基于更新径向基函数网络模型的广义Pareto分布函数拟合

摘要

Generalized Pareto Distribution (GPD)is a classical asymptotically motivated model for exce-sses above a high threshold based on the extreme value theory,which is useful for high reliability index estimation.The high computational cost restricts the application of this method.Though the radial basis function neural network (RBFNN)assisted sampling method was proposed to decrease the computa-tional cost,this method may fail when treating highly nonlinear problems.This paper proposes a method for updating the training samples to improve the accuracy of the RBFNN for predicting the tail samples. Compared with the GPD estimation based on the total sample set,the GPD estimation based on the upda-ting RBFNN assisted sampling method can obtain the same results accurately with less computational cost.%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。但这种方法要求样本空间较大,计算成本较高,尽管可以通过径向基函数网络 RBFNN(Radial Basis Function Neural Network)辅助抽样的方法削减计算成本,但对于非线性程度较高的问题,RBFNN精度问题使得辅助抽样方法失效。针对这类问题,根据 GPD 的特点,提出了高效的更新 RBFNN 训练样本的方法,改善了 RBFNN在功能函数分布尾部的精度,将 RBFNN 辅助抽样方法推广应用到非线性程度较高的问题,准确地得到了所有需要的尾部样本,基于该尾部样本集的 GPD拟合结果与基于直接计算所有样本的GPD拟合结果完全一致。