Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2023, Vol. 40 ›› Issue (6): 1011-1020.doi: 10.3969/j.issn.1005-3085.2023.06.012

Previous Articles    

Bootstrap Confidence Interval for Parameters of Generalized Pareto Distribution and Its Application

ZHANG Yanfang1,2,  ZHAO Yibin1,  REN Qingqing1   

  1. 1. Institute of Disaster Prevention, Sanhe, Hebei 065201
    2. Hebei Key Laboratory of Earthquake Dynamics, Sanhe, Hebei 065201
  • Received:2021-08-26 Accepted:2022-06-21 Online:2023-12-15 Published:2024-02-15
  • Contact: Y. Zhao. E-mail address: zhaoyibin5362@126.com
  • Supported by:
    The Fundamental Research Funds for the Central Universities (ZY20215140); the Science and Technology Project of Hebei Education Department (ZD2022160); the Science and Technology Research Project for Colleges and Universities in Hebei Province (Z2020224).

Abstract:

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.

Key words: generalized Pareto distribution, Bootstrap confidence interval, magnitude distribution, parameter estimation

CLC Number: