| Title:
|
Bivariate copulas: Transformations, asymmetry and measures of concordance (English) |
| Author:
|
Fuchs, Sebastian |
| Author:
|
Schmidt, Klaus D. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
109-125 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The present paper introduces a group of transformations on the collection of all bivariate copulas. This group contains an involution which is particularly useful since it provides (1) a criterion under which a given symmetric copula can be transformed into an asymmetric one and (2) a condition under which for a given copula the value of every measure of concordance is equal to zero. The group also contains a subgroup which is of particular interest since its four elements preserve symmetry, the order between two copulas and the value of every measure of concordance. (English) |
| Keyword:
|
bivariate copulas |
| Keyword:
|
transformations |
| Keyword:
|
asymmetry |
| Keyword:
|
measures of concordance |
| MSC:
|
20C99 |
| MSC:
|
60B15 |
| MSC:
|
60E05 |
| MSC:
|
62E10 |
| MSC:
|
62H20 |
| idZBL:
|
Zbl 06296994 |
| idMR:
|
MR3195007 |
| DOI:
|
10.14736/kyb-2014-1-0109 |
| . |
| Date available:
|
2014-05-02T06:48:53Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143766 |
| . |
| Reference:
|
[1] Baets, B. De, Meyer, H. De, Mesiar, R.: Asymmetric semilinear copulas..Kybernetika 43 (2007), 221-233. Zbl 1136.62350, MR 2343397 |
| Reference:
|
[2] Durante, F., Papini, P. L.: Componentwise concave copulas and their asymmetry..Kybernetika 45 (2009), 1003-1011. Zbl 1191.62095, MR 2650079 |
| Reference:
|
[3] Durante, F., Sempi, C.: Copula theory - an introduction..In: Copula Theory and Its Applications (P. Jaworski, F. Durante, W. K. Härdle and T. Rychlik, eds.), Springer, Berlin, Heidelberg 2010, pp. 3-31. MR 3051261 |
| Reference:
|
[4] Edwards, H. H., Mikusiński, P., Taylor, M. D.: Measures of concordance determined by $D_4$-invariant copulas..Internat. J. Math. Sci. 70 (2004), 3867-3875. Zbl 1075.62042, MR 2129414, 10.1155/S016117120440355X |
| Reference:
|
[5] Fuchs, S.: Multivariate copulas - Transformations, symmetry, order and measures of concordance..Submitted for publication (2013). |
| Reference:
|
[6] Klement, E. P., Mesiar, R., Pap, E.: Invariant copulas..Kybernetika 38 (2002), 275-285. Zbl 1264.62045, MR 1944309 |
| Reference:
|
[7] Liebscher, E.: Construction of asymmetric multivariate copulas..J. Multivariate Anal. 99 (2008), 2234-2250. Zbl 1151.62043, MR 2463386, 10.1016/j.jmva.2008.02.025 |
| Reference:
|
[8] Nelsen, R. B.: An Introduction to Copulas. Second edition..Springer, New York 2006. MR 2197664 |
| Reference:
|
[9] Nelsen, R. B.: Extremes of nonexchangeability..Statist. Papers 48 (2007), 329-336. Zbl 1110.62071, MR 2295821, 10.1007/s00362-006-0336-5 |
| Reference:
|
[10] Scarsini, M.: On measures of concordance..Stochastica 8 (1984), 201-218. Zbl 0582.62047, MR 0796650 |
| Reference:
|
[11] Taylor, M. D.: Multivariate measures of concordance..Ann. Inst. Statist. Math. 59 (2007), 789-806. Zbl 1131.62054, MR 2397737, 10.1007/s10463-006-0076-2 |
| . |
