A review and comparison of continuity correction rules: the normal approximation to the binomial distribution

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廖昱婷(Yu-Ting Liao) 查詢紙本館藏

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統計研究所

論文名稱

(A review and comparison of continuity correction rules: the normal approximation to the binomial distribution)

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摘要(中)

在應用統計中，使用二項分配近似常態分配使用連續性校正是非常有用的。首先，論文的第一部分，回顧二項分配和中央極限定理。如果樣本數較大，二項分配會近似於常態分配。連續性校正是為了進一步提高二項分配近似常態分配的準確，其中較廣為人知的連續性較正為Yates’s correction for continuity (Yates, 1934; Cox, 1970)。此外我們還介紹比較少人知道的Cressie’s finely tuned continuity correction (Cressie, 1978)。我們將連續性較正應用在統計製程的問題中。此外，我們進行數值模擬研究，比較Yates’s correction for continuity跟Cressie’s finely tuned continuity correction。

摘要(英)

In applied statistics, the continuity correction is useful when the binomial distribution is approximated by the normal distribution. In the first part of this thesis, we review the binomial distribution and the central limit theorem. If the sample size gets larger, the binomial distribution approaches to the normal distribution. The continuity correction is an adjustment that is made to further improve the normal approximation, also known as Yates’s correction for continuity (Yates, 1934; Cox, 1970). We also introduce Cressie’s finely tuned continuity correction (Cressie, 1978), which are less known for statisticians. We discuss the application of these continuity corrections to the problem of statistical process control and confidence limit. In addition, we perform numerical studies to compare these corrections.

關鍵字(中)

★ 二項分配
★ 信賴界線
★ 連續性校正
★ 控制圖
★ 常態近似
★ 統計製程管制

關鍵字(英)

★ Binomial distribution
★ Confidence limit
★ Continuity correction
★ Control chart
★ Normal approximation
★ Statistical process control

論文目次

1 Introduction ……………………………………………………………………...1
2 Normal approximation to binomial…………………………………………...…3
3 Application to statistical process control………………………………………9
4 Application to confidence limit………………………………………………………14
5 Numerical studies…………………………………………………………….24
6 Conclusion……………………………………………………………………………….33
Appendix A………………………….......…………………………………………………34
Appendix B………………………………………………………………………………...36
Appendix C………………………………………………………………………………..37
References…………………………………………………………………………………38

參考文獻

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指導教授

江村剛志(Takeshi Emura)

審核日期

2016-8-25

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