Asymptotic expansions of powered skew-normal extremes

Qian Xiong and Zuoxiang Peng

Statistics & Probability Letters, 2020, vol. 158, issue C

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 0Keywords: Rate of convergence; Higher-order expansion; Powered extreme; Skew-normal distribution (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2019.108667

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