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Archimedean copulas, exchangeability, and max-stability

Part of: Limit theorems Numerical analysis: Ordinary differential equations

Published online by Cambridge University Press:  14 July 2016

Rocco Ballerini
Rocco Ballerini*
Affiliation:
University of Florida
*
∗ Postal address: Department of Statistics, University of Florida, Gainesville, FL 32611, USA.
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Abstract

An exchangeable sequence of random variables is constructed with all finite-dimensional distribution functions having an Archimedean copula (as defined by Schweizer and Sklar (1983)). Through a monotone transformation of this exchangeable sequence, we obtain and characterize the class of exchangeable sequences possessing the max-stable property as defined by De Haan and Rachev (1989). Several parametric examples are given.

Keywords

REGULAR VARIATIONEXCHANGEABLE SEQUENCESMAX-STABLE PROCESSES

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 65L20: Stability and convergence of numerical methods
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 2 , June 1994 , pp. 383 - 390
Copyright
Copyright © Applied Probability Trust 1994 

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References

Bingham, N. H., Goldie, C. M. and Teugels, J. L. (1987) Regular Variation. Encyclopedia of Mathematics and its Applications, 27. Cambridge University Press.Google Scholar
De Haan, L. and Rachev, S. T. (1989) Estimates of the rate of convergence for max-stable processes. Ann. Prob. 17, 651–677.Google Scholar
Genest, C. and Rivest, L. (1989) A characterization of Gumbel's family of extreme value distributions. Statist. Prob. Lett. 8, 207–211.Google Scholar
Resnick, S. I. (1987) Extreme Values, Regular Variation, and Point Processes. Springer-Verlag, New York.Google Scholar
Schweizer, B. and Sklar, A. (1983) Probabilistic Metric Spaces. North-Holland, Amsterdam.Google Scholar
Widder, D. V. (1972) The Laplace Transform. Princeton University Press.Google Scholar