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題名 模糊卡方適合度檢定
Fuzzy Chi-square Test Statistic for goodness-of-fit
作者 林佩君
Lin,Pei Chun
貢獻者 吳柏林
wu,Berlin
林佩君
Lin,Pei Chun
關鍵詞 模糊思維
模糊邏輯
模糊集合理論
隸屬度函數
樣本調查
卡方適合度檢定
fuzzy thinking
fuzzy logic
fuzzy set theory
membership functions
sampling survey
chi-square test statistic for goodness-of-fit
日期 2006
上傳時間 8-Dec-2010 11:45:09 (UTC+8)
摘要 在資料分析上,調查者通常需要決定,不同的樣本是否可被視為來自相同的母體。一般最常使用的統計量為Pearson’s 統計量。然而,傳統的統計方法皆是利用二元邏輯觀念來呈現。如果我們想要用模糊邏輯的概念來做樣本調查,此時,使用傳統 檢定來分析這些模糊樣本資料是否仍然適當?透過這樣的觀念,我們使用傳統統計方法,找出一個能處理這些模糊樣本資料的公式,稱之為模糊 。結果顯示,此公式可用來檢定,模糊樣本資料在不同母體下機率的一致性。
In the analysis of research data, the investigator often needs to decide whether several independent samples may be regarded as having come from the same population. The most commonly used statistic is Pearson’s statistic. However, traditional statistics reflect the result from a two-valued logic concept. If we want to survey sampling with fuzzy logic concept, is it still appropriate to use the traditional -test for analysing those fuzzy sample data? Through this concept, we try to use a traditional statistic method to find out a formula, called fuzzy , that enables us to deal with those fuzzy sample data. The result shows that we can use the formula to test hypotheses about probabilities of various outcomes in fuzzy sample data.
參考文獻 [1] Arnold, Steven F. (1990). Mathematical statistics. Prentice-Hall, Englewood Cliffs, NJ.
[2] Hilton, James G. (1971). Probability and statistical analysis. Intext Educational Publishers, London.
[3] Hogg, Robert V. and Elliot A. Tanis, (1977). Probability and Statistical inference. Prentice-Hall, Upper Saddle River, NJ.
[4] H. Kwakernaak, Fuzzy random variables - I. Definitions and Theorems, Information Sciences, 15, (1978), 1-29, Fuzzy random variables – II. Algorithms and Examples for the Discrete Case, Information Sciences, 17, (1979), 253-278.
[5] Johnson, Richard A. and Gourik.Bhattacharyya, (1992). Statistics: Principles and Methods. (2nd ed.). Wiley, New York.
[6] Liu Yubin, Qiao Zhong and Wang Guangyuan, Fuzzy random reliability of structures based on fuzzy random variables, Fuzzy Sets and Systems, 86, (1997), 345-355.
[7] M.L. Puri and D. Ralescu, Fuzzy random variables, Journal of Mathematical Analysis and Applications,114, (1986), 409-422.
[8] Nguyen, H and Wu, B. (2006). Fundamentals of Statistics with Fuzzy Data. Springer, Netherlands.
[9] Pearson, K., (1900). “On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling.” Philosophy Magazine Series 5, 50, 157-172.
[10] Wu, B. and Chang, S. K. (2007), “On testing hypothesis of fuzzy mean”, Japan Journal of Industrial and Applied Mathematics. (will appear)
[11] Zadeh, L.A. (1965). Fuzzy Sets. Information and Control, 8,338-353.
[12] Zimmermann, H. J. (1996). Fuzzy set theorem and its applications. Kluwer Academic, Boston.
描述 碩士
國立政治大學
應用數學研究所
94751015
95
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0094751015
資料類型 thesis
dc.contributor.advisor 吳柏林zh_TW
dc.contributor.advisor wu,Berlinen_US
dc.contributor.author (Authors) 林佩君zh_TW
dc.contributor.author (Authors) Lin,Pei Chunen_US
dc.creator (作者) 林佩君zh_TW
dc.creator (作者) Lin,Pei Chunen_US
dc.date (日期) 2006en_US
dc.date.accessioned 8-Dec-2010 11:45:09 (UTC+8)-
dc.date.available 8-Dec-2010 11:45:09 (UTC+8)-
dc.date.issued (上傳時間) 8-Dec-2010 11:45:09 (UTC+8)-
dc.identifier (Other Identifiers) G0094751015en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/49452-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學研究所zh_TW
dc.description (描述) 94751015zh_TW
dc.description (描述) 95zh_TW
dc.description.abstract (摘要) 在資料分析上,調查者通常需要決定,不同的樣本是否可被視為來自相同的母體。一般最常使用的統計量為Pearson’s 統計量。然而,傳統的統計方法皆是利用二元邏輯觀念來呈現。如果我們想要用模糊邏輯的概念來做樣本調查,此時,使用傳統 檢定來分析這些模糊樣本資料是否仍然適當?透過這樣的觀念,我們使用傳統統計方法,找出一個能處理這些模糊樣本資料的公式,稱之為模糊 。結果顯示,此公式可用來檢定,模糊樣本資料在不同母體下機率的一致性。zh_TW
dc.description.abstract (摘要) In the analysis of research data, the investigator often needs to decide whether several independent samples may be regarded as having come from the same population. The most commonly used statistic is Pearson’s statistic. However, traditional statistics reflect the result from a two-valued logic concept. If we want to survey sampling with fuzzy logic concept, is it still appropriate to use the traditional -test for analysing those fuzzy sample data? Through this concept, we try to use a traditional statistic method to find out a formula, called fuzzy , that enables us to deal with those fuzzy sample data. The result shows that we can use the formula to test hypotheses about probabilities of various outcomes in fuzzy sample data.en_US
dc.description.tableofcontents Contents 1
1. Introduction 2
2. Fuzzy Statistic Analysis 3
2.1 Chi-square Test Statistic for Goodness-of-Fit 3
2.2 Fuzzy Set Theory and Fuzzy Numbers 5
2.3 Fuzzy Sampling Surveys 6
3. Fuzzy Statistic Distribution 9
3.1 Expected Value and Variance for Fuzzy Sample Data 9
3.2 Fuzzy Bernoulli and Fuzzy Binomial Distribution 9
3.3 Fuzzy Multinomial Distribution 15
3.4 Fuzzy Chi-square Test Statistic for Goodness-of-Fit 22
4. Empirical Studies 27
5. Conclusion 28
References 29
zh_TW
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0094751015en_US
dc.subject (關鍵詞) 模糊思維zh_TW
dc.subject (關鍵詞) 模糊邏輯zh_TW
dc.subject (關鍵詞) 模糊集合理論zh_TW
dc.subject (關鍵詞) 隸屬度函數zh_TW
dc.subject (關鍵詞) 樣本調查zh_TW
dc.subject (關鍵詞) 卡方適合度檢定zh_TW
dc.subject (關鍵詞) fuzzy thinkingen_US
dc.subject (關鍵詞) fuzzy logicen_US
dc.subject (關鍵詞) fuzzy set theoryen_US
dc.subject (關鍵詞) membership functionsen_US
dc.subject (關鍵詞) sampling surveyen_US
dc.subject (關鍵詞) chi-square test statistic for goodness-of-fiten_US
dc.title (題名) 模糊卡方適合度檢定zh_TW
dc.title (題名) Fuzzy Chi-square Test Statistic for goodness-of-fiten_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] Arnold, Steven F. (1990). Mathematical statistics. Prentice-Hall, Englewood Cliffs, NJ.zh_TW
dc.relation.reference (參考文獻) [2] Hilton, James G. (1971). Probability and statistical analysis. Intext Educational Publishers, London.zh_TW
dc.relation.reference (參考文獻) [3] Hogg, Robert V. and Elliot A. Tanis, (1977). Probability and Statistical inference. Prentice-Hall, Upper Saddle River, NJ.zh_TW
dc.relation.reference (參考文獻) [4] H. Kwakernaak, Fuzzy random variables - I. Definitions and Theorems, Information Sciences, 15, (1978), 1-29, Fuzzy random variables – II. Algorithms and Examples for the Discrete Case, Information Sciences, 17, (1979), 253-278.zh_TW
dc.relation.reference (參考文獻) [5] Johnson, Richard A. and Gourik.Bhattacharyya, (1992). Statistics: Principles and Methods. (2nd ed.). Wiley, New York.zh_TW
dc.relation.reference (參考文獻) [6] Liu Yubin, Qiao Zhong and Wang Guangyuan, Fuzzy random reliability of structures based on fuzzy random variables, Fuzzy Sets and Systems, 86, (1997), 345-355.zh_TW
dc.relation.reference (參考文獻) [7] M.L. Puri and D. Ralescu, Fuzzy random variables, Journal of Mathematical Analysis and Applications,114, (1986), 409-422.zh_TW
dc.relation.reference (參考文獻) [8] Nguyen, H and Wu, B. (2006). Fundamentals of Statistics with Fuzzy Data. Springer, Netherlands.zh_TW
dc.relation.reference (參考文獻) [9] Pearson, K., (1900). “On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling.” Philosophy Magazine Series 5, 50, 157-172.zh_TW
dc.relation.reference (參考文獻) [10] Wu, B. and Chang, S. K. (2007), “On testing hypothesis of fuzzy mean”, Japan Journal of Industrial and Applied Mathematics. (will appear)zh_TW
dc.relation.reference (參考文獻) [11] Zadeh, L.A. (1965). Fuzzy Sets. Information and Control, 8,338-353.zh_TW
dc.relation.reference (參考文獻) [12] Zimmermann, H. J. (1996). Fuzzy set theorem and its applications. Kluwer Academic, Boston.zh_TW