Siow Chen Sian This email address is being protected from spambots. You need JavaScript enabled to view it.1 and Darmesah Gabda1

1Department of Mathematics with Economics, Faculty of Science and Natural Resources, Universiti Malaysia Sabah, Jalan UMS, 88400 Kota Kinabalu, Sabah


Received: December 7, 2020
Accepted: March 8, 2021
Publication Date: October 11, 2021

 Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

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When the extreme data were obtained from several sites in a region, spatial extreme analysis is always been considered. In this paper, we model the annual maximum rainfall data by using generalized extreme value distribution. We fit the model independently for each site to prevent extreme value complex modeling. However, it also cause the statistical assumption of dependency between sites been violated. Therefore, we applied the sandwich estimator to correct the variance of the model. We also consider an analysis of small sample sizes of the observed data. The method of penalized maximum likelihood estimation was carried out to improve the inference of the model. In the end, the return levels of the annual maximum rainfall data were computed by using the corrected model.

Keywords: Generalized Extreme Value (GEV) distribution, Penalized Maximum Likelihood Estimation (PMLE), Sandwich Estimator, Return Level


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