Limit conditional distributions for bivariate vectors with polar representation

Stochastic Models

Volumn 26, Issue 1, 2010, Pages 54-77

  Fougères, Anne Laure ^a   Soulier, Philippe ^b  

^a UNIVERSITÉ LYON 1   (France)

^b UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

Author keywords

Asymptotic independence; Conditional excess probability; Conditional extreme value model; Elliptic distributions; Second order correction; varying tail

Indexed keywords

VECTORS;

ASYMPTOTIC INDEPENDENCE; CONDITIONAL DISTRIBUTION; CONDITIONAL EXTREME VALUE MODELS; DOMAIN OF ATTRACTION; ELLIPTIC DISTRIBUTIONS; EXTREME VALUE DISTRIBUTIONS; MAXIMUM DOMAIN OF ATTRACTION; SECOND-ORDER CORRECTION;

PROBABILITY DISTRIBUTIONS;

EID: 77951234991     PISSN: 15326349     EISSN: 15324214     Source Type: Journal    
DOI: 10.1080/15326340903291362     Document Type: Article

References (22)

1. Balkema, G.; Embrechts, P. High Risk Scenarios and Extremes. A Geometric Approach; Zurich Lectures in Advanced Mathematics; European Mathematical Society: Zürich, 2007.
2. Barbe, P. Approximation of integrals over asymptotic sets with applications to probability and statistics. Available at http://arxiv.org/abs/ math/0312132, 2003. Last accessed 5 December 2003.
3. Abdous, B.; Fougères, A.-L.; Ghoudi, K. Extreme behaviour for bivariate elliptical distributions. Revue Canadienne de Statistique 2005, 33, 1095-1107.
4. Abdous, B., Fougères, A.-L., Ghoudi, K.; Soulier, P. Estimation of bivariate excess probabilities for elliptical models. Bernoulli 2008, 14, 1065-1088.
5. Berman, S.M. Sojourns and extremes of Fourier sums and series with random coefficients. Stochastic Processes and Their Applications 1983, 15, 213-238.
6. Berman, S.M. Sojourns and Extremes of Stochastic Processes; The Wadsworth & Brooks/Cole Statistics/Probability Series; Wadsworth & Brooks/Cole Advanced Books & Software: Pacific Grove, CA, 1992.
7. Bingham, N.H.; Goldie, C.M.; Teugels, J.L. Regular variation. In Encyclopedia of Mathematics and Its Applications, Vol.27; Cambridge University Press: Cambridge, 1989.
8. Breiman, L. On some limit theorems similar to the arc-sin law. Theory of Probability and Its Applications 1965, 10, 351-360.
9. Cline, D.B.H.; Samorodnitsky, G. Subexponentiality of the product of independent random variables. Stochastic Process. Appl. 1994, 49, 75-98.
10. Das, B.; Resnick, S.I. Conditioning on an extreme component: model consistency and regular variation on cones. Available at http://arxiv.org/abs/ 0805.4373, 2008. Last accessed 11 July 2008.
11. Das, B.; Resnick, S.I. Detecting a conditional extreme value model. Extremes 2009, doi 10.1007/s10687-009-0097-3.
12. De Haan, L.; Ferreira, A. Extreme Value Theory. An Introduction. Springer Series in Operations Research and Financial Engineering; Springer: New York, NY, 2006.
13. Eddy, W.F.; Gale, J.D. The convex hull of a spherically symmetric sample. Advances in Applied Probability 1981, 13, 751-763.
14. Fougères, A.-L.; Soulier, P. Estimation of conditional laws given an extreme component. arXiv:0806.2426, 2008.
15. Hashorva, E. Extremes of asymptotically spherical and elliptical random vectors. Insurance: Mathematics & Economics 2005, 36, 285-302.
16. Hashorva, E. Gaussian approximation of conditional elliptic random vectors. Stoch. Models 2006, 22, 441-457.
17. Hashorva, E. Conditional limit results for type I polar distributions. Extremes 2008, 12, 239-263.
18. Hashorva, E., Kotz, S., Kume, A. Lp-norm generalised symmetrised Dirichlet distributions. Albanian Journal of Mathematics 2007, 1, 31-56.
19. Heffernan, J.E.; Resnick, S.I. Limit laws for random vectors with an extreme component. Annals of Applied Probability 2007, 17, 537-571.
20. Heffernan, J.E.; Tawn, J.A. A conditional approach for multivariate extreme values. Journal of the Royal Statistical Society, Series B 2004, 66 497-546.
21. Resnick, S. Hidden regular variation, second order regular variation and asymptotic independence. Extremes 2002, 5, 303-336.
22. Resnick, S.I. Extreme values, regular variation, and point processes, In Applied Probability. A Series of the Applied Probability Trust, Vol.4; Springer-Verlag: New York, 1987.