麦克斯韦序列幂的顺序统计量的高阶展开

黄建文, 刘芯菱, 贾金平, 王润科

doi:10.13371/j.cnki.chin.q.j.m.2026.02.005

数学季刊 >

2026 , Vol. 41 >Issue 2: 162 - 173

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2026.02.005

麦克斯韦序列幂的顺序统计量的高阶展开

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1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China; 2. College of Mathematics and Information, China West Normal University, Nanchong 637009, China; 3. Key Laboratory of Optimization Theory and Applications at China West Normal University of Sichuan Province, Nanchong 637009, China; 4. School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China; 5. College of Resources and Environmental Engineering, Tianshui
Normal University, Tianshui 741001, China

HUANG Jian-wen (1988-), male, native of Tianshui, Gansu, associate professor of Chongqing Normal University, engages in probability theory; LIU Xin-ling (1990-), male, native of Nanchong, Sichuan, associate professor of China West Normal University, engages in probability theory; JIA Jin-ping (1982-), male, native of Xihe, Gansu, associate professor of Tianshui Normal University, engages in nonlinear systems and sampled control; WANG Run-ke (1976-), male, native of Longnan, Gansu, associate professor of Tianshui Normal University, engages in surveying and mapping engineering.

LIU Xin-ling (1990-), male, native of Nanchong, Sichuan, associate professor of China West Normal University, engages in probability theory;

收稿日期: 2025-02-05

网络出版日期: 2026-06-30

基金资助

Supported by National Natural Science Foundation of China (Grant No. 12301594), Science and Technology Research Program of Chongqing Municipal Education Commission (Grant Nos. KJQN202400509 and KJQN202300555), Natural Science Foundation of Chongqing of China (Grant No. CSTB2025NSCQ-GPX1033), Chongqing Normal University Foundation Project (Grant No. 23XLB013), Fundamental Research Funds of China West Normal University (Grant No. 25kc008), the Initiative Projects for Ph.D. in China West Normal University (Grant No. 25KE025), Young Doctor Fundation Program of Gansu Province (Grant No. 2026QB-083), Research Project of Tianshui Normal University (Grant No. TDJ2023-02).

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Higher-Order Expansions of Powered Order Statistics of Maxwell Sequences

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1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China; 2. College of Mathematics and Information, China West Normal University, Nanchong 637009, China; 3. Key Laboratory of Optimization Theory and Applications at China West Normal University of Sichuan Province, Nanchong 637009, China; 4. School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China; 5. College of Resources and Environmental Engineering, Tianshui
Normal University, Tianshui 741001, China

LIU Xin-ling (1990-), male, native of Nanchong, Sichuan, associate professor of China West Normal University, engages in probability theory;

Received date: 2025-02-05

Online published: 2026-06-30

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摘要

Under the optimal norming constants, this paper studies the higher-order expansions of the distributions and densities of the powered order statistics of Maxwell sequence. As auxiliary results, the corresponding convergence rates are obtained. The results show that the convergence rates of distributions and densities of normalized power order statistics are related to power index in principle. Finally, we compared the accuracy of each approximations with its true values through numerical experiments.

关键词： Maxwell sequences; Powered order statistics; Higher-order expansion; Convergence rate

本文引用格式

黄建文, 刘芯菱, 贾金平, 王润科 . 麦克斯韦序列幂的顺序统计量的高阶展开[J]. 数学季刊, 2026 , 41(2) : 162 -173 . DOI: 10.13371/j.cnki.chin.q.j.m.2026.02.005

Abstract

Key words： Maxwell sequences; Powered order statistics; Higher-order expansion; Convergence rate

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