A Least-Squares Fitting Method for Generalized Pareto Distributions Based on Quantiles
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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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关键词:
- 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.-
Key words:
- generalized Pareto distribution /
- least-squares fitting method /
- quantile /
- Kriging model
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