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Inference of return level in non-stationary GEV distribution based on time varying stopping rules
Journal of the Korean Data & Information Science Society 2024;35:347-64
Published online May 31, 2024;
© 2024 Korean Data and Information Science Society.

Yujeong Lee1 · Kyoung Hee Kim2

12Department of Statistics, Korea University
Correspondence to: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2023R1A2C1003730 and No. RS-2023-00219212). This paper is based on the master’s thesis of the first author.
1 Master student, Department of Statistics, Korea University, Seoul 02841, Korea.
2 Associate professor, Department of Statistics, Korea University, Seoul 02841, Korea. E-mail:
Received February 6, 2024; Revised March 25, 2024; Accepted March 27, 2024.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper proposes a method for estimating the return level when the most recent observation in non-stationary process is extremely large compared to previous observations. The inclusion of trigger event has a substantial impact on the estimation of the return level. To address this issue, stopping rules based on a threshold considering the non-stationary distribution is proposed. Also, to reduce variance and bias, several likelihood functions are considered. Through comparisons between estimated return levels using each likelihood function and comparisons with previous study, this study demonstrates the suitability of the proposed approach under non-stationarity. Additionally, the applicability of the method is confirmed through the analysis of earthquakes data in South Korea.
Keywords : Generalized extreme value distribution, non-stationary, return level, stopping rule, trigger event