Acta mathematica scientia,Series A ›› 2026, Vol. 46 ›› Issue (3): 1183-1193.

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Asymptotics of Sample Median Range and Sample Range from Gaussian Distribution

Guang Tang1(), Yingyin Lu1,*(), Tingting Yu2()   

  1. 1 School of Sciences, Southwest Petroleum University, Chengdu 610500
    2 Department of Academic Affairs, Southwest Petroleum University, Sichuan Nanchong 637001
  • Received:2025-03-17 Revised:2026-01-19 Online:2026-06-26 Published:2026-06-16
  • Contact: Yingyin Lu E-mail:hhdtt1314@163.com;luyingyin93@163.com;ytt8624@163.com
  • Supported by:
    Research and Planning Project of Nanchong City on Philosophy and Social Science(NC23C194)

Abstract:

In this paper, we investigate the limiting distributions of the normalized sample median range and sample range from Gaussian distributions. Additionally, the distributional expansions are established with the same normalizing constants. A byproduct is to deduce the convergence rates of the distributions of the normalized sample median range and sample range to their limits, which shows they have the same convergence rate. Furthermore, numerical analysis is provided to illustrate the theoretical findings.

Key words: Gaussian distribution, sample median range, sample range, distributional expansion.

CLC Number: 

  • O212.2
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