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Hidden regular variation and the rank transform.

Research output: Contribution to journalJournal articlepeer-review

Published
  • J. E. Heffernan
  • S. I. Resnick
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<mark>Journal publication date</mark>2005
<mark>Journal</mark>Advances in Applied Probability
Issue number2
Volume37
Number of pages22
Pages (from-to)393-414
Publication StatusPublished
<mark>Original language</mark>English

Abstract

Random vectors in the positive orthant whose distributions possess hidden regular variation are a subclass of those whose distributions are multivariate regularly varying with asymptotic independence. The concept is an elaboration of the coefficient of tail dependence of Ledford and Tawn. We show that the rank transform that brings unequal marginals to the standard case also preserves the hidden regular variation. We discuss applications of the results to two examples, one involving flood risk and the other Internet data.