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Concomitant tail behaviour for extremes

Part of: Stochastic processes Nonparametric inference

Published online by Cambridge University Press:  01 July 2016

Anthony W. Ledford  and
Jonathan A. Tawn
Anthony W. Ledford*
Affiliation:
University of Surrey
Jonathan A. Tawn*
Affiliation:
Lancaster University
*
∗ Postal address: Department of Mathematical and Statistics, University of Surrey, Guildford, Surrey GU2 5XH, UK.
∗∗ Postal address: Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK.
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Abstract

The influence of bivariate extremal dependence on the limiting behaviour of the concomitant of the largest order statistic is examined. Our approach is to fix the marginal distributions and derive a general tail characterisation of the joint survivor function. From this, we identify the normalisation required to obtain the limiting distribution of the concomitant of the largest order statistic, obtain its tail form, and investigate the limiting probability that the vector of componentwise maxima occurs as an observation of the bivariate process. The results are illustrated for a range of extremal dependence forms.

Keywords

Asymptotic independencebivariate extreme value distributioncoefficient of tail dependenceconcomitantsextreme value theoryinduced order statisticsorder statisticsslowly varying functions

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 62G30: Order statistics; empirical distribution functions
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 1 , March 1998 , pp. 197 - 215
Copyright
Copyright © Applied Probability Trust 1998 

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