Sains Malaysiana 51(10)(2022): 3437-3448

http://doi.org/10.17576/jsm-2022-5110-26

Modeling the Incomes of the Upper-Class Group in Malaysia using New Pareto-Type Distribution

(Pemodelan Pendapatan Isi Rumah Kelas Atas di Malaysia menggunakan Taburan Pareto Jenis Baharu)

ANIS SYAZWANI ABD RAOF¹, MOHD AZMI HARON^1,*, MUHAMMAD ASLAM MOHD SAFARI² & ZAILAN SIRI¹

¹Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

²Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor Darul Ehsan, Malaysia

Received: 11 September 2021/Accepted: 23 May 2022

Abstract

The new Pareto-type distribution has been previously introduced as an alternative to the conventional Pareto distribution in modeling income distribution. It is claimed to provide better flexibility for mathematical simplicity of probability functions and has a more straightforward mathematical form. In this study, the new Pareto-type distribution is used to model the income of the Malaysian upper-class group. The threshold is determined using the fixed proportion technique and the maximum likelihood estimator method is used to estimate the shape parameter. Then, the goodness-of-fit of the fitted new Pareto model is measured using the coefficient of determination, R² and Kolmogorov–Smirnov statistics. We also measure the income inequality among the Malaysian top income earners using the Lorenz curve, Gini and Theil indices based on the fitted new Pareto model. Finally, the new Pareto distribution is compared to alternative distributions to analyze which model can give the best fit for the data. Our analysis shows that the Pareto type-1 and the new Pareto models are well fitted to the top income data for all years considered. However, the new Pareto model provides better flexibility which covering more incomes in the upper tail of the distribution than the Pareto type-1 model.

Keywords: Gini index; income inequality; Lorenz curve; Pareto model; Theil index

Abstrak

Taburan Pareto baharu telah diperkenalkan sebagai alternatif kepada taburan Pareto konvensional dalam permodelan taburan pendapatan. Kelebihan menggunakan taburan Pareto baharu dapat dilihat dari segi bentuk fungsinya yang mudah dan lebih fleksibel dalam memodelkan data. Dalam kajian ini, taburan Pareto baharu digunakan untuk memodelkan data pendapatan isi rumah kelas atas di Malaysia. Anggaran nilai ambang dan nilai parameter bentuk bagi taburan Pareto baharu, masing-masing ditentukan menggunakan teknik pernisbahan tetap dan kaedah anggaran kebolehjadian maksimum. Seterusnya, kebagusan penyuaian taburan Pareto baharu terhadap data pendapatan kelas atas dinilai menggunakan pekali penentuan, R² dan statistik Kolmogorov–Smirnov. Kajian ini juga mengukur ketaksamaan pendapatan antara golongan atas menggunakan keluk Lorenz, indeks Gini dan indeks Theil berdasarkan taburan Pareto baharu. Akhir sekali, perbandingan antara taburan Pareto baharu dan pelbagai taburan lain dilakukan bagi mengenal pasti taburan yang mampu memberikan penyuaian terbaik dalam menerangkan data pendapatan kelas atas. Hasil kajian mendapati kedua-dua taburan Pareto baharu dan Pareto jenis-1 mampu menerangkan data pendapatan kelas atas. Namun, taburan Pareto baharu memberikan kefleksibelan yang lebih baik dan taburan ini mampu untuk menerangkan data pendapatan yang lebih banyak berbanding taburan Pareto jenis-1.

Kata kunci: Indeks Gini; indeks Theil; keluk Lorenz; ketaksamaan pendapatan; model Pareto

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^*Corresponding author; email: azmiharon@um.edu.my