系統識別號 | U0002-2007201610344600 |
---|---|
DOI | 10.6846/TKU.2016.00624 |
論文名稱(中文) | Laplace排序統計量線性組合的分配之計算 |
論文名稱(英文) | Computing the Distribution of Linear Combinations of Laplace Order Statistics |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 數學學系碩士班 |
系所名稱(英文) | Department of Mathematics |
外國學位學校名稱 | |
外國學位學院名稱 | |
外國學位研究所名稱 | |
學年度 | 104 |
學期 | 2 |
出版年 | 105 |
研究生(中文) | 李柏毅 |
研究生(英文) | Bo-Yi Lee |
學號 | 603190157 |
學位類別 | 碩士 |
語言別 | 英文 |
第二語言別 | |
口試日期 | 2016-06-17 |
論文頁數 | 28頁 |
口試委員 |
指導教授
-
林千代
委員 - 吳碩傑 委員 - 陳麗霞 |
關鍵字(中) |
Spacings Laplace distribution Double exponential distribution |
關鍵字(英) |
Spacings Laplace distribution Double exponential distribution |
第三語言關鍵字 | |
學科別分類 | |
中文摘要 |
本論文根據Iliopoulos and Balakrishnan (2009)文中的區塊排序資料的條件獨立性之結果,以及Huffer and Lin(2001)的遞迴演算法求得Laplace排序統計量線性組合的分配之完整表示式。所求的表示式可以使用Maple數學軟體加以運算。 |
英文摘要 |
We apply the results of conditional independence of blocked ordered data in Iliopoulos and Balakrishnan (2009) and the algorithm of Huffer and Lin (2001) to compute the exact expressions for the distribution of linear combinations of laplace order statistics. These expressions can then be evaluated using symbolic math package Maple. |
第三語言摘要 | |
論文目次 |
Contents 1 Introduction 1 2 Main Tools 4 2.1 Conditional Independence Result for Order Statistics 4 2.2 Recursions 5 3 Main Results 7 4 Examples 9 5 Direction of Future Research 23 References 24 Appendix 26 |
參考文獻 |
Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1992). A First Course in Order Statistics. Wiley, New York. Balakrishnan, N. and Cutler, C. D. (1995). Maximum likelihood estimation of the Laplace parameters based on Type-II censored samples. In Statistical Theory and Applications: Papers in Honor of Herbert A. David (Eds., H. N. Nagaraja, P. K. Sen and D.F. Morrison), pp. 145-151. Springer-Verlag, New York. Childs, A. (1996). Advances in statistical inference and outliers related issues. Ph.D. Thesis, McMaster University, Hamilton, Canada. Childs, A. and Balakrishnan, N. (1996). Conditional inference procedures for the Laplace distribution based on Type-II right censored samples. Statistics and Probability Letters, 31, 31-39. Childs, A. and Balakrishnan, N. (1997a). Some extensions in the robust estimation of parameters of exponential and double exponential distributions in the presence of multiple outliers. In Handbook of Statistics { Robust Inference, Vol. 15 (Eds., C. R. Rao and G. S. Maddala), pp. 201-235. North-Holland, Amsterdam. Childs, A. and Balakrishnan, N. (1997b). Maximum likelihood estimation of Laplace parameters based on general type-II censored examples. Statistical Papers, 38, 343-349. Govindarajulu, Z. (1966). Best linear estimates under symmetric censoring of the parameters of a double exponential population. Journal of the American Statistical Association, 61, 248-258. Huffer, F. (1988). Divided di erences and the joint distribution of linear combinations of spacings. Journal of Applied Probability, 25, 346-354. Huffer, F. W. and Lin, C. T. (2001). Computing the joint distribution of general linear combinations of spacings or exponential variates. Statistica Sinica, 11, 1141-1157. Huffer, F. W. and Lin, C. T. (2006). Linear combinations of spacings. In Encyclopedia of Statistical Sciences, Volume 12, Second Edition (Eds., S. Kotz, N. Balakrishnan, C. B. Read and B. Vidakovic), pp. 7866-7875, John Wiley & Sons, Hoboken, New Jersey. Iliopoulos, G. and Balakrishnan, N. (2009). Conditional independence of blocked ordered data. Statistics and Probability Letters, 79, 1008-1015. Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995). Continuous Univariate Distributions, Vol. 2, Second edition. John Wiley & Sons, New York. Kappenman, R. F. (1975). Conditional con dence intervals for double exponential distribution parameters. Technometrics, 17, 233-235. Kappenman, R. F. (1977). Tolerance intervals for the double exponential distribution. Journal of The American Statistical Association, 72, 908-909. Nadarajah, S. and Kotz, S. (2005). On the linear combination of laplace random variables. Probability in the Engineering and Informational Sciences, 19, 463-470. Raghunandanan, K. and S nivasan, R. (1971). Simpli ed estimation of parameters in a double exponential distribution. Technometrics, 13, 689-691. |
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