Univariate generalized extreme value approach for spatial extreme event with small sample size: An application to extreme rainfall in Sabah

This study aims to model the extreme event with small sample sizes using a univariate Generalized Extreme Value (GEV) distribution. The Maximum Likelihood Estimation (MLE) is the most recommended method for parameter estimation with GEV distribution due to the consistency of the results and wide app...

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Main Author:	Siow, Chen Sian
Format:	Thesis
Language:	English English
Published:	2023
Subjects:	QA1-939 Mathematics
Online Access:	https://eprints.ums.edu.my/id/eprint/41490/1/24%20PAGES.pdf https://eprints.ums.edu.my/id/eprint/41490/2/FULLTEXT.pdf
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spelling	my-ums-ep.414902024-11-13T02:51:15Z Univariate generalized extreme value approach for spatial extreme event with small sample size: An application to extreme rainfall in Sabah 2023 Siow, Chen Sian QA1-939 Mathematics This study aims to model the extreme event with small sample sizes using a univariate Generalized Extreme Value (GEV) distribution. The Maximum Likelihood Estimation (MLE) is the most recommended method for parameter estimation with GEV distribution due to the consistency of the results and wide application in extreme value analysis. However, the MLE performs poorly in small sample sizes, creating uncertainties that may lead to inaccurate estimation. Therefore, the Generalized Maximum Likelihood Estimation (GMLE) was suggested to improve the performance of MLE in modelling the small sample sizes of extreme events. A simulation study was conducted using several methods which are probability weighted moment (PWM), MLE, and GMLE to choose the most suitable parameter estimation of GEV distribution base on bias and root mean square error (RMSE). Other than that, the simulation results showed that GMLE performs better than PWM and MLE for GEV parameter estimations. A case study was conducted by fitting Sabah’s annual maximum rainfall data with small sample sizes into GEV distribution with GMLE as the parameter estimation method. A stationary GEV model, which holds all parameters constant, is compared to a non-stationary model, consisting of a linear function of temperature as the covariate in the location parameter. From the results of the corrected Akaike’s Information Criterion (AICc) and likelihood ratio test, there was insufficient evidence to prove the existence of a trend to the extreme rainfall. Besides, homogeneity testing was conducted for each district using the likelihood ratio test. It showed that all the rainfall stations from these five districts should be modelled independently without common shape parameters. Since the GEV was fitted independently at each site and the inter-dependency between sites was ignored, we applied the sandwich estimator to adjust the standard error. Hence, the quantile estimation at 10-, 100-, and 1000-years return period was carried out using a modified model. Most of the stations were found to be exceeded the maximum level once every 100-years. 2023 Thesis https://eprints.ums.edu.my/id/eprint/41490/ https://eprints.ums.edu.my/id/eprint/41490/1/24%20PAGES.pdf text en public https://eprints.ums.edu.my/id/eprint/41490/2/FULLTEXT.pdf text en validuser Universiti Malaysia Sabah Faculty Of Science And Natural Resources
institution	Universiti Malaysia Sabah
collection	UMS Institutional Repository
language	English English
topic	QA1-939 Mathematics
spellingShingle	QA1-939 Mathematics Siow, Chen Sian Univariate generalized extreme value approach for spatial extreme event with small sample size: An application to extreme rainfall in Sabah
description	This study aims to model the extreme event with small sample sizes using a univariate Generalized Extreme Value (GEV) distribution. The Maximum Likelihood Estimation (MLE) is the most recommended method for parameter estimation with GEV distribution due to the consistency of the results and wide application in extreme value analysis. However, the MLE performs poorly in small sample sizes, creating uncertainties that may lead to inaccurate estimation. Therefore, the Generalized Maximum Likelihood Estimation (GMLE) was suggested to improve the performance of MLE in modelling the small sample sizes of extreme events. A simulation study was conducted using several methods which are probability weighted moment (PWM), MLE, and GMLE to choose the most suitable parameter estimation of GEV distribution base on bias and root mean square error (RMSE). Other than that, the simulation results showed that GMLE performs better than PWM and MLE for GEV parameter estimations. A case study was conducted by fitting Sabah’s annual maximum rainfall data with small sample sizes into GEV distribution with GMLE as the parameter estimation method. A stationary GEV model, which holds all parameters constant, is compared to a non-stationary model, consisting of a linear function of temperature as the covariate in the location parameter. From the results of the corrected Akaike’s Information Criterion (AICc) and likelihood ratio test, there was insufficient evidence to prove the existence of a trend to the extreme rainfall. Besides, homogeneity testing was conducted for each district using the likelihood ratio test. It showed that all the rainfall stations from these five districts should be modelled independently without common shape parameters. Since the GEV was fitted independently at each site and the inter-dependency between sites was ignored, we applied the sandwich estimator to adjust the standard error. Hence, the quantile estimation at 10-, 100-, and 1000-years return period was carried out using a modified model. Most of the stations were found to be exceeded the maximum level once every 100-years.
format	Thesis
author	Siow, Chen Sian
author_facet	Siow, Chen Sian
author_sort	Siow, Chen Sian
title	Univariate generalized extreme value approach for spatial extreme event with small sample size: An application to extreme rainfall in Sabah
title_short	Univariate generalized extreme value approach for spatial extreme event with small sample size: An application to extreme rainfall in Sabah
title_full	Univariate generalized extreme value approach for spatial extreme event with small sample size: An application to extreme rainfall in Sabah
title_fullStr	Univariate generalized extreme value approach for spatial extreme event with small sample size: An application to extreme rainfall in Sabah
title_full_unstemmed	Univariate generalized extreme value approach for spatial extreme event with small sample size: An application to extreme rainfall in Sabah
title_sort	univariate generalized extreme value approach for spatial extreme event with small sample size: an application to extreme rainfall in sabah
granting_institution	Universiti Malaysia Sabah
granting_department	Faculty Of Science And Natural Resources
publishDate	2023
url	https://eprints.ums.edu.my/id/eprint/41490/1/24%20PAGES.pdf https://eprints.ums.edu.my/id/eprint/41490/2/FULLTEXT.pdf
_version_	1818611411322929152

Univariate generalized extreme value approach for spatial extreme event with small sample size: An application to extreme rainfall in Sabah

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