Models for dependent extremes using stable mixtures

Scandinavian Journal of Statistics

Volumn 36, Issue 1, 2009, Pages 42-59

  FougÈres, Anne Laure ^a   Nolan, John P ^b   RootzÉn, Holger ^c  

^a UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

^b AMERICAN UNIVERSITY   (United States)

^c CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Logistic distribution; Max stable; Multivariate extreme value distribution; Pitting corrosion; Positive stable variables; Random effect

Indexed keywords

EID: 60249090955     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2008.00613.x     Document Type: Article

References (29)

1. Anderson, C. W. Nadarajah, S. (1993). Environmental factors affecting reservoir safety. In Statistics for the environment (eds V. Barnett K. F. Turkman 163 182. Wiley, New York.
2. Bruun, J. T. Tawn, J. A. (1998). Comparison of approaches for estimating the probability of coastal flooding. J. Roy. Statist. Soc. Ser. C 47, 405 423.
3. Chambers, J. L., Mallows, C. L. Stuck, B. W. (1976). A method for simulating stable random variables. J. Amer. Statist. Assoc. 71, 340 344.
4. Correction in J. Amer. Statist. Assoc. 82 (1987 704.
5. Coles, S. G. Tawn, J. A. (1991). Modelling multivariate extreme events. J. Roy. Statist. Soc. Ser. B 53, 377 392.
6. Crowder, M. J. (1985). A distributional model for repeated failure time measurements. J. Roy. Statist. Soc. Ser. B 47, 447 452.
7. Crowder, M. J. (1989). A multivariate distribution with Weibull components. J. Roy. Statist. Soc. Ser. B 51, 93 108.
8. Crowder, M. J. (1998). A multivariate model for repeated failure time measurements. Scand. J. Statist. 25, 53 67.
9. Crowder, M. J. Kimber, A. (1997). A score test for the multivariate Burr and other Weibull mixture distributions. Scand. J. Statist. 24, 419 432.
10. Fougères, A.-L. (2004). Multivariate extremes. In Extreme values in finance, telecommunications and the environment (eds B. Finkenstädt H. Rootzén 373 388. Chapman & Hall/CRC, Boca Raton.
11. de Haan, L. de Ronde, J. (1998). Sea and wind: multivariate extremes at work. Extremes 1, 7 45.
12. Heffernan, J. E. Tawn, J. A. (2004). A conditional approach for multivariate extreme values. J. Roy. Statist. Soc. Ser. B Stat. Methodol. 66, 497 546.
13. Hougaard, P. (1986). A class of multivariate failure time distributions. Biometrika 73, 671 678.
14. Kotz, S. Nadarajah, S. (2000). Extreme value distributions: theory and applications. Imperial College Press, London.
15. Kowaka, M. (1994). An introduction to life prediction of plant materials. Application of extreme value statistical methods for corrosion analysis. Allerton Press, New York.
16. Leadbetter, M. R., Lindgren, G. Rootzén, H. (1983). Extremes and related properties of random sequences and processes. Springer, New York.
17. Ledford, A. W. Tawn, J. A. (1996). Statistics for near independence in multivariate extreme values. Biometrika 83, 169 187.
18. McFadden, D. (1978). Modelling the choice of residential location. In Spatial interaction theory and planning models (eds A. Karlquist et al. 75 96. North-Holland, Amsterdam.
19. Mikosch, T. (2004). Modelling dependence and tails of financial time series. In Extreme values in finance, telecommunications and the environment (eds B. Finkenstädt H. Rootzén 185 286. Chapman & Hall/CRC, Boca Raton.
20. Nolan, J. P. (1997). Numerical calculation of stable densities and distribution functions. Comm. Statist. Stoch. Models 13, 759 774.
21. Samorodnitsky, G. Taqqu, M. S. (1994). Stable non-gaussian random processes. Chapman & Hall, New York.
22. Scarf, P. A. Laycock, P. J. (1994). Applications of extreme value theory in corrosion engineering. J. Res. Natl. Inst. Stand. Technol. 99, 313 320.
23. Shi, D. (1995). Fisher information for a multivariate extreme value distribution. Biometrika 82, 644 649.
24. Smith, R. L. (2004). Statistics of extremes, with applications in environment, insurance, and finance. In Extreme values in finance, telecommunications and the environment (eds B. Finkenstädt H. Rootzén 2 78. Chapman & Hall/CRC, Boca Raton.
25. Stǎricǎ, C. (1999). Multivariate extremes for models with constant conditional correlations. J. Empir. Finance 6, 515 553.
26. Stephenson, A. G. (2003). Simulating multivariate extreme value distributions of logistic type. Extremes 6, 49 59.
27. Tawn, J. A. (1990). Modelling multivariate extreme value distributions. Biometrika 77, 245 253.
28. Watson, A. S. Smith, R. L. (1985). An examination of statistical theories for fibrous materials in the light of experimental data. J. Mater. Sci. 20, 3260 3270.
29. Zolotarev, V. M. (1986). One-dimensional stable distributions. Amer. Math. Soc. Transl. of Math. Monographs, Vol. 65. Amer. Math. Soc., Providence, RI (Transl. of the original 1983 Russian).