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Geometric interpretation of the residual dependence coefficient

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  • Nolde, Natalia

Abstract

The residual dependence coefficient was originally introduced by Ledford and Tawn (1996) [25] as a measure of residual dependence between extreme values in the presence of asymptotic independence. We present a geometric interpretation of this coefficient with the additional assumptions that the random samples from a given distribution can be scaled to converge onto a limit set and that the marginal distributions have Weibull-type tails. This result leads to simple and intuitive computations of the residual dependence coefficient for a variety of distributions.

Suggested Citation

  • Nolde, Natalia, 2014. "Geometric interpretation of the residual dependence coefficient," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 85-95.
  • Handle: RePEc:eee:jmvana:v:123:y:2014:i:c:p:85-95
    DOI: 10.1016/j.jmva.2013.08.018
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    References listed on IDEAS

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    1. Hashorva, Enkelejd, 2010. "On the residual dependence index of elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1070-1078, July.
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    Cited by:

    1. Lars Nørvang Andersen & Patrick J. Laub & Leonardo Rojas-Nandayapa, 2018. "Efficient Simulation for Dependent Rare Events with Applications to Extremes," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 385-409, March.
    2. Simpson, Emma S. & Wadsworth, Jennifer L. & Tawn, Jonathan A., 2021. "A geometric investigation into the tail dependence of vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    3. Majid Asadi & Somayeh Zarezadeh, 2020. "A unified approach to constructing correlation coefficients between random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 657-676, August.
    4. de Valk, Cees, 2016. "A large deviations approach to the statistics of extreme events," Other publications TiSEM 117b3ba0-0e40-4277-b25e-d, Tilburg University, School of Economics and Management.
    5. Hu, Shuang & Peng, Zuoxiang & Nadarajah, Saralees, 2022. "Tail dependence functions of the bivariate Hüsler–Reiss model," Statistics & Probability Letters, Elsevier, vol. 180(C).

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