“指数分布抽样基本定理”之讨论
Discussion on “Basic Theorem of Exponential Distribution Sampling”
DOI: 10.12677/sa.2026.153058, PDF,    科研立项经费支持
作者: 陈宣戈, 顾蓓青, 徐晓岭：上海对外经贸大学统计与数据科学学院，上海；雷 平：上海对外经贸大学国际经贸学院，上海
关键词: 指数分布；次序统计量；抽样基本定理；Exponential Distribution； Order Statistic； Basic Theorem of Sampling
摘要: 论文针对李国安老师提出的“指数分布抽样基本定理”进行了讨论分析，简化了原文献中结论的相关证明，并修正了原文献中一些错误。论文最后通过两参数指数分布与三参数威布尔分布总体说明“指数分布抽样分布基本定理”的应用。
Abstract: This paper discusses and analyzes the “Basic Theorem of Exponential Distribution Sampling” proposed by Professor Li Guoan. It simplifies the relevant proofs of the conclusions in original literature and corrects some errors in this literature. Finally, the paper illustrates the application of the theorem using the two-parameter exponential distribution and the three-parameter Weibull distribution populations.
文章引用：陈宣戈, 顾蓓青, 雷平, 徐晓岭. “指数分布抽样基本定理”之讨论[J]. 统计学与应用, 2026, 15(3): 92-101. https://doi.org/10.12677/sa.2026.153058

参考文献

[1] 李国安. 指数分布抽样基本定理及在指数分布参数统计推断中的应用[J]. 大学数学, 2016, 32(5): 30-36.
[2] 李国安. 指数分布抽样基本定理及在四参数二元Marshall-Olkin型指数分布参数估计中的应用[J]. 统计研究, 2016, 33(7): 98-102.
[3] 李国安, 李建峰. 指数分布抽样基本定理及在三参数一般指数分布参数估计中的应用[J]. 数学的实践与认识, 2017, 47(3): 165-169.
[4] 李国安, 李穆真. 指数抽样分布定理及三个期望之极小方差无偏估计的有效性比较[J]. 纯粹数学与应用数学, 2017, 33(6): 568-577.
[5] Sukhatme, P.V. (1937) Tests of Significance for Samples of the X2‐Population with Two Degrees of Freedom. Annals of Eugenics, 8, 52-56. [Google Scholar] [CrossRef] 
[6] Rao, C.R. (1973) Linear Statistical Inference and Its Applications. 2nd Edition, Wiley, 43-46. [Google Scholar] [CrossRef] 
[7] Balakrishnan, N. and Clifford Cohen, A. (1991) Order Statistics and Inference Estimation Methods. Academic Press, 34-36.
[8] 曹晋华, 程侃. 可靠性数学引论[M]. 北京: 科学出版社, 1986: 383-385.
[9] 魏宗舒. 概率论与数理统计教程[M]. 北京: 高等教育出版社, 1983: 477-481.
[10] 徐晓岭, 王蓉华, 顾蓓青. 概率论与数理统计[M]. 第二版. 上海: 上海交通大学出版社, 2021: 233-238.
[11] 王蓉华, 徐晓岭, 顾蓓青. 概率论与数理统计案例分析[M]. 上海: 上海交通大学出版社, 2023: 122-125, 136-143.
[12] 王蓉华, 徐晓岭, 顾蓓青. 概率论与数理统计案例分析与提高[M]. 上海: 上海交通大学出版社, 2025: 69, 72-73.
[13] Baklizi, A. (2016) Confidence Intervals for the Two-Parameter Exponential Reliability with Type II Censored Data. American Journal of Mathematical and Management Sciences, 35, 297-308. [Google Scholar] [CrossRef] 
[14] 程绩, 李云飞. 不完全数据场合下双参数指数分布参数的区间估计[J]. 统计与决策, 2017(16): 15-18.
[15] Zhang, J. (2018) Minimum Volume Confidence Sets for Two-Parameter Exponential Distributions. The American Statistician, 72, 213-218. [Google Scholar] [CrossRef] 
[16] Bobotas, P. (2018) Estimation of the Smallest Scale Parameter of Two-Parameter Exponential Distributions. Communications in Statistics—Theory and Methods, 48, 2748-2765. [Google Scholar] [CrossRef] 
[17] Asgharzadeh, A., Bagheri, S.F., Ibrahim, N.A. and Abubakar, M.R. (2019) Optimal Confidence Regions for the Two-Parameter Exponential Distribution Based on Records. Computational Statistics, 35, 309-326. [Google Scholar] [CrossRef] 
[18] Akbari, M. and Akbari, M. (2020) Some Applications of Near-Order Statistics in Two-Parameter Exponential Distribution. Journal of Statistical Theory and Applications, 19, Article No. 21. [Google Scholar] [CrossRef] 
[19] El-Adll, M.E. (2019) Inference for the Two-Parameter Exponential Distribution with Generalized Order Statistics. Mathematical Population Studies, 28, 1-23. [Google Scholar] [CrossRef] 
[20] Malekzadeh, A., Jafari, A.A. and Mahmoudi, S.M. (2021) Inference on the Mean Parameter of a Two-Parameter Exponential Distribution: Complete, Censored and Record Data. Journal of Statistics and Management Systems, 24, 1233-1252. [Google Scholar] [CrossRef] 

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