Some notes on multivariate generalized Pareto distributions

Journal of Multivariate Analysis

Volumn 99, Issue 6, 2008, Pages 1288-1301

  Michel, René ^a  

^a Altran CIS GmbH   (Germany)

Author keywords

Angular measure; Extreme value distribution; Generalized Pareto distribution; Logistic GPD; Peaks over threshold

Indexed keywords

EID: 43049116195     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2007.08.007     Document Type: Article

References (22)

1. G. Balkema, P. Embrechts, Multivariate Excess Distributions, 2004, 〈http://www.math.ethz.ch/%7Ebaltes/ftp/guuspe08Jun04.pdf〉.
2. Beirlant J., Goegebeur Y., Segers J., and Teugels J. Statistics of Extremes, Theory and Applications (2005), Wiley, Chichester
3. Bhattacharya R., and Rao R. Normal Approximation and Asymptotic Expansions, Wiley Series in Probability and Mathematical Statistics (1976), Wiley, New York
4. Coles S. An Introduction to Statistical Modeling of Extreme Values, Springer Series in Statistics (2001), Springer, New York
5. Coles S., and Tawn J. Modelling extreme multivariate events. J. Roy. Statist. Soc. 53 (1991) 377-392
6. Coles S., and Tawn J. Statistical methods for multivariate extremes. Appl. Statist. 43 (1994) 1-48
7. Falk M., Hüsler J., and Reiss R.-D. Laws of Small Numbers: Extremes and Rare Events. second ed. (2004), Birkhäuser, Basel
8. Falk M., and Michel R. Testing for tail independence in extreme value models. Ann. Inst. Statist. Math. 58 (2006) 261-290
9. Heffernan J., and Tawn J. A conditional approach for multivariate extreme values. J. Roy. Statist. Soc. Ser. B 66 (2004) 497-564
10. D. Hofmann, Über die Darstellung multivariater Extremwertverteilungen mittels Normen, Diploma Thesis, Institut für Mathematik, Bayerische Julius-Maximilians-Universität Würzburg, 2006, 〈http://www.danielhofmann.com/downloads/Diplomarbeit.pdf〉.
11. Joe H., Smith R., and Weissman I. Bivariate threshold methods for extremes. J. Roy. Statist. Soc. 54 (1992) 171-183
12. Kaufmann E., and Reiss R.-D. Approximation rates for multivariate exceedances. J. Statist. Plann. Inference 45 (1995) 235-245
13. Kotz S., and Nadarajah S. Extreme Value Distributions, Theory and Applications (2000), Imperial College Press
14. Ledford A., and Tawn J. Statistics for near independence in multivariate extreme values. Biometrika 83 (1996) 169-187
15. R. Michel, Simulation and estimation in multivariate generalized Pareto models, Dissertation, Fakultät für Mathematik und Informatik, Bayerische Julius-Maximilians-Universität Würzburg, 2006.
16. Reiss R.-D., and Thomas M. Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields. second ed. (2001), Birkhäuser, Basel
17. Resnick S. Extreme Values, Regular Variation, and Point Processes, Springer Series of the Applied Probability Trust (1987), Springer, New York
18. H. Rootzén, N. Tajvidi, Multivariate Generalized Pareto Distributions, Chalmers Tekniska Högskola, Göteborg, 2005, preprint no. 38, 〈http://www.math.chalmers.se/Math/Research/Preprints/2005/38.pdf〉.
19. Smith R., Tawn J., and Coles S. Markov chain models for threshold exceedances. Biometrika 84 (1997) 249-268
20. Stephenson A. Simulating multivariate extreme value distributions of logistic type. Extremes 6 (2003) 49-59
21. N. Tajvidi, Characterisation and some statistical aspects of univariate and multivariate generalised Pareto distributions, Dissertation, Department of Mathematics, Chalmers Tekniska Högskola Göteborg, 1996, 〈http://www.math.chalmers.se/~nader/thesis.ps〉.
22. Tawn J. Modelling multivariate extreme value distributions. Biometrika 77 (1990) 245-253