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A note on the independence and total dependence of max i.d. distributions

Published online by Cambridge University Press:  01 July 2016

J. Hüsler
J. Hüsler*
Affiliation:
University of Bern
*
∗Postal address: Department of Math. Statistics, University of Bern, Sidlerstr. 5, CH-3012 Bern, Switzerland.
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Abstract

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We show that the simple characterizations given by Takahashi for the independence and the total dependence of a multivariate extreme value distribution do not hold for the larger class of maximum infinitely divisible (max i.d.) distributions. This holds also for sup self-decomposable distributions.

Keywords

INDEPENDENCETOTAL DEPENDENCEMAX INFINITELY DIVISIBLESUP SELF-DECOMPOSABLEMAX STABLEEXTREME VALUE DISTRIBUTION
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 21 , Issue 1 , March 1989 , pp. 231 - 232
Copyright
Copyright © Applied Probability Trust 1989 

References

1. Balkema, A. A. and Resnick, S. I. (1977) Max-infinite divisibility. J. Appl. Prob. 14, 309–313.Google Scholar
2. Galambos, J. (1978) The Asymptotic Theory of Extreme Order Statistics. Wiley, New York. (2nd edn (1987) Krieger, Florida).Google Scholar
3. Gerritse, G. (1986) Supremum self-decomposable random vectors. Prob. Theory. Rel. Fields 72, 17–33.Google Scholar
4. Hüsler, J. (1988a) Limit properties for multivariate extreme values in sequences of independent, non-identically distributed random vectors. Stoch. Proc. Appl. to appear.Google Scholar
5. Hüsler, J. (1988b) Limit distributions of multivariate extreme values in nonstationary sequences of random vectors. To be published.Google Scholar
6. Marshall, A. W. and Olkin, I. (1983) Domains of attraction of multivariate extreme value distributions. Ann. Prob. 11, 168–177.Google Scholar
7. Resnick, S. I. (1987) Extreme Values, Regular Variation, and Point Processes. Springer-Verlag, Berlin.Google Scholar
8. Takahashi, R. (1987) Some properties of multivariate extreme value distributions and multivariate tail equivalence. Ann. Inst. Statist. Math. 39, A, 637–647.Google Scholar
9. Takahashi, R. (1988) Characterizations of a multivariate extreme value distribution. Adv. Appl. Prob. 20, 235–236.Google Scholar