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Hidden regular variation and the rank transform

Part of: Stochastic processes Distribution theory - Probability Multivariate analysis

Published online by Cambridge University Press:  01 July 2016

Janet Heffernan  and
Sidney Resnick
Janet Heffernan*
Affiliation:
Lancaster University
Sidney Resnick*
Affiliation:
Cornell University
*
∗ Postal address: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK. Email address: j.heffernan@lancaster.ac.uk
∗∗ Postal address: School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, USA. Email address: sir1@cornell.edu
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Abstract

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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.

Keywords

Heavy tailregular variationPareto tailcoefficient of tail dependencehidden regular variationrank transformasymptotic independenceInternet trafficflood risk

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 62H05: Characterization and structure theory 62H20: Measures of association (correlation, canonical correlation, etc.) 60E05: Distributions

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 37 , Issue 2 , June 2005 , pp. 393 - 414
Copyright
Copyright © Applied Probability Trust 2005 

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