Page 422 - Contributed Paper Session (CPS) - Volume 6

CPS2008 Syafrina A.H et al.

Fitting statistical models to daily rainfall data
using gamma and weibull distributions
Syafrina Abdul Halim, Aqilah Halit
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM
Serdang, Selangor

Abstract
Rainfall modelling is valuable to predict the rainfall pattern and assist to
prepare for awareness of the extreme weather. In this study, two probability
distributions namely Gamma and Weibull distributions were fitted to daily
rainfall data for a period of 27 years (1990-2017) at Penang International
Airport. The parameters for each distribution were estimated by using
Maximum Likelihood Estimation (MLE) method. The model that best described
the data was chosen by using Goodness of Fit (GOF) test, known as Cramer-
Von Mises (CvM) and Kolmogorov-Smirnov (K-S). Based on the result of the
GOF test, Weibull distribution was the best model.

Keywords
Cramer-Von Mises; Gamma; Kolmogorov-Smirnov; Maximum Likelihood
Estimation; Weibull

1. Introduction
Malaysia is one of the Southeast Asia’s country that has tropical climate
seasons. Malaysia is located at north of the equator which has two non-
contiguous regions namely West Malaysia (Peninsular Malaysia) and East
Malaysia. By lying on the equator gives the climate being hot and humid
throughout the year with the average temperatures between 22°C and 32°C.
The humidity commonly affected by four seasonal monsoons, specifically
named as Southwest monsoon (May to August), Northeast monsoon
(November to February) and two inter-monsoon seasons (March to April and
September to October) (Syafrina et al., 2015). Minimal rain was received at
northern region in Peninsular Malaysia such as Perlis, Kedah, Penang and
Perak since Titiwangsa Range blocks the region from getting rain by the north
easterly winds (Syafrina et al., 2015). However, in many decades ago, Penang
recorded a history due to the widespread flooding on 24 November 1932
when 15 inches (about 380mm) of rainfall was recorded over a 14-hour spell
(Netto, 2017). As a result, there are various natural disasters such as flash
floods, fallen trees, landslides and home roof damage. According to Suhaila
and Abdul (2007), mathematical modelling could be used to get better
information on rainfall pattern and its characteristics. In Southwestern region

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