Title:
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Componentwise concave copulas and their asymmetry (English) |
Author:
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Durante, Fabrizio |
Author:
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Papini, Pier Luigi |
Language:
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English |
Journal:
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Kybernetika |
ISSN:
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0023-5954 |
Volume:
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45 |
Issue:
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6 |
Year:
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2009 |
Pages:
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1003-1011 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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. (English) |
Keyword:
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copulas |
Keyword:
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exchangeability |
Keyword:
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positive regression dependence |
MSC:
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60E05 |
MSC:
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60G09 |
MSC:
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62H05 |
MSC:
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62H20 |
idZBL:
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Zbl 1191.62095 |
idMR:
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MR2650079 |
. |
Date available:
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2010-06-02T19:32:12Z |
Last updated:
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2013-09-21 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/140027 |
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Reference:
|
[1] C. Alsina, M. J. Frank, and B. Schweizer: Associative Functions.Triangular Norms and Copulas. World Scientific, Hackensack, NJ 2006. MR 2222258 |
Reference:
|
[2] E. Alvoni, F. Durante, P.-L. Papini, and C. Sempi: 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. |
Reference:
|
[3] E. Alvoni and P. L. Papini: Quasi-concave copulas, asymmetry and transformations.Comment. Math. Univ. Carolin. 48 (2007), 311–319. MR 2338099 |
Reference:
|
[4] E. Alvoni, P.-L. Papini, and F. Spizzichino: On a class of transformations of copulas and quasi-copulas.Fuzzy Sets and Systems 160 (2009), 334–343. MR 2473107 |
Reference:
|
[5] P. Capérà and C. Genest: Spearman’s $\rho $ is larger than Kendall’s $\tau $ for positively dependent random variables.J. Nonparametr. Statist. 2 (1993), 183–194. MR 1256381 |
Reference:
|
[6] B. De Baets, H. De Meyer, and R. Mesiar: Asymmetric semilinear copulas.Kybernetika 43 (2007), 221–233. MR 2343397 |
Reference:
|
[7] F. Durante, E. P. Klement, C. Sempi, and M. Úbeda-Flores: Measures of non-exchangeability for bivariate random vectors.Statist. Papers (2009), to appear (doi:10.1007/s00362-008-0153-0). MR 2679341 |
Reference:
|
[8] F. Durante, A. Kolesárová, R. Mesiar, and C. Sempi: Copulas with given values on a horizontal and a vertical section.Kybernetika 43 (2007), 209–220. MR 2343396 |
Reference:
|
[9] F. Durante, R. Mesiar, P.-L. Papini, and C. Sempi: 2-increasing binary aggregation operators.Inform. Sci. 177 (2007), 111–129. MR 2272737 |
Reference:
|
[10] F. Durante and P.-L. Papini: A weakening of Schur-concavity for copulas.Fuzzy Sets and Systems 158 (2007), 1378–1383. MR 2321982 |
Reference:
|
[11] F. Durante and P.-L. Papini: Non-exchangeability of negatively dependent random variables.Metrika (2009), to appear (doi:10.1007/s00184-008-0207-2). MR 2602184 |
Reference:
|
[12] F. Durante, S. Saminger-Platz, and P. Sarkoci: Rectangular patchwork for bivariate copulas and tail dependence.Comm. Statist. Theory Methods 38 (2009), 2515–2527. MR 2596930 |
Reference:
|
[13] F. Durante and C. Sempi: Copulæ and Schur-concavity.Internat. Math. J. 3 (2003), 893–905. MR 1990502 |
Reference:
|
[14] F. Durante and C. Sempi: Copula and semicopula transforms.Internat. J. Math. Math. Sci. 2005 (2005), 645–655. MR 2172400 |
Reference:
|
[15] F. Durante and C. Sempi: On the characterization of a class of binary operations on bivariate distribution functions.Publ. Math. Debrecen 69 (2006), 47–63. MR 2228476 |
Reference:
|
[16] H. Joe: Multivariate Models and Dependence Concepts.Chapman and Hall, London 1997. Zbl 0990.62517, MR 1462613 |
Reference:
|
[17] E. P. Klement and A. Kolesárová: Intervals of 1-Lipschitz aggregation operators, quasi-copulas, and copulas with given affine section.Monatsh. Math. 152 (2007), 151–167. MR 2346431 |
Reference:
|
[18] E. P. Klement, A. Kolesárová, R. Mesiar, and A. Stupňanová: Lipschitz continuity of discrete universal integrals based on copulas.Internat. J. Uncertain. Fuzziness Knowledge-Based Systems (to appear). MR 2654366 |
Reference:
|
[19] E. P. Klement and R. Mesiar: How non-symmetric can a copula be? Comment.Math. Univ. Carolin. 47 (2006), 141–148. MR 2223973 |
Reference:
|
[20] E. P. Klement, R. Mesiar, and E. Pap: Transformations of copulas.Kybernetika 41 (2005), 425–434. MR 2180355 |
Reference:
|
[21] M. Marinacci and L. Montrucchio: Ultramodular functions.Math. Oper. Res. 30 (2005), 311–332. MR 2142035 |
Reference:
|
[22] A. W. Marshall and I. Olkin: Inequalities: Theory of Majorization and its Applications.Academic Press, New York 1979. MR 0552278 |
Reference:
|
[23] A. J. Mc Neil and J. Nešlehová: Multivariate Archimedean copulas, d-monotone functions and $\ell _1$-norm symmetric distributions.Ann. Statist. 37 (2009), 3059–3097. MR 2541455 |
Reference:
|
[24] A. J. McNeil, R. Frey, and P. Embrechts: Quantitative Risk Management.Concepts, Techniques and Tools. Princeton University Press, Princeton, NJ 2005. MR 2175089 |
Reference:
|
[25] P. M. Morillas: A method to obtain new copulas from a given one.Metrika 61 (2005), 169–184. Zbl 1079.62056, MR 2159414 |
Reference:
|
[26] R. B. Nelsen: An Introduction to Copulas.Second edition. Springer, New York 2006. Zbl 1152.62030, MR 2197664 |
Reference:
|
[27] R. B. Nelsen: Extremes of nonexchangeability.Statist. Papers 48 (2007), 329–336. Zbl 1110.62071, MR 2295821 |
Reference:
|
[28] G. Salvadori, C. De Michele, N. T. Kottegoda, and R. Rosso: Extremes in Nature.An Approach Using Copulas. Springer, Dordrecht 2007. |
Reference:
|
[29] B. Schweizer and A. Sklar: Probabilistic Metric Spaces.Dover Publications, Mineola, N.Y. 2006. |
Reference:
|
[30] A. Sklar: Fonctions de répartition à $n$ dimensions et leurs marges.Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231. MR 0125600 |
Reference:
|
[31] A. Sklar: Random variables, joint distributions, and copulas.Kybernetika 9 (1973), 449–460. MR 0345164 |
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