数学季刊 ›› 2026, Vol. 41 ›› Issue (2): 162-173.doi: 10.13371/j.cnki.chin.q.j.m.2026.02.005

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  1. 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
  • 收稿日期:2025-02-05 出版日期:2026-06-30 发布日期:2026-06-30
  • 作者简介: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.
  • 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).

Higher-Order Expansions of Powered Order Statistics of Maxwell Sequences

  1. 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
  • Received:2025-02-05 Online:2026-06-30 Published:2026-06-30
  • About author: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.
  • Supported by:
    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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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

Abstract: 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.

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

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