关于两参数Birnbaum-Saunders疲劳寿命分布统计分析的2个注记
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摘要
通过Monte-Carlo模拟说明目前用于求解两参数Birnbaum-Saunders疲劳寿命分布尺度参数的2种方法可能无法得到尺度参数的区间估计.进一步指出,在利用广义枢轴量法给出尺度参数以及参数函数的置信区间过程中存在错误,并用反例进行了说明,同时给出了正确的证明.
We know that two methods about interval estimate of scale parameter for two-parameter Birnbaum-Saunders fatigue life distribution are shown not always capable of obtaining the interval estimate of scale parameter based on the results of Monte Carlo simulations.Moreover,there is a mistake in deriving the confidence intervals of scale parameter and parameter function with the generalized pivot method.A corresponding counter example is illustrated,and the correct proof is provided.
We know that two methods about interval estimate of scale parameter for two-parameter Birnbaum-Saunders fatigue life distribution are shown not always capable of obtaining the interval estimate of scale parameter based on the results of Monte Carlo simulations.Moreover,there is a mistake in deriving the confidence intervals of scale parameter and parameter function with the generalized pivot method.A corresponding counter example is illustrated,and the correct proof is provided.
引文
[1]BIRNBAUM Z W,SAUNDERS S C.A new family of life distribution[J].Journal of Applied Probability,1969(6):319-322.
[2]DESMOND A F.Stochastic models of failure in random environments[J].The Canadian Journal of Statistics,1985(2):171-176.
[3]DESMOND A F.On the relationship between two fatigue-life models[J].IEEE Transactions on Reliability,1986(2):167-171.
[4]BIRNBAUM Z W,SAUNDERS S C.Estimation for a family of life distributions with applications to fatigue[J].Appl Prob,1969(6):328-347.
[5]ENGELHARDT M,WRIGHT F T.Inferences on the parameters of the Birnbaum Saunders fatigue life distribution based on maximum likelihood estimation[J].Technometrics,1981,23(3):251-256.
[6]RIECK J R,NEDELMAN J R.A log-linear model for the Birnbaum Saunders distribution[J].Techanometrics,1991,33(1):51-60.
[7]NG H K T,KUNDU D,BALAKRISHNAN N.Modified moment estimation for the two-parameter Birnbaum-Saunders distribution[J].Computational Statistics and Data Analysis,2003,43:283-298.
[8]DUPUIS D J,MILLS J E.Robust estimation of the Birnbaum distribution[J].IEEE Transactions on Reliability,1998,47(1):88-95.
[9]CHANG D S,TANG L C.Reliability bounds and critical time for the Birnbaum-Saunders distribution[J].Reliability,IEEE Transactions on Reliability,1993,42:464-469.
[10]RIECK J R.Parametric estimation for the BirnbaumSaunders distribution based on symmetrically censored samples[J].Communication Statistics-Theory Methods,1995,24:1721-1736.
[11]OWEN W J,PADGETT W J.A Birnbaum-Saunders accelerated life model[J].IEEE Transactions on Reliability,2000,49(2):224-229.
[12]OWEN W J,PADGETT W J.Acceleration models for system strength based on Birnbaum-Saunders distribution[J].Lifetime Data Analysis,1999(5):133-147.
[13]OWEN W J,PADGETT W J.Power-law accelerated Birnbaum-Saunders life models[J].International Journal of Reliability,Quality and Safety Engineering,2000,7(1):1-15.
[14]KUNDU D,KANNAN N,BALAKRISHNAN N.On the hazard function of Birnbaum-Saunders distribution and associated inference[J].Computational Statistics&Data Analysis,2008,52(5):2692-2702.
[15]王炳兴,王玲玲.Birnbaum-Saunders疲劳寿命分布的参数估计[J].华东师范大学学报,1996(4):10-15.WANG Bingxing,WAGN Lingling.Parameter estimation of Birnbaum-Saunders fatigue life distribution[J].Journal of East China Normal University,1996(4):10-15.
[16]王炳兴,王玲玲.Birnbaum-Saunders疲劳寿命分布在截尾试验情形的统计分析[J].应用概率统计,1996,12(4):369-375.WANG Bingxing,WAGN Lingling.Statistical analysis of Birnbaum-Saunders fatigue life distribution in the censored test case[J].Applied Probability and Statistics,1996,12(4):369-375.
[17]王蓉华,费鹤良.双边截尾场合下BS疲劳寿命分布的参数估计[J].上海师范大学学报,1999,28(2):17-22.WANG Ronghua,FEI Heliang.Parameter estimation for the BS fatigue life distribution under bilateral censoring[J].Journal of Shanghai Normal University,1999,28(2):17-22.
[18]WANG Ronghua,FEI Heliang.Statistical analysis for the Birnbaum-Saunders fatigue life distribution under multiply type II censoring[J].Chin Quart J of Math,2006,21(1):15-27.
[19]WANG Ronghua,FEI Heliang.Statistical analysis for the Birnbaum-Saunders fatigue life distribution under type II bilateral censoring and multiply type II censoring[J].Chin Quart J of Math,2004,19(2):126-132.
[20]孙祝岭.Birnbaum-Saunders疲劳寿命分布尺度参数的区间估计[J].兵工学报,2009,30(11):1558-1561.SUN Zhuling.Interval estimation of scale parameter for Birnbaum-Saunders fatigue life distribution[J].Acta Armamentarii,2009,30(11):1158-1561.
[21]孙祝岭.Birnbaum-Saunders疲劳寿命分布参数的回归估计方法[J].兵工学报,2010,31(9):1260-1262.SUN Zhuling.Regression estimation method of parameters for Birnbaum-Saunders fatigue life distribution[J].Acta Armamentarii,2010,31(9):1260-1262.
[22]孙祝岭.疲劳寿命分布变异系数的统计推断[J].质量与可靠性,2013(1):13-15.SUN Zhuling.Statistical inference of variable coefficient for fatigue life distribution[J].Quality and Reliability,2013(1):13-15.
[23]孙祝岭.Birnbaum-Saunders分布环境因子的置信限[J].强度与环境,2012,39(4):51-55.SUN Zhuling.Confidence limit of environmental factor for Birnbaum-Saunders distribution[J].Structure&Environment Engineering,2012,39(4):51-55.
[24]WANG B X.Generalized interval estimation for the Birnbaum-Saunders distribution[J].Computational Statistics and Data Analysis,2012,56:4320-4326.
[25]NIU Cuizhen,GUO Xu,XU Wangli,et al.Comparison of several Birnbaum-Saunders distributions[J].Journal of Statistical Computation and Simulation,2014,84(12):2721-2733.
[26]周磊,孙玲玲.一种基于概率解释的新型互连线时延Slew模型[J].电路与系统学报,2009,14(2):7-10.ZHOU Lei,SUN Lingling.A new Slew interconnect delay model Based on probability interpretation[J].Journal of Circuits and Systems,2009,14(2):7-10.
[27]赵建印,孙权,彭宝华,等.基于加速退化数据的BS分布的统计推断[J].电子产品可靠性与环境试验,2006(1):11-14.ZHAO Jianyin,SUN Quan,PENG Baohua,et al.Statistical inference for BS distribution based on the accelerated degradation data[J].Electronic Product Reliability and Environmental Test,2006(1):11-14.
[28]徐晓岭,王蓉华.概率论与数理统计[M].北京:人民邮电出版社,2014:48-52.XU Xiaoling,WANG Ronghua.Probability and Mathematical Statistics[M].Beijing:Posts and Telecom Press,2014:48-52.
[2]DESMOND A F.Stochastic models of failure in random environments[J].The Canadian Journal of Statistics,1985(2):171-176.
[3]DESMOND A F.On the relationship between two fatigue-life models[J].IEEE Transactions on Reliability,1986(2):167-171.
[4]BIRNBAUM Z W,SAUNDERS S C.Estimation for a family of life distributions with applications to fatigue[J].Appl Prob,1969(6):328-347.
[5]ENGELHARDT M,WRIGHT F T.Inferences on the parameters of the Birnbaum Saunders fatigue life distribution based on maximum likelihood estimation[J].Technometrics,1981,23(3):251-256.
[6]RIECK J R,NEDELMAN J R.A log-linear model for the Birnbaum Saunders distribution[J].Techanometrics,1991,33(1):51-60.
[7]NG H K T,KUNDU D,BALAKRISHNAN N.Modified moment estimation for the two-parameter Birnbaum-Saunders distribution[J].Computational Statistics and Data Analysis,2003,43:283-298.
[8]DUPUIS D J,MILLS J E.Robust estimation of the Birnbaum distribution[J].IEEE Transactions on Reliability,1998,47(1):88-95.
[9]CHANG D S,TANG L C.Reliability bounds and critical time for the Birnbaum-Saunders distribution[J].Reliability,IEEE Transactions on Reliability,1993,42:464-469.
[10]RIECK J R.Parametric estimation for the BirnbaumSaunders distribution based on symmetrically censored samples[J].Communication Statistics-Theory Methods,1995,24:1721-1736.
[11]OWEN W J,PADGETT W J.A Birnbaum-Saunders accelerated life model[J].IEEE Transactions on Reliability,2000,49(2):224-229.
[12]OWEN W J,PADGETT W J.Acceleration models for system strength based on Birnbaum-Saunders distribution[J].Lifetime Data Analysis,1999(5):133-147.
[13]OWEN W J,PADGETT W J.Power-law accelerated Birnbaum-Saunders life models[J].International Journal of Reliability,Quality and Safety Engineering,2000,7(1):1-15.
[14]KUNDU D,KANNAN N,BALAKRISHNAN N.On the hazard function of Birnbaum-Saunders distribution and associated inference[J].Computational Statistics&Data Analysis,2008,52(5):2692-2702.
[15]王炳兴,王玲玲.Birnbaum-Saunders疲劳寿命分布的参数估计[J].华东师范大学学报,1996(4):10-15.WANG Bingxing,WAGN Lingling.Parameter estimation of Birnbaum-Saunders fatigue life distribution[J].Journal of East China Normal University,1996(4):10-15.
[16]王炳兴,王玲玲.Birnbaum-Saunders疲劳寿命分布在截尾试验情形的统计分析[J].应用概率统计,1996,12(4):369-375.WANG Bingxing,WAGN Lingling.Statistical analysis of Birnbaum-Saunders fatigue life distribution in the censored test case[J].Applied Probability and Statistics,1996,12(4):369-375.
[17]王蓉华,费鹤良.双边截尾场合下BS疲劳寿命分布的参数估计[J].上海师范大学学报,1999,28(2):17-22.WANG Ronghua,FEI Heliang.Parameter estimation for the BS fatigue life distribution under bilateral censoring[J].Journal of Shanghai Normal University,1999,28(2):17-22.
[18]WANG Ronghua,FEI Heliang.Statistical analysis for the Birnbaum-Saunders fatigue life distribution under multiply type II censoring[J].Chin Quart J of Math,2006,21(1):15-27.
[19]WANG Ronghua,FEI Heliang.Statistical analysis for the Birnbaum-Saunders fatigue life distribution under type II bilateral censoring and multiply type II censoring[J].Chin Quart J of Math,2004,19(2):126-132.
[20]孙祝岭.Birnbaum-Saunders疲劳寿命分布尺度参数的区间估计[J].兵工学报,2009,30(11):1558-1561.SUN Zhuling.Interval estimation of scale parameter for Birnbaum-Saunders fatigue life distribution[J].Acta Armamentarii,2009,30(11):1158-1561.
[21]孙祝岭.Birnbaum-Saunders疲劳寿命分布参数的回归估计方法[J].兵工学报,2010,31(9):1260-1262.SUN Zhuling.Regression estimation method of parameters for Birnbaum-Saunders fatigue life distribution[J].Acta Armamentarii,2010,31(9):1260-1262.
[22]孙祝岭.疲劳寿命分布变异系数的统计推断[J].质量与可靠性,2013(1):13-15.SUN Zhuling.Statistical inference of variable coefficient for fatigue life distribution[J].Quality and Reliability,2013(1):13-15.
[23]孙祝岭.Birnbaum-Saunders分布环境因子的置信限[J].强度与环境,2012,39(4):51-55.SUN Zhuling.Confidence limit of environmental factor for Birnbaum-Saunders distribution[J].Structure&Environment Engineering,2012,39(4):51-55.
[24]WANG B X.Generalized interval estimation for the Birnbaum-Saunders distribution[J].Computational Statistics and Data Analysis,2012,56:4320-4326.
[25]NIU Cuizhen,GUO Xu,XU Wangli,et al.Comparison of several Birnbaum-Saunders distributions[J].Journal of Statistical Computation and Simulation,2014,84(12):2721-2733.
[26]周磊,孙玲玲.一种基于概率解释的新型互连线时延Slew模型[J].电路与系统学报,2009,14(2):7-10.ZHOU Lei,SUN Lingling.A new Slew interconnect delay model Based on probability interpretation[J].Journal of Circuits and Systems,2009,14(2):7-10.
[27]赵建印,孙权,彭宝华,等.基于加速退化数据的BS分布的统计推断[J].电子产品可靠性与环境试验,2006(1):11-14.ZHAO Jianyin,SUN Quan,PENG Baohua,et al.Statistical inference for BS distribution based on the accelerated degradation data[J].Electronic Product Reliability and Environmental Test,2006(1):11-14.
[28]徐晓岭,王蓉华.概率论与数理统计[M].北京:人民邮电出版社,2014:48-52.XU Xiaoling,WANG Ronghua.Probability and Mathematical Statistics[M].Beijing:Posts and Telecom Press,2014:48-52.