广义Pareto分布参数的Bootstrap置信区间及应用  

Bootstrap Con dence Interval for Parameters of Generalized Pareto Distribution and Its Application

作　　者：张艳芳[1,2] 赵宜宾 任晴晴[1] ZHANG Yanfang;ZHAO Yibin;REN Qingqing(Institute of Disaster Prevention,Sanhe,Hebei 065201;Hebei Key Laboratory of Earthquake Dynamics,Sanhe,Hebei 065201)

机构地区：[1]防灾科技学院,河北三河065201 [2]河北省地震动力学重点实验室,河北三河065201

出　　处：《工程数学学报》2023年第6期1011-1020,共10页Chinese Journal of Engineering Mathematics

基　　金：中央高校基本科研业务费专题项目(ZY20215140);河北省教育厅科学技术研究项目(ZD2022160);河北省高等学校科学技术研究项目(Z2020224).

摘　　要：针对广义Pareto分布应用于超阈值数据拟合时尾部数据较少的情况,将参数的极大似然估计与Bootstrap方法相结合,给出参数的Bootstrap置信区间。Bootstrap置信区间计算方法既可以通过重复抽样充分利用样本信息,又可以避免样本较少时估计量方差偏大的情况。理论证明参数的Bootstrap置信区间是渐近有效的。数值模拟结果表明在一定的置信度下,置信区间的区间长度和覆盖率比较合理。应用建立的Pareto模型对巴颜喀拉地震带震级数据进行分析,结果表明在相同的置信度下,采用Bootstrap方法计算的置信区间比由近似协方差矩阵计算的区间长度更短,这为广义Pareto模型描述地震震级分布的适用性提供了支撑。Since there are few tail data when the generalized Pareto distribution is applied to the data beyond the threshold,the Bootstrap confidence interval for the parameters is derived by combining the maximum likelihood estimation of the parameters with the Bootstrap method.The Bootstrap method can not only make full use of the sample information by resampling,but also avoid the estimation of the variance of the estimation when there are fewer samples.Bootstrap confidence intervals for parameters are proved being asymptotically efficient.Numerical simulation results show that the interval length and coverage are reasonable under a certain confidence level.The established Pareto model is used to analyze the magnitude data of the Bayan Har seismic zone.The results show that under the same confidence level,the length of the confidence interval determined by the Bootstrap method is shorter than that calculated by the approximate covariance matrix,which supports the applicability of the generalized Pareto model to describe the earthquake magnitude.

关 键 词：广义PARETO分布 Bootstrap置信区间 震级分布 参数估计 

分 类 号：O213[理学—概率论与数理统计]