Analysis of maximum temperature using generalized extreme value distribution and four parameter kappa distribution for r-largest order statistics†
Yire Shin1 · Eunsik Park2
12Department of Mathematics and Statistics, Chonnam National University
Correspondence to: † This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (RS-2023-00248434).
1 Post Doctor, Department of Mathematics and Statistics, Chonnam National University, Gwangju 61186, Korea.
2 Corresponding author: Professor, Department of Mathematics and Statistics, Chonnam National University, Gwangju 61186, Korea. E-mail: espark02@jnu.ac.kr
1 Post Doctor, Department of Mathematics and Statistics, Chonnam National University, Gwangju 61186, Korea.
2 Corresponding author: Professor, Department of Mathematics and Statistics, Chonnam National University, Gwangju 61186, Korea. E-mail: espark02@jnu.ac.kr
Received July 10, 2023; Revised July 31, 2023; Accepted August 11, 2023.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Abstract
- Accurate estimation of T-year return levels of extreme climate are important for disaster response and the projection of future climate. To improve the accuracy of return levels, it is important to capture the variability of extreme observations. Considering not only the block maxima but also the r-order statistics is useful to improve the model fit and to reduce the uncertainty of the estimates. In this study, we fitted a generalized extreme value distribution for the r-largest order statistics (rGEVD) and a four-parameter kappa distribution for the r-largest order statistics (rK4D) to analyze daily maximum temperatures in Seoul and six other metropolitan cities (Incheon, Daejeon, Daegu, Ulsan, Gwangju, and Busan). Parameter estimation and goodness-of-fit tests were performed at each location. Also, 100 and 200-year return levels for daily maximum temperatures were estimated. Consideration of extreme value distributions for the r-largest order statistics improved the fit of underestimated extreme value distributions. In particular, rK4D was found to be more flexible when capturing the maximum and upper tail of extreme observations compared to rGEVD. We expect that extreme value distributions for the r-largest order statistics will be useful in analyzing extreme values in many research areas, including climatology and hydrology.
- Keywords : Extreme climate, extreme value distributions, return level
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