Sains Malaysiana 41(11)(2012): 1403–1410

Preliminary Study on Bayesian Extreme Rainfall Analysis: A Case Study

of Alor Setar, Kedah, Malaysia

(Kajian Awal bagi Analisis Kehujanan Melampau Bayes: Kajian Kes

di Alor Setar, Kedah, Malaysia)

Annazirin Eli*

Department of Science in Engineering, Faculty of Engineering

International Islamic University Malaysia, 50728 Gombak, Kuala Lumpur, Malaysia

Mardhiyyah Shaffie & Wan Zawiah Wan Zin

School of Mathematical Siences, Faculty of Science and Technology

Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Diserahkan: 10 Oktober 2011 / Diterima: 18 Jun 2012

ABSTRACT

Statistical modeling of extreme rainfall is essential since the results can often facilitate civil engineers and planners to estimate the ability of building structures to survive under the utmost extreme conditions. Data comprising of annual maximum series (AMS) of extreme rainfall in Alor Setar were fitted to generalized extreme value (GEV) distribution using method of maximum likelihood (ML) and Bayesian Markov Chain Monte Carlo (MCMC) simulations. The weakness of ML method in handling small sample is hoped to be tackled by means of Bayesian MCMC simulations in this study. In order to obtain the posterior densities, non-informative and independent priors were employed. Performances of parameter estimations were verified by conducting several goodness-of-fit tests. The results showed that Bayesian MCMC method was slightly better than ML method in estimating GEV parameters.

Keywords: Annual maximum series; Bayesian MCMC; extreme rainfall analysis; extreme value distribution; generalized maximum likelihood

ABSTRAK

Pemodelan statistik bagi hujan melampau amat penting, memandangkan hasil dapatannya mampu membantu jurutera awam dan pakar runding untuk menjangka kebolehan struktur sesebuah bangunan untuk bertahan dalam situasi yang paling melampau. Data daripada siri maksimum tahunan (AMS) disuaikan menggunakan taburan nilai melampau teritlak (GEV) dengan menggunakan kaedah kebolehjadian maksimum (ML) dan kaedah simulasi Markov Chain Monte Carlo (MCMC) Bayes. Kelemahan kaedah ML dalam pengendalian sampel kecil diharap dapat diatasi dengan kaedah simulasi MCMC Bayes. Bagi mendapatkan taburan posterior, taburan prior tak-bermaklumat dan tak-bersandar digunakan. Padanan bagi parameter yang dicadangkan disahkan dengan menjalankan beberapa ujian kebagusan penyuaian (GOF). Hasilnya, didapati kaedah MCMC Bayes memberikan anggaran yang sedikit lebih baik berbanding kaedah ML bagi menganggar nilai-nilai parameter taburan GEV.

Kata kunci: Kaedah kebolehjadian maksimum; kajian hujan ekstrem; MCMC Bayes; siri maksimum tahunan; taburan nilai ekstrim teritlak

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*Pengarang surat-menyurat; email: annazirin@iium.edu.my