Let {Xn,n≥1}{Xn,n≥1} be a sequence of independent random variables with common general error distribution GED(v)GED(v) with shape parameter v>0, and let Mn,rMn,r denote the rth largest order statistics of X1,X2,…,XnX1,X2,…,Xn. With different normalizing constants the distributional expansions and the uniform convergence rates of normalized powered order statistics |Mn,r|p|Mn,r|p are established. An alternative method is presented to estimate the probability of the rth extremes. Numerical analyses are provided to support the main results.

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To cite this article: Yuhan Zou, Yingyin Lu & Zuoxiang Peng (2023) Rates of convergence of powered order statistics from general error distribution, Statistical Theory and Related Fields, 7:1, 1-29, DOI: 10.1080/24754269.2022.2146955 To link to this article: https://doi.org/10.1080/24754269.2022.2146955