@article{Huang2026, 
author = {Jianwen Huang and Xinling Liu and Jinping Jia and Runke Wang},
title = {Asymptotic expansions of powered order statistics for generalized Maxwell distribution},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {3},
pages = {8842-8858},
keywords = {asymptotic expansion, convergence rate, generalized Maxwell distribution, powered order statistic},
url = {https://www.sciopen.com/article/10.3934/math.2026364},
doi = {10.3934/math.2026364},
abstract = {Let        M          n      ,      r       denote the    rth largest-order statistics of a sequence of independent random variables with common generalized Maxwell distribution with positive parameter    k. This paper mainly considers the higher-order asymptotic expansions of the distribution of normalized powered order statistics        |        M          n      ,      r                  |        t   and the corresponding convergence rates under different norming constants. The results show that when    t  =  2  k and the optimal norming constants are selected, and the convergence speed of the distribution of        |        M          n      ,      r                  |        t   toward its extreme limit is proportional to    1      /    (  log  ⁡  n      )    2  , and for the case of    t  ≠  2  k, the convergence rate is proportional to    1      /    log  ⁡  n. The main results are confirmed by some numerical analysis.}
}