Componentwise concave copulas and their asymmetry

Fabrizio Durante; Pier Luigi Papini

Kybernetika (2009)

  • Volume: 45, Issue: 6, page 1003-1011
  • ISSN: 0023-5954

Abstract

top
The class of componentwise concave copulas is considered, with particular emphasis on its closure under some constructions of copulas (e.g., ordinal sum) and its relations with other classes of copulas characterized by some notions of concavity and/or convexity. Then, a sharp upper bound is given for the L ∞ -measure of non-exchangeability for copulas belonging to this class.

How to cite

top

Durante, Fabrizio, and Papini, Pier Luigi. "Componentwise concave copulas and their asymmetry." Kybernetika 45.6 (2009): 1003-1011. <http://eudml.org/doc/37685>.

@article{Durante2009,
abstract = {The class of componentwise concave copulas is considered, with particular emphasis on its closure under some constructions of copulas (e.g., ordinal sum) and its relations with other classes of copulas characterized by some notions of concavity and/or convexity. Then, a sharp upper bound is given for the $L^\{\infty \}$-measure of non-exchangeability for copulas belonging to this class.},
author = {Durante, Fabrizio, Papini, Pier Luigi},
journal = {Kybernetika},
keywords = {copulas; exchangeability; positive regression dependence; copulas; exchangeability; positive regression dependence},
language = {eng},
number = {6},
pages = {1003-1011},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Componentwise concave copulas and their asymmetry},
url = {http://eudml.org/doc/37685},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Durante, Fabrizio
AU - Papini, Pier Luigi
TI - Componentwise concave copulas and their asymmetry
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 6
SP - 1003
EP - 1011
AB - The class of componentwise concave copulas is considered, with particular emphasis on its closure under some constructions of copulas (e.g., ordinal sum) and its relations with other classes of copulas characterized by some notions of concavity and/or convexity. Then, a sharp upper bound is given for the $L^{\infty }$-measure of non-exchangeability for copulas belonging to this class.
LA - eng
KW - copulas; exchangeability; positive regression dependence; copulas; exchangeability; positive regression dependence
UR - http://eudml.org/doc/37685
ER -

References

top
  1. Associative Functions, Triangular Norms and Copulas. World Scientific, Hackensack, NJ 2006. MR2222258
  2. Different types of convexity and concavity for copulas, In: New Dimensions in Fuzzy Logic and related Technologies – Proc. 5th EUSFLAT Conference (M. Štěpnička, V. Novák, and U. Bodenhofer, eds.), Volume 1, University of Ostrava 2007, pp. 185–189. 
  3. Quasi-concave copulas, asymmetry and transformations, Comment. Math. Univ. Carolin. 48 (2007), 311–319. MR2338099
  4. On a class of transformations of copulas and quasi-copulas, Fuzzy Sets and Systems 160 (2009), 334–343. MR2473107
  5. Spearman’s ρ is larger than Kendall’s τ for positively dependent random variables, J. Nonparametr. Statist. 2 (1993), 183–194. MR1256381
  6. Asymmetric semilinear copulas, Kybernetika 43 (2007), 221–233. MR2343397
  7. Measures of non-exchangeability for bivariate random vectors, Statist. Papers (2009), to appear (doi:10.1007/s00362-008-0153-0). MR2679341
  8. Copulas with given values on a horizontal and a vertical section, Kybernetika 43 (2007), 209–220. MR2343396
  9. 2-increasing binary aggregation operators, Inform. Sci. 177 (2007), 111–129. MR2272737
  10. A weakening of Schur-concavity for copulas, Fuzzy Sets and Systems 158 (2007), 1378–1383. MR2321982
  11. Non-exchangeability of negatively dependent random variables, Metrika (2009), to appear (doi:10.1007/s00184-008-0207-2). MR2602184
  12. Rectangular patchwork for bivariate copulas and tail dependence, Comm. Statist. Theory Methods 38 (2009), 2515–2527. MR2596930
  13. Copulæ  and Schur-concavity, Internat. Math. J. 3 (2003), 893–905. MR1990502
  14. Copula and semicopula transforms, Internat. J. Math. Math. Sci. 2005 (2005), 645–655. MR2172400
  15. On the characterization of a class of binary operations on bivariate distribution functions, Publ. Math. Debrecen 69 (2006), 47–63. MR2228476
  16. Multivariate Models and Dependence Concepts, Chapman and Hall, London 1997. Zbl0990.62517MR1462613
  17. Intervals of 1-Lipschitz aggregation operators, quasi-copulas, and copulas with given affine section, Monatsh. Math. 152 (2007), 151–167. MR2346431
  18. Lipschitz continuity of discrete universal integrals based on copulas, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems (to appear). MR2654366
  19. How non-symmetric can a copula be? Comment, Math. Univ. Carolin. 47 (2006), 141–148. MR2223973
  20. Transformations of copulas, Kybernetika 41 (2005), 425–434. MR2180355
  21. Ultramodular functions, Math. Oper. Res. 30 (2005), 311–332. MR2142035
  22. Inequalities: Theory of Majorization and its Applications, Academic Press, New York 1979. MR0552278
  23. Multivariate Archimedean copulas, d-monotone functions and ℓ 1 -norm symmetric distributions, Ann. Statist. 37 (2009), 3059–3097. MR2541455
  24. Quantitative Risk Management, Concepts, Techniques and Tools. Princeton University Press, Princeton, NJ 2005. MR2175089
  25. A method to obtain new copulas from a given one, Metrika 61 (2005), 169–184. Zbl1079.62056MR2159414
  26. An Introduction to Copulas, Second edition. Springer, New York 2006. Zbl1152.62030MR2197664
  27. Extremes of nonexchangeability, Statist. Papers 48 (2007), 329–336. Zbl1110.62071MR2295821
  28. Extremes in Nature, An Approach Using Copulas. Springer, Dordrecht 2007. 
  29. Probabilistic Metric Spaces, Dover Publications, Mineola, N.Y. 2006. 
  30. Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231. MR0125600
  31. Random variables, joint distributions, and copulas, Kybernetika 9 (1973), 449–460. MR0345164

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.