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Second order expansions of distributions of maxima of bivariate Gaussian triangular arrays under power normalization

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  • Weng, Zhichao
  • Liao, Xin

Abstract

In this paper, we study second order expansions of distributions of maxima of bivariate Gaussian triangular arrays under power normalization. Numerical analysis is given to compare the asymptotic behaviors under power normalization with the asymptotic behaviors under linear normalization derived by Hashorva et al. (2016).

Suggested Citation

  • Weng, Zhichao & Liao, Xin, 2017. "Second order expansions of distributions of maxima of bivariate Gaussian triangular arrays under power normalization," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 33-43.
    • Handle: RePEc:eee:stapro:v:125:y:2017:i:c:p:33-43
    DOI: 10.1016/j.spl.2017.01.024
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    References listed on IDEAS

    as
    1. 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.
    2. Hashorva, Enkelejd, 2006. "On the multivariate Hüsler-Reiss distribution attracting the maxima of elliptical triangular arrays," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 2027-2035, December.
    3. Hashorva, Enkelejd, 2005. "Elliptical triangular arrays in the max-domain of attraction of Hüsler-Reiss distribution," Statistics & Probability Letters, Elsevier, vol. 72(2), pages 125-135, April.
    4. Subramanya, U. R., 1994. "On max domains of attraction of univariate p-max stable laws," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 271-279, March.
    5. 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.
    6. H. Barakat & E. Nigm & Magdy El-Adll, 2010. "Comparison between the rates of convergence of extremes under linear and under power normalization," Statistical Papers, Springer, vol. 51(1), pages 149-164, January.
    7. 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.
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