## 留言板

 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.
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.

• 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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