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系統識別號 U0026-0812200913374218
論文名稱(中文) 二項與波氏分配之等價檢定
論文名稱(英文) Testing the Equivalence of Binomial and Poisson Distributions
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 95
學期 2
出版年 96
研究生(中文) 陳妍孜
研究生(英文) Yen-Tzu Chen
電子信箱 tzu1028@stat.ncku.edu.tw
學號 r2694404
學位類別 碩士
語文別 英文
論文頁數 79頁
口試委員 口試委員-吳宗正
口試委員-陳占平
指導教授-溫敏杰
中文關鍵字 無差異區間  全距檢定  最保守均數組合  水準與檢定力 
英文關鍵字 Range test  Least favorable configuration  Indifference zone  Level and power 
學科別分類
中文摘要 全距檢定法是在檢定二項分配比例與波氏分配參數等價假設,相對於對立假設則為不等價。為了消除變異數未知情況,使用了二項及波氏隨機變數兩者的變異數穩定轉換,在最保守參數均數組合下,關於這些假設檢定的最大水準和最小檢定力趨近於常態定理。在給予水準與檢定力下,實驗的臨界值和所須的樣本數可以被同時決定,而電腦程式也在此目的下形成。
英文摘要 A range test is proposed for testing the hypothesis of equivalence of binomial proportions and Poisson parameters, respectively against the alternative hypothesis of inequivalence. Variance stabilization
transformations for both binomial and Poisson random variables are used to remove unknown parameters in the variances. Both the maximum level and the minimum power of the proposed test associated with these hypotheses can be approximated by normal theory at the corresponding least favorable configurations of parameters. For a given level and a given power, the critical value and the required
sample size for an experiment can be simultaneously determined, and a computer program is developed for such purpose.
論文目次 1 Introduction 1
2 One-Sample Sampling Procedure and Range Test of Binomial Distribution 2
3 One-Sample Sampling Procedure and Range Test of Poisson Distribution 6
4 Example 10
5 Summary and Conclusion 11
6 Acknowledgement 12
References 12
Appendix A 29
Appendix B 66
Appendix C 73
參考文獻 Bau, J. J., Chen, H. J. and Xiong, M. (1993). Percentage Point of the Studentized Range Test for Dispersion of Normal Means. J. Statist. Comput. Simul., Vol. 44, 149-263.
Berger, J. O. (1985). Statistical Decision Theory, 2nd edition, Springer-Verlag, N.Y.
Chen, H. J., Xiong, M. and Lam, K. (1993). Range Tests for the Dispersion of Several Location Parameters. Journal of Statistical Planning and Inference, 36, 15-25.
Chow, S. C. and Liu, J. P. (1992). Design and Analysis of Bioavailability and Bioequivalence Studies, New York: Marcel Dekker.
Hayter, A. J. and Liu, W. (1990). The Power Function of the Studentized Range Test. The Annals of Statistics, 18, 465-468.
Lehmann, E. L. (1986). Testing Statistical Hypothesis, 2nd edition, Wiley, N. Y.
Wen, M. J. and Chen, H. J. (2005). A Studentized Range Test for the Equivalency of Normal Means under Heteroscedasticity. Computational Statistics and Data Analysis. To appear.
Wen, M. J., Chen, H. J. and Chuang, C. J. (2005). The Level and Power of a Studentized Range Test for Testing the Dispersion of Normal Mean. Technical Report No. 68, July 2005, Department of Statistics, National Cheng Kung University, Tainan, Taiwan. This manuscript can be viewed on http://www.stat.ncku.edu.tw/faculty/mjwen/MjWenTR.htm (TR68DispersionofNormalMean940707).
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