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研究生:吳尚剛
論文名稱:混合二項分配之容許區間
論文名稱(外文):Tolerance Limits for a Binomial Mixture Model
指導教授:王秀瑛王秀瑛引用關係
學位類別:碩士
校院名稱:國立交通大學
系所名稱:統計學研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2010
畢業學年度:98
語文別:英文
論文頁數:24
中文關鍵詞:容許界限混合二項分配信賴區間覆蓋率
外文關鍵詞:Tolerance limitBinomial mixture modelCoverage probabilityConfidence interval
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建立容許區間衡量製程特性在製造業與醫藥等領域廣泛地被使用於制定品質控制系統。我們在本論文中分別提出有母數與無母數的兩種方法,用以建立混合二項分配的容忍界限,而這兩種方法亦可以被使用於許多應用問題之中。本文將其進行模擬並比較兩種方法,而無母數的方法在此表現較佳因為它的覆蓋率可以達到我們給定的標準且容許界限也有令人滿意的結果。
1 Introduction 1
2 Mixture Model 2
2.1 Binomial Mixture Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Gibbs sampler 5
3.1 The algorithm for GIBBS sampling . . . . . . . . . . . . . . . . . . . . . . 6
4 Condence Interval for a Binomial Distribution 7
5 Tolerance limit for a Binomial Distribution 8
6 Tolerance limit for a Binomial Mixture Model 9
6.1 Tolerance limit based on a mixture model . . . . . . . . . . . . . . . . . . 9
6.2 Distribution-Free Tolerance Interval . . . . . . . . . . . . . . . . . . . . . . 10
7 Simulation 11
8 Conclusions 17
Reference 18
1] Agresti, A., and Coull, B. (1998), Approximate Is Better Than ’Exact’ for
Interval Estimation of Binomial Proportions. The American Statistician, 52, 119-126.
[2] Fernholz, L. T, and Gillespie, J. A. (2001), Content-Correct Tolerance Limits
Based on the Bootstrap. Technometrics, 43, 147-155.
[3] Geman, S., and Geman, D. (1984), Stochastic Relaxation, Gibbs Distributions,
and the Bayesian Restoration of Images. IEEE Transactions on Pattern Analysis and
Machine Intelligence, 6 , 721-741.
[4] Hahn, G. J, and Chamdra, R. (1981), Tolerance intervals for Poisson and
Binomial variables. Journal of Quality Technology, 13, 100-110.
[5] Hahn, G. J, and Meeker, W. Q. (1991), Statistical Intervals: A Guide for
Practitioners. John Wiley & Sons, Inc.
[6] Hamada, M., Johnson, V., Moore, L. M., and Wendelberger, J. (2004),
Bayesian Prediction Intervals and Their Relationship to Tolerance Intervals. Technometrics,
46 , 452-459.
[7] Krishnamoorthy, K., and Mathew, T. (2004), One-Sided Tolerance Limits
in Balanced and Unbalanced One-Way Random Models Based on Generalized Confidence
Intervals. Technometrics, 46 , 44-52.
[8] Liao, C. T., Lin, T. Y., and Iyer, H. K. (2005), One- and Two-Sided Tolerance
Intervals for General Balanced Mixed Models and Unbalanced One-Way Random
Effects Model. John Wiley & Sons, Inc.
[9] McLachlan, G., and Peel, D. (2000), Finite Mixture Models. Technometrics,
47, 323-335.
[10] Odeh, R. E, and Owen, D. B. (1980), Tables for Normal Tolerance Limits,
Sampling Plans, and Screening. Marcel Dekker Inc.
[11] Van Der Merwe, A. J., Pretorius, A. L., and Meyer, J. H. (2006),
Bayesian Tolerance Intervals for the Unbalanced One-Way Random Effects Model.
Journal of Quality Technology, 38, 280-293.
[12] Wald, A., andWolfowitz, J. (1946), Tolerance Limits for Normal Distribution.
Annals of Mathematical Statistics, 17, 208-215.
[13] Wang, C. M., and Iyer, H. K. (1994), Tolerance Intervals for the Distribution
of True Values in the Presence of Measurement Error. Technometrics, 36, 162-170.
[14] Wang, H., and Tsung, F. (2009), Tolerance Intervals With Improved Coverage
Probabilities for Binomial and Poisson Variables. Technometrics, 51(1), 25-33.
[15] Wolfinger, R. D. (1998) Tolerance Intervals for Variance Component Models
Using Bayesian Simulation. Journal of Quality Technology, 30, 18-32.
[16] Zacks, S. (1970) Uniformly Most Accurate Upper Tolerance Limits for Monotone
Likelihood Ratio Families of Discrete Distributions. Journal of Quality Technology,
65, 307-316.
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