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Extremal properties of the univariate extended skew-normal distribution, Part A

Author

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

Abstract

We consider the extremal properties of the highly flexible univariate extended skew-normal distribution. We derive the well-known Mills’ inequalities and Mills’ ratio for the extended skew-normal distribution and establish the asymptotic extreme-value distribution for the maximum of samples drawn from this distribution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:147:y:2019:i:c:p:73-82
    DOI: 10.1016/j.spl.2018.09.018
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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. 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.
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    Cited by:

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    2. Xiong, Qian & Peng, Zuoxiang, 2020. "Asymptotic expansions of powered skew-normal extremes," Statistics & Probability Letters, Elsevier, vol. 158(C).
    3. 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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