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Asymptotic expansions of powered skew-normal extremes

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  • Xiong, Qian
  • Peng, Zuoxiang

Abstract

Let Mn denote the partial maximum of a sequence of independent random variables with common skew-normal distribution Fλ(x) with parameter λ. In this paper, higher-order distributional expansions and convergence rates of powered skew-normal extremes are considered. It is shown that with optimal normalizing constants the convergence rate of the distribution of |Mn|t to its ultimate extreme value distribution is the order of 1∕(logn)2 as t=2, and the convergence rate is the order of 1∕logn for the case of 0

Suggested Citation

  • Xiong, Qian & Peng, Zuoxiang, 2020. "Asymptotic expansions of powered skew-normal extremes," Statistics & Probability Letters, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:stapro:v:158:y:2020:i:c:s016771521930313x
    DOI: 10.1016/j.spl.2019.108667
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    References listed on IDEAS

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    1. 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.
    2. Liao, Xin & Peng, Zuoxiang & Nadarajah, Saralees, 2013. "Asymptotic expansions for moments of skew-normal extremes," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1321-1329.
    3. 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.
    4. Arellano-Valle, Reinaldo B. & Ferreira, Clécio S. & Genton, Marc G., 2018. "Scale and shape mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 98-110.
    5. Xin Liao & Zuoxiang Peng & Saralees Nadarajah, 2014. "Tail Behavior and Limit Distribution of Maximum of Logarithmic General Error Distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(24), pages 5276-5289, December.
    6. Zhou, Wei & Ling, Chengxiu, 2016. "Higher-order expansions of powered extremes of normal samples," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 12-17.
    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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