基于分位点的广义Pareto分布函数最小二乘拟合方法
摘要
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.