两参数对数正态分布与威布尔分布的近似极大似然估计
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摘要
在可靠性和生存分析领域中,由于时间和成本等因素的限制,在实际中逐步增加的Ⅱ型截尾寿命试验被广泛应用。文章主要研究了逐步增加Ⅱ型截尾寿命试验下两参数对数正态分布和威布尔分布的参数近似极大似然估计方法,并考虑了近似极大似然估计过程中涉及到的函数一阶泰勒展开的两种展开方式,通过大量的Monte-Carlo模拟比较了这两种方法下估计的精度。
In the field of reliability and survival analysis, because of the limitation of time, cost and other factors, progressive Type-Ⅱ censoring life test is widely used in practice. This paper mainly studies the approximate maximum likelihood estimation methods of two-parameter lognormal distribution and Weibull distribution under progressive Type-Ⅱ censoring life test. Two methods of the first order Taylor expansion of function involved in the process of approximate maximum likelihood estimation are also considered in the paper. Finally the paper makes a large number of Monte Carlo simulations to compare the estimation accuracy of the two methods.
In the field of reliability and survival analysis, because of the limitation of time, cost and other factors, progressive Type-Ⅱ censoring life test is widely used in practice. This paper mainly studies the approximate maximum likelihood estimation methods of two-parameter lognormal distribution and Weibull distribution under progressive Type-Ⅱ censoring life test. Two methods of the first order Taylor expansion of function involved in the process of approximate maximum likelihood estimation are also considered in the paper. Finally the paper makes a large number of Monte Carlo simulations to compare the estimation accuracy of the two methods.
引文
[1]徐晓岭,王蓉华.Weibull分布逐步增加的Ⅱ型截尾试验的统计分析[J].强度与环境,2003,30(2).
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[7]杨君慧,师义民,曹弘毅.逐步增加Ⅱ型截尾试验下广义指数分布的参数估计[J].纺织高校基础科学学报,2014,27(3).
[8]杨君慧,师义民,曹弘毅.逐步增加Ⅱ型截尾试验下广义指数分布的统计分析[J].统计与决策,2014,(16).
[9]Balakrishnan N,Clifford Cohen A.Order Statistics and Inference Estimation Methods[M].Boston:Academic Press,1991.
[10]王蓉华,徐晓岭,费鹤良.对数正态分布参数的近似极大似然估计[J].上海师范大学学报(自然科学版),2000,29(1).
[11]顾益明.分组型数据的产品可靠性的近似极大似然估计[J].上海师范大学学报(自然科学版),2001,30(2).
[12]杨振海,程维虎.基于Logistic总体II型截尾样本分布参数的近似极大似然估计[J].北京工业大学学报,2004,30(2).
[13]王娟,陆志峰.一般II型逐步删失下对数正态模型的近似极大似然估计[J].南通大学学报(自然科学版),2008,7(1).
[14]张莉.分组数据在指数分布下的近似极大似然估计[J].统计与决策,2009,(17).
[2]王炳兴.Weibull分布基于定数逐次截尾寿命数据的统计分析[J].科技通报,2004,20(6).
[3]李凤,师义民,田亚爱.逐步增加II型截尾下Weibull分布的Bayes估计[J].工程数学学报,2008,25(4).
[4]李中恢.逐步II型寿命下逆Rayleigh分布参数的估计[J].宜春学院学报,2012,34(8).
[5]李琼,武东.逐步增加II型截尾下Pareto分布的贝叶斯分析[J].上海第二工业大学学报,2012,29(2).
[6]卫超,师义民.逐步II型混合截尾下Pareto分布的统计分析[J].火力与指挥控制,2014,39(4).
[7]杨君慧,师义民,曹弘毅.逐步增加Ⅱ型截尾试验下广义指数分布的参数估计[J].纺织高校基础科学学报,2014,27(3).
[8]杨君慧,师义民,曹弘毅.逐步增加Ⅱ型截尾试验下广义指数分布的统计分析[J].统计与决策,2014,(16).
[9]Balakrishnan N,Clifford Cohen A.Order Statistics and Inference Estimation Methods[M].Boston:Academic Press,1991.
[10]王蓉华,徐晓岭,费鹤良.对数正态分布参数的近似极大似然估计[J].上海师范大学学报(自然科学版),2000,29(1).
[11]顾益明.分组型数据的产品可靠性的近似极大似然估计[J].上海师范大学学报(自然科学版),2001,30(2).
[12]杨振海,程维虎.基于Logistic总体II型截尾样本分布参数的近似极大似然估计[J].北京工业大学学报,2004,30(2).
[13]王娟,陆志峰.一般II型逐步删失下对数正态模型的近似极大似然估计[J].南通大学学报(自然科学版),2008,7(1).
[14]张莉.分组数据在指数分布下的近似极大似然估计[J].统计与决策,2009,(17).