School of Mathematics and Statistics, Southwest University, Chongqing, People's Republic of China
School of Science, Southwest Petroleum University, Chengdu, People's Republic of China
School of Mathematics and Statistics, Southwest University, Chongqing, People's Republic of China
pzx@swu.edu.cn
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.
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