摘要
广义Pareto分布函数(GPD,generalized Pareto distribution)是一种针对随机参数尾部进行渐进插值的方法,能够对高可靠性问题进行评估.应用该函数进行随机参数尾部近似时,需要对函数中的两个重要未知参数进行拟合确定.最常用的拟合方法是最大似然拟合和最小二乘拟合,需要将所有的尾部样本进行计算;需要大量尾部样本,计算效率低.该文提出依据少量的分位点进行最小二乘拟合,既保证了尾部样本空间足够大,同时又降低了计算成本;进一步提出了Kriging模型的两阶段更新,实现了分位点求解的快速收敛.算例表明,该文提出的方法能够快速提高模型精度,求得指定的分位点,而且与基于大量尾部样本的最大似然拟合结果精度一致.
The generalized Pareto distribution（ GPD） is a classical asymptotically motivated model for excesses above a high threshold based on the extreme value theory,which is useful for the high reliability index estimation. In the GPD there are 2 unknown parameters which could be estimated with the leastsquares fitting method and the maximum likelihood method. Both methods need all the tail samples of a distribution in previous studies. However,for the GPD estimation,the better accuracy would lead to a much higher computational cost. So a least-squares fitting method based on the quantiles was proposed to obtain the unknown parameters in the GPD. The 2-stage-updating method for the Kriging model was also given to calculate the quantiles. Compared with the GPD based on the maximum likelihood method and the Monte-Carlo method,the 2-stage-updating method for the Kriging model helps find the specified quantiles accurately and efficiently,and the least-squares fitting method based on the quantiles also performs well.
作者
赵刚
李刚
ZHAO Gang;LI Gang(State Key Laboratory of Structural Analysis for Industrial Equipment （ Dalian University of Technology） , Department of Engineering Mechanics, Dalian University of Technology, Dalian , Liaoning 115024, P.R. China ） （Recommended by ZHANG Yahui, M. AMM Editorial Board)
出处
《应用数学和力学》
CSCD
北大核心
2018年第4期415-423,共9页
Applied Mathematics and Mechanics
基金
国家重点基础研究发展计划(973计划)(2016CB046506)
