Concomitant tail behaviour for extremes

  • Ledford A
  • Tawn J
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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.

Author-supplied keywords

  • Asymptotic independence
  • Bivariate extreme value distribution
  • Coefficient of tail dependence
  • Concomitants
  • Extreme value theory
  • Induced order statistics
  • Order statistics
  • Slowly varying functions

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Authors

  • Anthony W. Ledford

  • Jonathan A. Tawn

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