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Multivariate extremes of generalized skew-normal distributions

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  • Lysenko, Natalia
  • Roy, Parthanil
  • Waeber, Rolf

Abstract

We explore extremal properties of a family of skewed distributions extended from the multivariate normal distribution by introducing a skewing function [pi]. We give sufficient conditions on the skewing function for the pairwise asymptotic independence to hold. We apply our results to a special case of the bivariate skew-normal distribution and finally support our conclusions by a simulation study which indicates that the rate of convergence is quite slow.

Suggested Citation

  • Lysenko, Natalia & Roy, Parthanil & Waeber, Rolf, 2009. "Multivariate extremes of generalized skew-normal distributions," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 525-533, February.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:4:p:525-533
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    References listed on IDEAS

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    1. Lane, Morton N., 2000. "Pricing Risk Transfer Transactions1," ASTIN Bulletin, Cambridge University Press, vol. 30(2), pages 259-293, November.
    2. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    3. Yanyuan Ma & Marc G. Genton, 2004. "Flexible Class of Skew‐Symmetric Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 459-468, September.
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    1. Boris Beranger & Simone A. Padoan & Scott A. Sisson, 2017. "Models for Extremal Dependence Derived from Skew-symmetric Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 21-45, March.
    2. Padoan, Simone A., 2011. "Multivariate extreme models based on underlying skew-t and skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 977-991, May.
    3. Peng, Zuoxiang & Li, Chunqiao & Nadarajah, Saralees, 2016. "Extremal properties of the skew-t distribution," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 10-19.
    4. Fung, Thomas & Seneta, Eugene, 2016. "Tail asymptotics for the bivariate skew normal," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 129-138.
    5. Mahdiyeh, Zahra & Kazemi, Iraj, 2019. "An innovative strategy on the construction of multivariate multimodal linear mixed-effects models," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    6. Fung, Thomas & Seneta, Eugene, 2014. "Convergence rate to a lower tail dependence coefficient of a skew-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 62-72.
    7. Beranger, B. & Padoan, S.A. & Xu, Y. & Sisson, S.A., 2019. "Extremal properties of the multivariate extended skew-normal distribution, Part B," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 105-114.

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