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Measuring the extremal dependence

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  • Martins, A.P.
  • Ferreira, H.

Abstract

We deal with the problem of how to measure the strength of the dependence in the extremes. Probabilistic and statistical methods for multivariate extreme values motivate an adjustment in the definition of the extremal coefficient. We point out that the available extremal coefficient does not measure correctly the dependence in the limiting distribution of maxima when a multivariate extremal index is present and propose an adjustment of this coefficient in order to cover this case and preserve its main properties. We will present a new definition for the extremal coefficient and relate it with the tail dependence. Finally, we illustrate this contribution with examples.

Suggested Citation

  • Martins, A.P. & Ferreira, H., 2005. "Measuring the extremal dependence," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 99-103, June.
    • Handle: RePEc:eee:stapro:v:73:y:2005:i:2:p:99-103
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    References listed on IDEAS

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    1. Joe, H., 1993. "Parametric Families of Multivariate Distributions with Given Margins," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 262-282, August.
    2. Hsing, Tailen, 1989. "Extreme value theory for multivariate stationary sequences," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 274-291, May.
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    Cited by:

    1. Li, Haijun, 2009. "Orthant tail dependence of multivariate extreme value distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 243-256, January.

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