两重两参数威布尔分布混合模型的拟合
Fitting of Twofold Mixed Model for Two-Parameter Weibull Distribution
DOI:10.12677/SA.2012.12005,PDF,HTML,下载: 3,139浏览: 11,898国家自然科学基金支持
作者:徐晓岭,顾蓓青：上海对外贸易学院商务信息学院，上海；王蓉华：上海师范大学数理学院，上海；吴生荣：宜兴出入境检验检疫局，宜兴
关键词:威布尔分布；两重混合模型；胸腺淋巴瘤；网状细胞肉瘤；逆矩估计；区间估计；Weibull Distribution; Twofold Mixed Model; Thymus Lymphoma; Reticulum Cell Sarcoma; Inverse Moment Estimate; Interval Estimate
摘要:

考虑被辐射的老鼠的存活时间的数据，当老鼠死之后，可以经解剖知道其死亡原因，一类原因为胸腺淋巴瘤，另一类原因为网状细胞肉瘤。本文给出在不经解剖的情形下如何将两种原因引起的存活数据进行分离的统计方法，认为这类老鼠存活时间可用两重两参数威布尔分布混合模型来拟合，同时提出了一个优选准则，并得到了参数的逆矩估计和区间估计。计算结果表明本文方法的简便易行。

Abstract: Considering the data of survival time of raying mice, we can know the reason of death by dissection after the mice died. One reason is thymus lymphoma, and the other is reticulum cell sarcoma. In this paper, we give the statistical method to separate the survival data caused by two reasons without dissection. It is also considered that this kind of mice survival time can be fitted by twofold mixed model of two-parameter Weibull distribution. Besides, the optimum selection criterion is proposed, and the inverse moment estimates and interval estimates of parameters are obtained. The calculated results indicate that the method is simple and feasible.

文章引用：徐晓岭, 王蓉华, 顾蓓青, 吴生荣. 两重两参数威布尔分布混合模型的拟合[J]. 统计学与应用, 2012, 1(2): 20-25. http://dx.doi.org/10.12677/SA.2012.12005

参考文献

[1] R. C. Elandt-Johnson, N. L. Johson. Survival model and data analysis. New York: John Wiley & Sons, 1980: 193.
[2] G. J. MaLachlan, D. Peel. Finite mixture models. New York: Wiley, 2000.
[3] B. G. Lindsay, Mixture model: Theory, geometry and application. Hayward: Institute for mathematical Statistics, 1995.
[4] G. J. MaLachlan, K. E. Basford, Mixture models, inference and application to clustering. New York and Basel: Marcel Dekker, 1988.
[5] D. M. Titterington. Statistical analysis of finite mixture distribu- tion. New York: John Wiley & Sons Ltd., 1985.
[6] K. C. Lanf. Introduction to the special issue on finite mixture models. Social Research Methods, 2001, 29(3): 275-281.
[7] W. Mendenhall, R. J. Hader. Estimation of parameters of mixed exponential distributed failure times from censored life test data. Biometrical, 1958, 45(3-4): 504-520.
[8] G. M. Tallis, R. Light. The use of fractional moments for esti- mating the parameters of a mixed exponential distribution. Tech- nometrics, 1968, 10(1): 161-175.
[9] J. H. K. Kao. A graphical estimation of mixed Weibull parame- ters in life testing of electron tubes. Technometrics, 1959, 1(4): 389-407.
[10] L. W. Falls. Estimation of parameters in compound Weibull dis- tributions. Technometrics, 1970, 12(2): 399-407.
[11] J. P. Dickinson. On the resolution of a mixture of observations from two gamma distributions by the method of maximum likelihood. Metrika, 1974, 21(1): 133-141.
[12] 蒋仁言. 威布尔模型族特性、参数估计和应用[M]. 北京: 科学出版社, 1998: 62-65, 122-125, 172-174, 199-202.
[13] 蒋仁言, 左明健. 可靠性模型与应用[M]. 北京: 机械工业出版社, 1999: 20, 124, 126-127, 169-170.
[14] A. C. Cohen. Estimation of mixtures of poisson and mixtures of exponential distributions. NASA Technical Memorandum NASA TMX 53235, 1965.
[15] 金国騿, 胡文忠. 风速频率分布混合模型的研究[J]. 太阳能学报, 1994, 15(4): 353-356.
[16] 朱利平, 卢一强, 茆诗松. 混合指数分布的参数估计[J]. 应用概率统计, 2006, 22(2): 137-150.
[17] G. N. Michael. A finite mixture distribution model for data collected from twins. Twin Research, 2003, 6(3): 235-239.
[18] D. Kalis, E. Xekalaki. Robust inference for finite Poisson mix- tures. Journal of Statistical Planning and Inference, 2001, 93(1- 2): 93- 115.
[19] 王炳兴. Weibull分布的统计推断[J]. 应用概率统计, 1992, 8(4): 357-364.
[20] 王蓉华, 徐晓岭. 三参数Weibull分布的统计推断[J]. 数理统计与应用概率, 1997, 12(1): 86-100.
[21] 中国电子技术标准化研究所. 可靠性试验用表(增订本)[M]. 北京: 国防工业出版社, 1987.
[22] J. F. Lawless. Statistical models and methods for lifetime data. New York: John Wiley & Sons, Inc., 1982.
[23] D. B. Kececioglu. Reliability Engineering Handbook (Volume 1). Endlewood Cliffs: Prentice Hall Inc., 1996.

为你推荐



Baidu
map