Sains Malaysiana 46(6)(2017): 989–999

http://dx.doi.org/10.17576/jsm-2017-4606-19

 

Pemodelan Taburan Kebarangkalian Zarah Terampai Melampau di Lembah Klang

(Modelling of Probability Distributions of Extreme Particulate Matter in Klang Valley)

 

MUHAMMAD ASLAM MOHD SAFARI* & WAN ZAWIAH WAN ZIN

 

Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

 

Diserahkan: 2 Oktober 2015/Diterima: 7 Disember 2016

 

 

ABSTRAK

Kajian ini bertujuan untuk mengenal pasti model statistik terbaik bagi mewakili set data melampau untuk salah satu bahan pencemaran udara iaitu zarah terampai (PM10). Data dari enam buah stesen pengawasan kualiti udara di sekitar Lembah Klang dari tahun 2009 hingga 2011 digunakan dalam kajian ini. Dalam penentuan taburan terbaik, taburan parametrik dan taburan tak berparameter telah diuji. Dua siri data melampau yang digunakan ialah siri data maksimum bulanan dan siri data melangkaui ambang bagi PM10. Seterusnya, dua taburan parametrik iaitu Taburan Melampau Teritlak (GEV) dan Taburan Pareto Teritlak (GPD) masing-masing dipadankan kepada siri data maksimum bulanan dan siri data melangkaui ambang. Kaedah penganggaran parameter L-momen dan ujian kebagusan penyuaian Anderson Darling digunakan dalam pemilihan taburan parametrik terbaik yang juga menentukan kaedah pemilihan data melampau yang mana lebih baik. Bagi kaedah tak berparameter, penganggaran fungsi ketumpatan kernel (KDE) digunakan untuk menentukan taburan terbaik PM10 melampau. Hasil pengiraan ralat min kuasa dua (MSE) mendapati taburan tak berparameter merupakan taburan terbaik bagi data melampau PM10 di kebanyakan stesen kajian. Taburan terbaik bagi setiap stesen kajian seterusnya digunakan bagi menghitung tempoh ulangan PM10 yang sangat berguna bagi pihak yang terbabit.

 

Kata kunci: Fungsi ketumpatan kernel; L-momen; PM10; taburan Nilai Melampau Teritlak; taburan pareto teritlak; taburan tak berparameter; ujian penyuaian Anderson Darling

 

ABSTRACT

This study aims to identify the best statistical model to represent the data set for one of the air pollutants that is the particulate matter with diameters smaller than 10 micrometers (PM10). Data from six air quality monitoring stations in the Klang Valley from 2009 to 2011 were used in this study. In determining the more appropriate probability distribution, both parametric and non-parametric approaches were tested. Two series of extreme data for PM10 were used, which are the monthly maximum and the Peak over threshold data series. Next, two parametric distributions, which are the Generalized Extreme Value (GEV) and Generalized Pareto (GPD) were fitted to the monthly maximum and the Peak over threshold data series, respectively. L-moment parameter estimation method and Anderson Darling goodness of fit test were used to identify the best parametric distribution as well as the more suitable data series to represent extreme data. For the non-parametric approach, the kernel density estimation (KDE) is used in this study to determine the best distribution for extreme PM10. Based on the mean squared error (MSE) results, it is found that the nonparametric distribution is the best distribution for extreme PM10 data from most of the air quality monitoring stations. The best distribution for each air quality monitoring station is then used to estimate several return periods for extreme PM10 which are very useful for relevant authorities.

 

Keywords: Anderson Darling goodness of fit test; generalized extreme value; generalized pareto; kernel density estimation; L-moments; non-parametric distribution; PM10

 

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*Pengarang untuk surat-menyurat; email: aslammohdsafari@gmail.com

 

 

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