应用数学和力学2018，Vol.39Issue(4)：415-423,9.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
A Least-Squares Fitting Method for Generalized Pareto Distributions Based on Quantiles
摘要
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.关键词
广义Pareto分布/最小二乘拟合/分位点/Kriging模型Key words
generalized Pareto distribution/least-squares fitting method/quantile/Kriging model分类
数理科学引用本文复制引用
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):415-423,9.基金项目
The National Basic Research Program of China (973 Program)(2016CB046506)国家重点基础研究发展计划(973计划)(2016CB046506) （973 Program）
