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Multivariate extremal processes generated by independent non-identically distributed random variables

Published online by Cambridge University Press:  14 July 2016

Ishay Weissman
Ishay Weissman*
Affiliation:
Tel-Aviv University
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Abstract

Let be the kth largest among Xn1, …, Xn[nt], where Xni = (Xi – an)/bn, {Xi} is a sequence of independent random variables and bn > 0 and an are norming constants. Suppose that for each converges in distribution. Then all the finite-dimensional laws of converge. The limiting process is represented in terms of a non-homogeneous two-dimensional Poisson process.

Keywords

MULTIVARIATE K-DIMENSIONAL EXTREMAL PROCESSNON-HOMOGENEOUS TWO-DIMENSIONAL POISSON PROCESSCONVERGENCE OF FINITE-DIMENSIONAL LAWS
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 477 - 487
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Berman, S. M. (1962) Limiting distribution of the maximum term in sequences of dependent random variables. Ann. Math. Statist. 35, 894–908.Google Scholar
[2] Dwass, M. (1964) Extremal processes. Ann. Math. Statist. 33, 1718–1725.CrossRefGoogle Scholar
[3] Dwass, M. (1966) Extremal processes II. Ill. J. Math. 10, 381–391.Google Scholar
[4] Lamperti, J. (1964). On extreme order statistics. Ann. Math. Statist. 35, 1726–1737.CrossRefGoogle Scholar
[5] Loève, M. (1956) Ranking limit problem. Proc. Third Berkeley Symp. Math. Statist. Prob. 2, 177–194.Google Scholar
[6] Pickands, J. III (1971) The two-dimensional Poisson process and extremal process. J. Appl. Prob. 8, 745–756.CrossRefGoogle Scholar
[7] Resnick, S. I. and Rubinovitch, M. (1973) The structure of extremal processes. Adv. Appl. Prob. 5, 287–307.CrossRefGoogle Scholar
[8] Smirnov, N. V. (1952) Limit distributions for the terms of a variational series. Amer. Math. Soc. Transl. 67, 1–67.Google Scholar
[9] Weissman, I. (1974) Extremal processes generated by independent nonidentically distributed random variables. Ann. Prob. 3, 172–177.Google Scholar
[10] Weissman, I. (1974) On location and scale functions of a class of limiting processes with application to extreme value theory. Ann. Prob. 3, 178–181.Google Scholar