可靠性设计变量样本极值的区间估计法
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摘要
工程系统设计的变量大且多具有不确定性,它们的极大值和极小值同样也具有不确定性。传统的极值理论尚未很好地解决一组样本的极大值和极小值的区间估计问题。本文从次序统计理论出发,建立了该样本的极大值与极小值的区间估计算法,并对大容量和小容量样本的情况分别进行了讨论,获得了在小样本情况下可用母体均匀分布获得的结果来估计样本极值区间的结论。算例结果表明本文提出的方法可以较好地进行样本极大值与极小值的区间估计。
For an engineering system,most of the design variables have an uncertainty,and the sample extremes of these variables also have an uncertainty.Interval estimation problem of sample extremes is not yet solved in classic extreme value theory.Based on the order statistic theory,the interval estimation of sample extremes on large and small samples is given.And then it was deduced that the extreme intervals of small sample can be estimated with the assumption.And the random variable follows uniform distribution.The example demonstrates the suitability of the method for interval estimation of sample extremes.
For an engineering system,most of the design variables have an uncertainty,and the sample extremes of these variables also have an uncertainty.Interval estimation problem of sample extremes is not yet solved in classic extreme value theory.Based on the order statistic theory,the interval estimation of sample extremes on large and small samples is given.And then it was deduced that the extreme intervals of small sample can be estimated with the assumption.And the random variable follows uniform distribution.The example demonstrates the suitability of the method for interval estimation of sample extremes.
引文
[1]姚卫星,顾怡.结构可靠性设计[M].北京:航空工业出版社,1997.
[2]刘国光,王慧敏.沪深股市收益分布尾部特征研究[J].数理统计与管理,2005,24(3):108-112.
[3]董双林.气象要素极值统计的稳定性、多母体现象和区域极值[J].气象学报,1993,51(1):34-43.
[4]陈培善,林邦慧.极值理论在中长期地震预报中的应用[J].地球物理学报,1973,9(16):6-24.
[5]曹天捷,周则恭.最小二乘法在估计概率分布参数中的应用[J].机械强度,1997,19(4):34-36.
[6]Palutiko J P,Brabson B B,Lister D H.A review ofmethod to calculated extreme wind speeds[J].Me-teorol App,1999,38(6):119-132.
[7]Gran G W.Moments estimators for the 3-parameterweibull distribution[J].IEEE Trans on Reliability,1988,37(4):360-363.
[8]数理统计编写组.数理统计[M].西安:西北工业大学出版社,1999.
[9]段忠东,周道成.极值概率分布参数估计方法的比较研究[J].哈尔滨工业大学学报,2004,36(12):1605-1609.
[10]陈希孺.数理统计引论[M].北京:科学出版社,1981.
[11]谢盛荣.序列极值理论导引[M].重庆:重庆出版社,1993.
[12]尚英姿,安润秋.极值分布的极大似然估计及计算机实现[J].河北师范大学学报,2006,30(6):643-646.
[13]曹天捷,周则恭.最小二乘法在估计概率分布参数中的运用[J].机械强度,1997,19(4):34-36.
[14]Li Yongming.A general linear-regression analysis tothe 3-parameter Weibull distribution[J].IEEETrans on Reliability,1994,43(2):255-263.
[15]Lechner J A,Simiu E,Heckert N A.Assessment of“peaks over threshold”method for estimating ex-treme value distribution tail[J].Structural Safety,1993,12(4):305-314.
[16]Tanaka S,Ichikawa M,Akita S.A probabilistic in-vestigation of fatigue life and cumulative cycle ratio[J].Engineering Fracture Mechanics,1984,20(3):501-513.
[2]刘国光,王慧敏.沪深股市收益分布尾部特征研究[J].数理统计与管理,2005,24(3):108-112.
[3]董双林.气象要素极值统计的稳定性、多母体现象和区域极值[J].气象学报,1993,51(1):34-43.
[4]陈培善,林邦慧.极值理论在中长期地震预报中的应用[J].地球物理学报,1973,9(16):6-24.
[5]曹天捷,周则恭.最小二乘法在估计概率分布参数中的应用[J].机械强度,1997,19(4):34-36.
[6]Palutiko J P,Brabson B B,Lister D H.A review ofmethod to calculated extreme wind speeds[J].Me-teorol App,1999,38(6):119-132.
[7]Gran G W.Moments estimators for the 3-parameterweibull distribution[J].IEEE Trans on Reliability,1988,37(4):360-363.
[8]数理统计编写组.数理统计[M].西安:西北工业大学出版社,1999.
[9]段忠东,周道成.极值概率分布参数估计方法的比较研究[J].哈尔滨工业大学学报,2004,36(12):1605-1609.
[10]陈希孺.数理统计引论[M].北京:科学出版社,1981.
[11]谢盛荣.序列极值理论导引[M].重庆:重庆出版社,1993.
[12]尚英姿,安润秋.极值分布的极大似然估计及计算机实现[J].河北师范大学学报,2006,30(6):643-646.
[13]曹天捷,周则恭.最小二乘法在估计概率分布参数中的运用[J].机械强度,1997,19(4):34-36.
[14]Li Yongming.A general linear-regression analysis tothe 3-parameter Weibull distribution[J].IEEETrans on Reliability,1994,43(2):255-263.
[15]Lechner J A,Simiu E,Heckert N A.Assessment of“peaks over threshold”method for estimating ex-treme value distribution tail[J].Structural Safety,1993,12(4):305-314.
[16]Tanaka S,Ichikawa M,Akita S.A probabilistic in-vestigation of fatigue life and cumulative cycle ratio[J].Engineering Fracture Mechanics,1984,20(3):501-513.
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