基于信息准则的Gumbel分布变点检测模型及其应用  

Change-point Model and Its Applications of the Gumbel Distribution Based on Information Criteria

作　　者：蔡霞[1] 樊培 CAI Xia;FAN Pei(School of Science,Hebei University of Science and Technology,Shijiazhuang 050018,China)

机构地区：[1]河北科技大学理学院,河北石家庄050018

出　　处：《数学的实践与认识》2021年第21期207-215,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(12001155,72071071);河北省自然科学基金(A2018208058)。

摘　　要：Gumbel分布是极值分布中一种常见类型,在气象、水文等领域有广泛应用.建立二参数Gumbel分布的变点检测模型,并将其看做是模型选择问题,运用Schwarz信息准则法对位置参数和尺度参数均发生变化的Gumbel分布变点问题进行分析.引入临界值c_(a),比较原假设和备择假设下SIC统计量的大小,进而做出是否拒绝原假设的判断.通过数值模拟,分析了不同参数组合下检验功效的大小.最后,对北京气象站1951年到2018年共68年的月降雨量数据进行实证分析.The Gumbel distribution is a type of extreme value distribution.It is widely used in meteorology,hydrology and other fields.In this paper,two-parameter Gumbel changepoint model is established.This change-point model is considered as the model selection problem.The Schwarz information criterion is used to analyze the proposed Gumbel changepoint model with both the location parameter and the scale parameter changing.The critical value ca is derived.The decision is made by comparing the values of the SIC statistics under the null hypo thesis and the alternative hypo thesis.Numerical simulations are conducted to illustrate the performance of the proposed procedure.The method is successfully applied to the monthly rainfall data of Beijing Meteorological Station from 1951 to 2018.

关 键 词：Gumbel分布 变点检测 信息准则 临界值 

分 类 号：P413[天文地球—大气科学及气象学] O212[理学—概率论与数理统计]