Sains Malaysiana 50(7)(2021): 2047-2058

http://doi.org/10.17576/jsm-2021-5007-19

Composite Pareto Distributions for Modelling Household Income Distribution in Malaysia

(Taburan Komposit Pareto untuk Pemodelan Taburan Pendapatan Isi Rumah di Malaysia)

MUHAMMAD HILMI ABDUL MAJID* & KAMARULZAMAN IBRAHIM

Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

Received: 19 June 2020/Accepted: 19 November 2020

ABSTRACT

Composite Pareto distributions are flexible as the models allow for data to be described by two distributions: a Pareto distribution for the data above a threshold value and another separate distribution for data below the threshold value. It is noted in some previous literatures that the Paretian tail behaviour can be observed in the distribution of Malaysian household income. In this paper, the composite Pareto models are fitted to the Malaysian household income data of several years. These fitted composite Pareto models are then compared to several univariate models for describing income distribution using pseudo-likelihood based AIC, BIC and Kolmogorov-Smirnov goodness-of-fit test. It is found that the income distributions in Malaysia can be best described by the lognormal-Pareto (II) model as compared to other candidate models.

Keywords: Composite model; goodness-of-fit; income distribution; Pareto distribution; pseudo-likelihood

ABSTRAK

Taburan komposit Pareto adalah luwes kerana model ini boleh menerangkan sesuatu data menggunakan dua taburan: taburan Pareto untuk data di atas suatu nilai ambang dan taburan yang berasingan untuk data di bawah nilai ambang tersebut. Kajian sebelum ini telah menyatakan bahawa ciri-ciri ekor Pareto dapat diperhatikan pada taburan pendapatan isi rumah di Malaysia. Dalam kajian ini, model komposit Pareto disuaikan ke atas data pendapatan isi rumah di Malaysia. Model komposit Pareto ini akan dibandingkan dengan model univariat lain untuk menerangkan taburan pendapatan dengan menggunakan AIC, BIC dan ujian kebagusan penyuaian Kolmogorov-Smirnov berasaskan pseudo-kebolehjadian. Kajian mendapati taburan pendapatan di Malaysia boleh diterangkan menggunakan model lognormal-Pareto (II) lebih baik berbanding calon model lain.

Kata kunci: Kebagusan penyuaian; model komposit; pseudo-kebolehjadian; taburan Pareto; taburan pendapatan

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*Corresponding author; email: hilmi.majid@ukm.edu.my