluwer Academic Publishers Group, Dordrecht 1991. Beyond the Copulas, Papers from the Symposium on Distributions with Given Marginals held in Rome 1990. Zbl0722.00031MR1215942
  4. P. Deheuvels, Indépendance multivariée partielle et inégalités de Fréchet., In: Studies in Probability and Related Topics, Nagard, Rome 1983, pp. 145-155. Zbl0557.60013MR0778216
  5. F. Durante, E. P. Klement, J. J. Quesada-Molina, Bounds for trivariate copulas with given bivariate marginals., J. Inequal. Appl. 2008 (2008), 1-9. Zbl1162.62047MR2481572
  6. P. Jaworski, F. Durante, W. Härdle, T. Rychlik, eds., Copula Theory and its Applications., Lecture Notes in Statistics - Proceedings 198, Springer, Berlin - Heidelberg 2010. Zbl1194.62077
  7. H. Joe, Multivariate Models and Dependence Concepts., Monographs on Statistics and Applied Probability 73, Chapman & Hall, London 1997. Zbl0990.62517MR1462613
  8. R. B. Nelsen, An Introduction to Copulas. Second edition., Springer Series in Statistics, Springer, New York 2006. MR2197664
  9. L. Rüschendorf, B. Schweizer, M. D. Taylor, eds., Distributions with Fixed Marginals and Related Topics., Institute of Mathematical Statistics, Lecture Notes - Monograph Series 28, Hayward 1996. Zbl0944.60012MR1485518
  10. B. Schweizer, A. Sklar, Probabilistic Metric Spaces., North-Holland Series in Probability and Applied Mathematics. North-Holland Publishing Co., New York 1983. Reprinted, Dover, Mineola 2005. Zbl0546.60010MR0790314
  11. K. F. Siburg, P. A. Stoimenov, 10.1080/03610920802074844, Comm. Statist. Theory Methods 37 (2008), 19, 3124-3134. MR2467756DOI10.1080/03610920802074844
  12. A. Sklar, Fonctions de répartition à n dimensions et leurs marges., Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231. MR0125600

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.