Sains Malaysiana 47(8)(2018): 1931–1940

http://dx.doi.org/10.17576/jsm-2018-4708-35

 

The Extra Zeros in Traffic Accident Data: A Study on the Mixture of Discrete Distributions

(Lebihan Sifar dalam Data Kemalangan Jalan Raya: Satu Kajian bagi Taburan Diskret Campuran)

 

ZAMIRA HASANAH ZAMZURI*, MOHD SYAFIQ SAPUAN & KAMARULZAMAN IBRAHIM

 

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

 

Diserahkan: 29 Mac 2018/Diterima: 2 April 2018

 

 

ABSTRACT

The presence of extra zeros is commonly observed in traffic accident count data. Past research opt to the zero altered models and explain that the zeros are sourced from under reporting situation. However, there is also an argument against this statement since the zeros could be sourced from Poisson trial process. Motivated by the argument, we explore the possibility of mixing several discrete distributions that can contribute to the presence of extra zeros. Four simulation studies were conducted based on two accident scenarios and two discrete distributions: Poisson and negative binomial; by considering six combinations of proportion values correspond to low, moderate and high mean values in the distribution. The results of the simulation studies concur with the claim as the presence of extra zeros is detected in most cases of mixed Poisson and mixed negative binomial data. Data sets that are dominated by Poisson (or negative binomial) with low mean show an apparent existence of extra zeros although the sample size is only 30. An illustration using a real data set concur the same findings. Hence, it is essential to consider the mixed discrete distributions as potential distributions when dealing with count data with extra zeros. This study contributes on creating awareness of the possible alternative distributions for count data with extra zeros especially in traffic accident applications.

 

Keywords: Hurdle models; negative binomial; Poisson; proportion; simulation study; traffic accident; zero-inflated models

 

ABSTRAK

Kehadiran lebihan sifar sering dicerap dalam data bilangan kemalangan jalan raya. Kajian lepas cenderung kepada penggunaan model dengan ubah suaian sifar dan menjelaskan bahawa lebihan sifar ini berpunca daripada keadaan kemalangan tidak terlapor. Walau bagaimanapun, terdapat tentangan terhadap pernyataan ini dengan kehadiran lebihan sifar ini boleh berpunca daripada campuran beberapa taburan diskret yang mewakili taburan bagi masa atau lokasi berbeza. Maka, kajian ini bermatlamat untuk meneroka teori bahawa taburan disket tercampur boleh menyumbang kepada lebihan sifar dalam data bilangan. Empat kajian simulasi dijalankan berdasarkan dua senario kemalangan dan dua taburan diskret: Poisson dan binomial negatif; dengan mengambil kira enam gabungan nilai perkadaran bagi nilai purata rendah, sederhana dan tinggi dalam taburan tersebut. Keputusan kajian bersetuju dengan teori tersebut dengan kehadiran lebihan sifar dapat dikenal pasti dalam kebanyakan kes data Poisson tercampur dan binomial negatif tercampur. Set data yang didominasi oleh Poisson (atau binomial negatif) dengan nilai purata rendah menunjukkan bilangan lebihan sifar yang ketara walaupun saiz sampel hanyalah 30. Oleh itu, adalah amat penting bagi pengkaji untuk mengambil kira taburan diskret tercampur ini apabila berhadapan data bilangan dengan lebihan sifar. Kajian ini menyumbang dalam mencetus kesedaran berkenaan potensi taburan alternatif untuk data bilangan terlebih sifar terutamanya dalam aplikasi kemalangan jalan raya.

 

Kata kunci: Binomial negatif; kajian simulasi; kemalangan jalan raya; model lebihan sifar; model terpangkas; perkadaran; Poisson

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*Pengarang untuk surat-menyurat; email: zamira@ukm.edu.my