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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
https://eprints.ums.edu.my/id/eprint/41490/
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spelling my.ums.eprints.414902024-11-13T02:51:15Z https://eprints.ums.edu.my/id/eprint/41490/ Univariate generalized extreme value approach for spatial extreme event with small sample size: An application to extreme rainfall in Sabah 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 NonPeerReviewed text en https://eprints.ums.edu.my/id/eprint/41490/1/24%20PAGES.pdf text en https://eprints.ums.edu.my/id/eprint/41490/2/FULLTEXT.pdf Siow, Chen Sian (2023) Univariate generalized extreme value approach for spatial extreme event with small sample size: An application to extreme rainfall in Sabah. UNSPECIFIED thesis, Universiti Malaysia Sabah.
institution Universiti Malaysia Sabah
building UMS Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Sabah
content_source UMS Institutional Repository
url_provider http://eprints.ums.edu.my/
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
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
https://eprints.ums.edu.my/id/eprint/41490/
_version_ 1816131854064943104
score 13.222552

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