全样本场合下两参数Birnbaum-Saunders疲劳寿命分布的统计分析
|
摘要
通过对数变换给出了求两参数Birnbaum-Saunders(BS)疲劳寿命分布BS(α,β)在全样本场合下参数的对数矩估计,并通过大量Monte-Carlo模拟比较了各种点估计方法的精度.基于对数变换通过一阶泰勒展开,将两参数BS疲劳寿命分布BS(α,β)近似看作两参数对数正态分布,由此得到了2个参数α,β的近似区间估计,通过Monte-Carlo模拟发现,所给出的近似方法比原有方法更精确.最后通过若干实例说明了方法的可行性.
The logarithmic moment estimations of parameters are proposed by logarithmic transformation for two-parameter Birnbaum-Saunders(BS)fatigue life distribution BS(α,β)under the full sample.The precisions of various point estimation methods are compared by a large number of Monte-Carlo simulations.Two-parameter BS fatigue life distribution BS(α,β)is approximately regarded as two-parameter lognormal distribution through the first order Taylor expansion based on logarithmic transformation.Then,the approximate interval estimations of two parametersα,βare obtained,and it can be found that this approximate method is more accurate than the original method by Monte-Carlo simulations.Finally,several examples show the feasibility of the methods.
The logarithmic moment estimations of parameters are proposed by logarithmic transformation for two-parameter Birnbaum-Saunders(BS)fatigue life distribution BS(α,β)under the full sample.The precisions of various point estimation methods are compared by a large number of Monte-Carlo simulations.Two-parameter BS fatigue life distribution BS(α,β)is approximately regarded as two-parameter lognormal distribution through the first order Taylor expansion based on logarithmic transformation.Then,the approximate interval estimations of two parametersα,βare obtained,and it can be found that this approximate method is more accurate than the original method by Monte-Carlo simulations.Finally,several examples show the feasibility of the methods.
引文
[1]BIRNBAUM Z W,SAUNDERS S C.A new family of life distribution[J].Journal of Applied Probability,1969,6(2):319-327.
[2]DESMOND A F.Stochastic models of failure in random environments[J].Canadian Journal of Statistics,1985,13(3):171-183.
[3]DESMOND A F.On the relationship between two fatigue-life models[J].IEEE Transactions on Reliability,1986,35(2):167-169.
[4]BIRNBAUM Z W,SAUNDERS S C.Estimation for a family of life distributions with applications to fatigue[J].Journal of Applied Probability,1969,6(2):328-347.
[5]ENGELHARDT M,BAIN L J,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(3):283-298.
[8]DUPUIS D J,MILLS J E.Robust estimation of the Birnbaum-Saunders 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].IEEE Transactions on Reliability,1993,42(3):464-469.
[10]RIECK J R.Parametric estimation for the BirnbaumSaunders distribution based on symmetrically censored samples[J].Communication in Statistics-Theory and Methods,1995,24(7):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(2):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(7):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:自然科学版,1996(4):10-15.WANG B X,WANG L L.Parameter estimation of Birnbaum–Saunders fatigue life distribution[J].Journal of East China Normal University:Natural Sciences,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 B X,WANG L L.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:自然科学版,1999,28(2):17-22.WANG R H,FEI H L.Parameter estimation for the BS fatigue life distribution under bilateral censoring[J].Journal of Shanghai Normal University:Natural Sciences,1999,28(2):17-22.
[18]WANG R H,FEI H L.Statistical analysis for the Birnbaum-Saunders fatigue life distribution under multiply type II censoring[J].Chinese Quarterly Journal of Mathematics,2006,21(1):15-27.
[19]WANG R H,FEI H L.Statistical analysis for the Birnbaum-Saunders fatigue life distribution under type II bilateral censoring and multiply type II censoring[J].Chinese Quarterly Journal of Mathematics,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 Z L.Interval estimation of scale parameter for Birnbaum-Saunders fatigue life distribution[J].Acta Armamentarii,2009,30(11):1558-1561.
[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 Z L.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 Z L.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 Z L.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(12):4320-4326.
[25]NIU C Z,GUO X,XU W L,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 L,SUN L L.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,2006,24(1):11-14.ZHAO J Y,SUN Q,PENG B H,et al.Statistical inference for BS distribution based on the accelerated degradation data[J].Electronic Product Reliability and Environmental Test,2006,24(1):11-14.
[28]BALAKRISHNAN N,ZHU X J.On the existence and uniqueness of the maximum likelihood estimates of the parameters of Birnbaum-Saunders distribution based on type-I,type-II and hybrid censored samples[J].Statistics,2014,48(5):1013-1032.
[29]徐晓岭,王蓉华,顾蓓青.关于两参数BirnbaumSaunders疲劳寿命分布统计分析的2个注记[J].浙江大学学报:理学版,2016,43(5):539-544.XU X L,WANG R H,GU B Q.Two notes of statistical analysis about two-parameter Birnbaum-Saunders fatigue life distribution[J].Journal of Zhejiang University:Science Edition,2016,43(5):539-544.
[30]徐晓岭,王蓉华.概率论与数理统计[M].北京:人民邮电出版社,2014:48-52,174-178.XU X L,WANG R H.Probability and Mathematical Statistics[M].Beijing:Posts and Telecom Press,2014:48-52,174-178.
[31]VILCA F,SANTANA L,VICTOR LEIVA V,et al.Estimation of extreme percentiles in Birnbaum–Saunders distributions[J].Computational Statistics and Data Analysis,2011,55(4):1665-1678.
[32]CORDEIRO G M,LEMONTE A J.The exponentiated generalized Birnbaum-Saunders distribution[J].Applied Mathematics and Computation,2014,247:762-779.
[2]DESMOND A F.Stochastic models of failure in random environments[J].Canadian Journal of Statistics,1985,13(3):171-183.
[3]DESMOND A F.On the relationship between two fatigue-life models[J].IEEE Transactions on Reliability,1986,35(2):167-169.
[4]BIRNBAUM Z W,SAUNDERS S C.Estimation for a family of life distributions with applications to fatigue[J].Journal of Applied Probability,1969,6(2):328-347.
[5]ENGELHARDT M,BAIN L J,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(3):283-298.
[8]DUPUIS D J,MILLS J E.Robust estimation of the Birnbaum-Saunders 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].IEEE Transactions on Reliability,1993,42(3):464-469.
[10]RIECK J R.Parametric estimation for the BirnbaumSaunders distribution based on symmetrically censored samples[J].Communication in Statistics-Theory and Methods,1995,24(7):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(2):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(7):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:自然科学版,1996(4):10-15.WANG B X,WANG L L.Parameter estimation of Birnbaum–Saunders fatigue life distribution[J].Journal of East China Normal University:Natural Sciences,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 B X,WANG L L.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:自然科学版,1999,28(2):17-22.WANG R H,FEI H L.Parameter estimation for the BS fatigue life distribution under bilateral censoring[J].Journal of Shanghai Normal University:Natural Sciences,1999,28(2):17-22.
[18]WANG R H,FEI H L.Statistical analysis for the Birnbaum-Saunders fatigue life distribution under multiply type II censoring[J].Chinese Quarterly Journal of Mathematics,2006,21(1):15-27.
[19]WANG R H,FEI H L.Statistical analysis for the Birnbaum-Saunders fatigue life distribution under type II bilateral censoring and multiply type II censoring[J].Chinese Quarterly Journal of Mathematics,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 Z L.Interval estimation of scale parameter for Birnbaum-Saunders fatigue life distribution[J].Acta Armamentarii,2009,30(11):1558-1561.
[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 Z L.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 Z L.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 Z L.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(12):4320-4326.
[25]NIU C Z,GUO X,XU W L,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 L,SUN L L.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,2006,24(1):11-14.ZHAO J Y,SUN Q,PENG B H,et al.Statistical inference for BS distribution based on the accelerated degradation data[J].Electronic Product Reliability and Environmental Test,2006,24(1):11-14.
[28]BALAKRISHNAN N,ZHU X J.On the existence and uniqueness of the maximum likelihood estimates of the parameters of Birnbaum-Saunders distribution based on type-I,type-II and hybrid censored samples[J].Statistics,2014,48(5):1013-1032.
[29]徐晓岭,王蓉华,顾蓓青.关于两参数BirnbaumSaunders疲劳寿命分布统计分析的2个注记[J].浙江大学学报:理学版,2016,43(5):539-544.XU X L,WANG R H,GU B Q.Two notes of statistical analysis about two-parameter Birnbaum-Saunders fatigue life distribution[J].Journal of Zhejiang University:Science Edition,2016,43(5):539-544.
[30]徐晓岭,王蓉华.概率论与数理统计[M].北京:人民邮电出版社,2014:48-52,174-178.XU X L,WANG R H.Probability and Mathematical Statistics[M].Beijing:Posts and Telecom Press,2014:48-52,174-178.
[31]VILCA F,SANTANA L,VICTOR LEIVA V,et al.Estimation of extreme percentiles in Birnbaum–Saunders distributions[J].Computational Statistics and Data Analysis,2011,55(4):1665-1678.
[32]CORDEIRO G M,LEMONTE A J.The exponentiated generalized Birnbaum-Saunders distribution[J].Applied Mathematics and Computation,2014,247:762-779.