On the construction of multivariate extreme value models via copulas

Environmetrics

Volumn 21, Issue 2, 2010, Pages 143-161

  Durante, F ^a   Salvadori, G ^b  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^b UNIVERSITY OF SALENTO   (Italy)

Author keywords

Extreme value copulas; Marshall olkin models; Multivariate extreme value distributions; Multivariate return periods; Random variates generation

Indexed keywords

GAUGE; MULTIVARIATE ANALYSIS; NUMERICAL MODEL; PROBABILITY; STATISTICAL DISTRIBUTION;

EID: 77949550776     PISSN: 11804009     EISSN: 1099095X     Source Type: Journal    
DOI: 10.1002/env.988     Document Type: Article

References (40)

1. Balkema G, Embrechts P. 2007. High risk scenarios and extremes. Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS): Zürich.
2. Barbe P, Genest C, Ghoudi K, Rémillard B. 1996. On Kendall's process. Journal of Multivariate Analysis 58(2): 197-229.
3. Beirlant J, Goegebeur Y, Teugels J, Segers J. 2004. Statistics of Extremes. Wiley Series in Probability and Statistics. John Wiley & Sons Ltd.: Chichester.
4. Cuadras CM, Augé J. 1981. A continuous general multivariate distribution and its properties. Communications in Statistics A-Theory Methods 10(4): 339-353.
5. De Haan L, De Ronde J. 1998. Sea and wind: multivariate extremes at work. Extremes 1(1): 7-45.
6. de Haan L, Ferreira A. 2006. Extreme Value Theory. An Introduction. Springer Series in Operations Research and Financial Engineering. Springer: New York.
7. De Michele C. 2008. Department of Hydraulic, Environmental, Roads and Surveying Engineering, Polytechnic of Milan, Milan (Italy). Private Communication.
8. Durante F. 2009. Construction of non-exchangeable bivariate distribution functions. Statistics Papers 50(2): 383-391.
9. Durante F, Hofert M, Scherer M. 2008. Multivariate hierarchical copulas with shocks. Working paper.
10. Durante F, Quesada-Molina JJ, Úbeda-Flores M. 2007. On a family of multivariate copulas for aggregation processes. Information Sciences 177: 5715-5724.
11. Fredericks GA, Nelsen RB. 2007. On the relationship between Spearman's rho and Kendall's tau for pairs of continuous variables. Journal of Statistical Planning and Inference 137: 2143-2150.
12. Galambos J. 1987. The Asymptotic Theory of Extreme Order Statistics (2 nd edn). Robert E. Krieger Publishing Co. Inc.: Melbourne, FL.
13. Genest C. 1987. Frank's family of bivariate distributions. Biometrika 743: 549-555.
14. Genest C, Favre AC. 2007. Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering 12(4): 347-368.
15. Genest C, Ghoudi K, Rivest L-P. 1998. Understanding relationships using copulas, by Edward Frees and Emiliano Valdez, January 1998. North American Actuarial Journal 2(3): 143-149.
16. Genest C, Rémillard B, Beaudoin D. 2009. Goodness-of-fit tests for copulas: a review and a power study. Insurance: Mathematics and Economics (in press).
17. Genest C, Rivest L-P. 1989. A characterization of Gumbel's family of extreme value distributions. Statistics & Probability Letters 8(3): 207-211.
18. Genest C, Rivest L-P. 1993. Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association 88(423): 1034-1043.
19. Genest C, Rivest L-P. 2001. On the multivariate probability integral transformation. Statistics & Probability Letters 53(4): 391-399.
20. Ghoudi K, Khoudraji A, Rivest L-P. 1998. Propriétés statistiques des copules de valeurs extrêmes bidimensionnelles. Canadian Journal of Statistics 26: 187-197.
21. Joe H. 1997. Multivariate Models and Dependence Concepts. Chapman & Hall: London.
22. Khoudraji A. 1995. Contributions à l'étude des copules et à la modélisation des valeurs extrêmes bivariées. PhD thesis, Université de Laval, Québec (Canada).
23. Liebscher E. 2008. Construction of asymmetric multivariate copulas. Journal of Multivariate Analysis 99(10): 2234-2250.
24. Mai JF, Scherer M. 2008. Efficiently sampling exchangeable Cuadras-Augé copulas in high dimensions. Information Sciences (in press).
25. Mai JF, Scherer M. 2008. Lévy frailty copulas. Journal of Multivariate Analysis (in press).
26. Marshall AW, Olkin I. 1967. A multivariate exponential distribution. Journal of the American Statistical Association 62: 30-44.
27. Mikosch T. 2005. How to model multivariate extremes if one must? Statistica Neerlandica 59(3): 324-338.
28. Nelsen RB, Quesada-Molina JJ, Rodríguez-Lallena JA, Úbeda-Flores M. 2003. Kendall distribution functions. Statistics & Probability Letters 65(3): 263-268.
29. Nelsen RB. 1996. Nonparametric measures of multivariate association. In Distributions with fixed marginals and related topics (Seattle, WA, 1993), Vol. 28 of IMS Lecture Notes Monograph Series, Institute of Mathematical Statistics, Hayward, CA, 1996; 223-232.
30. Nelsen RB. 2006. An Introduction to Copulas (2nd edn). Springer-Verlag: New York.
31. Oakes D. 1982. A model for association in bivariate survival data. Journal of the Royal Statistical Society-B 44: 414-422.
32. Pickands J. 1981. Multivariate extreme value distributions. Bulletin of International Statistical Institute 49: 859-878.
33. Reiss R-D, Thomas M. 2001. Statistical Analysis of Extreme Values (2nd edn). Birkhäuser Verlag: Basel.
34. Salvadori G. 2004. Bivariate return periods via 2-copulas. Statistical Methodology 1: 129-144.
35. Salvadori G, De Michele C, Kottegoda NT, Rosso R. 2007. Extremes in nature. An approach using copulas, volume 56 of Water Science and Technology Library. Springer: Dordrecht.
36. Schmid F, Schmidt R. 2007. Multivariate extensions of Spearman's Rho and related statistics. Statistics & Probability Letters 77: 407-416.
37. Sklar A. 1959. Fonctions de répartition à n dimensions et leurs marges. Publications de l'Institut de Statistique de L'Université de Paris 8: 229-231.
38. Yue S. 2000a. The Gumbel logistic model for representing a multivariate storm event. Advances in Water Resources 24: 179-185.
39. Yue S. 2000b. The Gumbel mixed model applied to storm frequency analysis. Water Resources Management 14: 377-389.
40. Zhang L. 2005. Multivariate hydrological frequency analysis and risk mapping. PhD thesis, Louisiana State University, Baton Rouge, Louisiana (USA).