基于分位点的广义Pareto分布函数最小二乘拟合方法

赵刚; 李刚

doi:10.21656/1000-0887.380196

基于分位点的广义Pareto分布函数最小二乘拟合方法

doi: 10.21656/1000-0887.380196

赵刚,
李刚

大连理工大学工程力学系;工业装备结构分析国家重点实验室(大连理工大学), 辽宁大连 116024

基金项目: 国家重点基础研究发展计划(973计划)（2016CB046506）

详细信息

作者简介:
赵刚(1987—)，男，博士生(E-mail: zhaogang54@126.com)；李刚(1966—)，男，教授，博士生导师(通讯作者. E-mail: ligang@dlut.edu.cn）.

中图分类号: O302
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- 文章访问数: 1539
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出版历程
- 收稿日期: 2017-07-14
- 修回日期: 2018-01-09
- 刊出日期: 2018-04-15

A Least-Squares Fitting Method for Generalized Pareto Distributions Based on Quantiles

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 116024, P.R.China

Funds: The National Basic Research Program of China(973 Program)（2016CB046506）

摘要

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.
- 广义Pareto分布 /
- 最小二乘拟合 /
- 分位点 /
- Kriging模型
Abstract: 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 least-squares 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.
- generalized Pareto distribution /
- least-squares fitting method /
- quantile /
- Kriging model

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参考文献(17)

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基于分位点的广义Pareto分布函数最小二乘拟合方法

doi: 10.21656/1000-0887.380196

作者简介:
赵刚(1987—)，男，博士生(E-mail: zhaogang54@126.com)；李刚(1966—)，男，教授，博士生导师(通讯作者. E-mail: ligang@dlut.edu.cn）.

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A Least-Squares Fitting Method for Generalized Pareto Distributions Based on Quantiles

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留言板

基于分位点的广义Pareto分布函数最小二乘拟合方法

doi: 10.21656/1000-0887.380196

作者简介: 赵刚(1987—)，男，博士生(E-mail: zhaogang54@126.com)；李刚(1966—)，男，教授，博士生导师(通讯作者. E-mail: ligang@dlut.edu.cn）.

计量

出版历程

A Least-Squares Fitting Method for Generalized Pareto Distributions Based on Quantiles

计量

出版历程

目录

作者简介:
赵刚(1987—)，男，博士生(E-mail: zhaogang54@126.com)；李刚(1966—)，男，教授，博士生导师(通讯作者. E-mail: ligang@dlut.edu.cn）.