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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

赵刚 李刚

赵刚, 李刚. 基于分位点的广义Pareto分布函数最小二乘拟合方法[J]. 应用数学和力学, 2018, 39(4): 415-423. doi: 10.21656/1000-0887.380196
引用本文: 赵刚, 李刚. 基于分位点的广义Pareto分布函数最小二乘拟合方法[J]. 应用数学和力学, 2018, 39(4): 415-423. doi: 10.21656/1000-0887.380196
ZHAO Gang, LI Gang. A Least-Squares Fitting Method for Generalized Pareto Distributions Based on Quantiles[J]. Applied Mathematics and Mechanics, 2018, 39(4): 415-423. doi: 10.21656/1000-0887.380196
Citation: ZHAO Gang, LI Gang. A Least-Squares Fitting Method for Generalized Pareto Distributions Based on Quantiles[J]. Applied Mathematics and Mechanics, 2018, 39(4): 415-423. 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
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

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

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

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