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Multivariate extreme models based on underlying skew-t and skew-normal distributions

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  • Padoan, Simone A.

Abstract

We derive for the first time the limiting distribution of maxima of skew-t random vectors and we show that its limiting case, as the degree of freedom goes to infinity, is the skewed version of the well-known Hüsler-Reiss model. The advantage of the new families of models is that they are particularly flexible, allowing for both symmetric and asymmetric dependence structures and permitting the modelling of multivariate extremes with dimensions greater than two.

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  • 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.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:5:p:977-991
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    Cited by:

    1. 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.
    2. 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.
    3. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    4. Padoan, Simone A., 2013. "Extreme dependence models based on event magnitude," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 1-19.
    5. 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.
    6. Samuel A. Morris & Brian J. Reich & Emeric Thibaud & Daniel Cooley, 2017. "A space-time skew-t model for threshold exceedances," Biometrics, The International Biometric Society, vol. 73(3), pages 749-758, September.
    7. Frick, Melanie & Reiss, Rolf-Dieter, 2013. "Expansions and penultimate distributions of maxima of bivariate normal random vectors," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2563-2568.
    8. Joe, Harry & Li, Haijun, 2019. "Tail densities of skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 421-435.
    9. Peng, Zuoxiang & Li, Chunqiao & Nadarajah, Saralees, 2016. "Extremal properties of the skew-t distribution," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 10-19.
    10. Andréas Heinen & Alfonso Valdesogo, 2022. "The Kendall and Spearman rank correlations of the bivariate skew normal distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1669-1698, December.
    11. Hashorva, Enkelejd, 2018. "Representations of max-stable processes via exponential tilting," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2952-2978.
    12. Fung, Thomas & Seneta, Eugene, 2016. "Tail asymptotics for the bivariate skew normal," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 129-138.
    13. Marcon, Giulia & Padoan, Simone & Naveau, Philippe & Muliere, Pietro & Segers, Johan, 2016. "Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials," LIDAM Discussion Papers ISBA 2016020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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