广义Pareto分布变点检测似然比模型

A Likelihood Ratio Model for Change Point Detection of Generalized Pareto Distribution

为检测极端事件的状态变化,基于似然比方法研究了广义Pareto分布(Generalized Pareto Distribution,GPD)变点检测模型.考虑三参数GPD变点的检验问题,提出了最大似然比检验统计量.通过证明参数变换后GPD的对数似然和检验统计量的一系列极限性质,得到了检验统计量的渐近分布.通过模拟研究,对该方法的有限样本性质进行了评价,实例分析也验证了该方法的可行性.

To detect state changes in extreme events,the generalized Pareto distribution(GPD)change point detection model was studied based on likelihood ratio method.This paper considered the testing problem of the GPD change point with three parameters,and proposed maximization likelihood ratio test statistics.The asymptotic distribution of test statistic was obtained by proving a series of limit properties of the log-likelihood of GPD after parameter transformation and the test statistic.We evaluated the finite sample properties of the proposed method through simulation studies.The case study also verified the feasibility of the proposed method.