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Mathematics > Probability

arXiv:1512.08879 (math)
[Submitted on 30 Dec 2015 (v1), last revised 2 Jan 2016 (this version, v2)]

Title:Higher-order expansions of powered extremes of normal samples

Authors:Wei Zhou, Chengxiu Ling
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Abstract:In this paper, higher-order expansions for distributions and densities of powered extremes of standard normal random sequences are established under an optimal choice of normalized constants. Our findings refine the related results in Hall (1980). Furthermore, it is shown that the rate of convergence of distributions/densities of normalized extremes depends in principle on the power index.
Subjects: Probability (math.PR)
MSC classes: Primary 62E20, 60E05, secondary 60F15, 60G15
Cite as: arXiv:1512.08879 [math.PR]
  (or arXiv:1512.08879v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1512.08879

Submission history

From: Chengxiu Ling [view email]
[v1] Wed, 30 Dec 2015 08:44:11 UTC (9 KB)
[v2] Sat, 2 Jan 2016 03:35:01 UTC (9 KB)
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