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系統識別號 U0002-2007201610344600
中文論文名稱 Laplace排序統計量線性組合的分配之計算
英文論文名稱 Computing the Distribution of Linear Combinations of Laplace Order Statistics
校院名稱 淡江大學
系所名稱(中) 數學學系碩士班
系所名稱(英) Department of Mathematics
學年度 104
學期 2
出版年 105
研究生中文姓名 李柏毅
研究生英文姓名 Bo-Yi Lee
學號 603190157
學位類別 碩士
語文別 英文
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
中文關鍵字 Spacings  Laplace distribution  Double exponential distribution 
英文關鍵字 Spacings  Laplace distribution  Double exponential distribution 
學科別分類 學科別自然科學數學
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.

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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