中心极限定理介绍  

An Introduction to the Central Limit Theorems

作　　者：王筑娟[1] 

机构地区：[1]上海应用技术学院理学院,上海201418

出　　处：《上海应用技术学院学报（自然科学版）》2013年第4期325-328,共4页Journal of Shanghai Institute of Technology: Natural Science

基　　金：上海应用技术学院科技发展基金资助项目(KJ2008-15)

摘　　要：对中心极限定理作了简明的介绍,包括独立同分布样本的经典中心极限定理,独立但不同分布的Lindeberg-Feller中心极限定理和m-相依序列的中心极限定理。特别对m-相依序列中心极限定理,给出了一个新的、更为简单易懂的证明。还讨论了对经典中心极限定理的近似的改进,包括Berry-Essen界和Edgeworth展式。Abstraet.A concise introduction to the central limit theorems was made, including the classical version to IID samples, Lindeberg-Feller version for independently but not identically distributed sequences, and a version for m-dependent sequences was given, for which a new and esay-to-follow proof was provided as well. Moreover, some improvement of the classical central limit theorems was also discussed, including Berry-Essen Bounds and Edgeworth expansions. Key words： m-dependent stationary; central limit theorem; Berry-Essen bounds; Edgeworth expansions

关 键 词：m-相依平稳序列 中心极限定理 Berry-Essen界 Edgeworth展式 

分 类 号：O211.4[理学—概率论与数理统计]