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Extremal properties of the multivariate extended skew-normal distribution, Part B

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  • Beranger, B.
  • Padoan, S.A.
  • Xu, Y.
  • Sisson, S.A.

Abstract

The skew-normal and related families are flexible and asymmetric parametric models suitable for modelling a diverse range of systems. We show that the multivariate maximum of a high-dimensional extended skew-normal random sample has asymptotically independent components and derive the speed of convergence of the joint tail. To describe the possible dependence among the components of the multivariate maximum, we show that under appropriate conditions an approximate multivariate extreme-value distribution that leads to a rich dependence structure can be derived.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:147:y:2019:i:c:p:105-114
    DOI: 10.1016/j.spl.2018.11.031
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Liao, Xin & Peng, Zuoxiang & Nadarajah, Saralees & Wang, Xiaoqian, 2014. "Rates of convergence of extremes from skew-normal samples," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 40-47.
    4. 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.
    5. Beranger, B. & Padoan, S.A. & Xu, Y. & Sisson, S.A., 2019. "Extremal properties of the univariate extended skew-normal distribution, Part A," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 73-82.
    6. Reinaldo B. Arellano-Valle & Marc G. Genton, 2010. "Multivariate extended skew-t distributions and related families," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 201-234.
    7. Peng, Zuoxiang & Li, Chunqiao & Nadarajah, Saralees, 2016. "Extremal properties of the skew-t distribution," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 10-19.
    8. Enkelejd Hashorva & Chengxiu Ling, 2016. "Maxima of skew elliptical triangular arrays," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(12), pages 3692-3705, June.
    9. Li, Haijun, 2009. "Orthant tail dependence of multivariate extreme value distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 243-256, January.
    10. Hüsler, Jürg & Reiss, Rolf-Dieter, 1989. "Maxima of normal random vectors: Between independence and complete dependence," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 283-286, February.
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