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研究生:王世賢
研究生(外文):Shih-Shian Wang
論文名稱:累進設限樣本之珈瑪分配
論文名稱(外文):Progressively Censored Sampling in the Gamma Distribution
指導教授:黃提源黃提源引用關係
指導教授(外文):Tea-Yuan Hwang
學位類別:碩士
校院名稱:國立清華大學
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:2001
畢業學年度:90
語文別:英文
論文頁數:43
中文關鍵詞:設限樣本珈瑪分配
外文關鍵詞:censored samplegamma distribution
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在本論文中,是假設以珈瑪分配作為生命累進設限樣本之模型,我們利用Hwang,T.Y. 和 Hu,C.Y. [2],[3]中的新動差法的特性和最大概似法來估計珈瑪分配中的兩個參數,並且比較上述兩種方法的估計量,得出以前者為較佳的估計量.

In this paper, the gamma distribution is assumed as a model for the lifetime of progressively censored sampling, we use the new moment estimation method using characterization which has been found by Hwang,T.Y. and Hu,C.Y. [2],[3] and the maximum likelihood method to estimate the two parameters of gamma distribution, and then the comparison of two kinds of estimators mentioned above has been done and the former would be better.

Abstract..................................................1
1.Introduction..............................................1
2.The Sample................................................2
3.Maximum Likelihood Estimation Method......................4
4.New Moment Estimation Method..............................6
5.Comparisons Between Two Estimators by Simulation..........8
6.Application to an Actual Data............................16
Reference................................................19
Appendix.................................................20
Table 1..................................................20
Table 2..................................................24
Table 3..................................................28
Table 4..................................................32

[1]Gross, Alan, J. and Clark, Virginia, A. (1975). Survival distribution: reliability applications in the biomedical science. John Wiley & Sons, New York.
[2]Hwang, T. Y. and Hu, C. Y. (1999). On a characterization of the gamma distribution: The independence of the sample mean and the sample coefficient of Variation, Annals of the Institute of Statistics Mathematics, 51, 749-753, Japan.
[3]Hwang, T. Y. and Hu, C. Y. (2000). On same characterization of population distribution, Taiwanese Journal of Mathematics, 4, 3, 427-437, ROC.
[4]Johnson, Normal L. and Kotz, Samuel (1970). Continuous univariate distribution 1. Houghton Mifflin Co., Boston.
[5]Shih-Tai Kao (2000). On the probability model of the failure time for the air conditioning system, Master Thesis, Institute of Statistics, National Tsing Hua University, Taiwan.
[6]Lawless, J. F. (1982). Statistics model and methods for lifetime data, Canada Wiley.
[7]Norgaard, Nicholas, J. (1977). Progressively censored Sampling in the three parameter gamma distribution. Technometics, 19, 333-340
[8]Wilk, M. B., R. Gnanadesikan, and M. J. Huyett. (1962b). Estimation of parameter of the gamma distribution using order statistics. Biometrika, 49, 525-545.

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