簡易檢索 / 詳目顯示
| 研究生： |
陳宗萍 |
|---|---|
| 論文名稱： |
粗化數據之統計分析 Statistucal Analysis with Coarse Data |
| 指導教授： | 吳柏林 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2008 |
| 畢業學年度： | 96 |
| 語文別： | 中文 |
| 論文頁數： | 32 |
| 中文關鍵詞： | 粗化數據 、隨機集合 、隸屬度函數 |
| 相關次數： | 點閱：82 下載：48 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
本文討論在抽樣調查中被視為隨機集合模型的樣本，並試著架構基於模糊統計邏輯的粗化數據(coarse data)之理論與特性。因為有些抽樣調查中的數據可以視為隨機集合模型所得出的新數據。如何應用數學分析方法，配合軟計算技術以達到有效之資料處理與統計分析就是本研究之重點。我們將隨機抽樣樣本當作隨機實驗所做出來的結果，而這個論點可以幫助我們分析粗化數據。在探索抽樣調查的隨機集合和分佈的時候，機率測度論提供了很多種非精確數據給予統計學推測結論(statistical inference)，我們推廣傳統理論，以模糊集合及隸屬度為基礎，作為集合元素運算之依據。
關鍵字：粗化數據、隨機集合、隸屬度函數
In this paper we discuss the sample in the random set model for the sampling survey. Since the data from sampling survey can be treated as a new type of data from the random set model. How to apply the mathematical analyzing methods as well as soft computing techniques to reach an efficient propose is our main goal. We treat random sampling data as the result of random experimental design. And this concept will help us to analyze the coarse data. Finally, in investigating the random set and its distributions for the random sampling survey, traditional probability measure theory serves an important role in the statistical inference, while we use the membership function and fuzzy operations to extend traditional concept into a more general case.
Keywords： Coarse data, Random set, Membership function
1. 前言 1
2. 抽樣調查中的粗化集合 3
2. 1統計模型 3
2. 2 隨機集合和分佈 5
2. 3 粗化機制 6
3. 基於模糊集合架構之粗化數據 10
3. 1 隸屬度函數與模糊集合 10
3. 2 架構模糊統計與軟計算法 17
3. 3 顯著水準與擴大原理 22
3. 4模糊集合與隨機集合的關聯性 24
4. 結論 29
參考文獻 31
1. Aigner, M. (1979), Combinatorial Theory, Springer-Verlag, N. Y.
2. Aumann, R. J. and Shapley, L. S. (1974), Values of Non-Atomic Games, Princeton University Press, Princeton, NJ.
3. Deville, J. C. and Sarndal, C. E. (1992), Calibration Estimators in Survey Sampling, Journal of the American Statistical Association 87, 376-382.
4. Foreman, E. K. (1991), Survey Sampling Principles, Marcel-Dekker, N. Y.
5. Georges, M. (1975), Random Sets and Integral Geometry, Wiley, N. Y.
6. Goodman, P. S. (1982), Social Comparison Processes in Organizations, In B. Staw and G. Salancik (Ends) New directions in organizational behavior, Malabar, FL: Krieger, 97-132.
7. Goutsias, J., Mahler, R., and Nguyen, H. T. (1997). Random Sets: Theory and Applications, Springer-Verlag, N. Y.
8. Hajek, J. (1981), Sampling from a Finite Population, Marcel-Dekker, N. Y.
9. Hartigan, J. A. (1975), Clustering Algorithms, Wiley.
10. Heitjan, D. F. and Rubin, D. B. (1991), Ignorability and Coarse Data, Ann. Math. Statis 23, 774-786.
11. Knottnerus, P. (2003), Sample Survey Theory, Springer-Verlag, N. Y.
12. Li, B. and Wang, T. (2004), Computational Aspects of the CAR Model and the Shapley Value, to appear in J. Information Sciences.
13. Mosteller, F. and Youtz, C. (1990), Quantifying Probabilistic Expressions, J. Statist. Sci 15, 2-34.
14. Nguyen, H. (2002), Random Sets for Statistics, Lukacs Lecture Notes, Bowling Green State University, Ohio.
15. Nguyen, H. (2005), An Introduction to Random Sets, Chapman and Hall/CRC, Boca Raton, Florida.
16. Nguyen, H. and Wang. T. (2004), A First Course in Probability and Statistics, Volume I, Tsinghua University Press, Beijing.
17. Nguyen, H. and Wu, B. (2006), Random and Fuzzy Sets in Coarse Data Analysis, Computational Statistics and Data Analysis 51, 70-85.
18. Norberg, T. (1992), On the Existence of Ordered Couplings of Random Sets with Applications, Israel J. Math 17, 241-264.
19. Robbins, H. E. (1944), On the Measure of a Random Set, Ann. Math. Statist 15, 70-74.
20. Sarndal, C. E., Swensson, B., and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlag, N. Y.
21. Zimmermann, H. J. (1991), Fuzzy Set Theory and its Applications, Kluwer, Dordrecht.