Univariate generalized extreme value approach for spatial extreme event with small sample size: An application to extreme rainfall in Sabah - Siow, Chen Sian (2023)
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.