| 中心极限定理介绍 |
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| 引用本文： | 王筑娟.中心极限定理介绍[J].上海应用技术学院学报,2013,13(4):325-328. |
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| 作者姓名： | 王筑娟 |
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| 作者单位： | 上海应用技术学院理学院,上海201418 |
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| 基金项目： | 上海应用技术学院科技发展基金资助项目（KJ2008-15） |
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| 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一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。
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| 关 键 词： | m-相依平稳序列 中心极限定理 Berry-Essen界 Edgeworth展式 |
An Introduction to the Central Limit Theorems |
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| WANG Zhu-juan.An Introduction to the Central Limit Theorems[J].Journal of Shanghai Institute of Technology: Natural Science,2013,13(4):325-328. |
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| Authors: | WANG Zhu-juan |
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| Institution: | WANG Zhu-juan (School of Sciences, Shanghai Institute of Technology, Shanghai 201418, China) |
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| Abstract: | 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 |
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| Keywords: | m-dependent stationary central limit theorem Berry-Essen bounds Edgeworth expansions |
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