A. Nurul Amalia(1*), Muhammad Arif Tiro(2), Aswi Aswi(3),

(1) Prodi Statistika, FMIPA, Universitas Negeri Makassar
(2) Prodi Statistika, FMIPA, Universitas Negeri Makassar
(3) Prodi Statistika, FMIPA, Universitas Negeri Makassar
(*) Corresponding Author



This study examines the estimation of Pareto distribution parameters using three different methods, namely the Moment, Maximum Likelihood, and Bayesian methods. The Pareto distribution is a continuous distribution with parameters k > 0 and α > 0. These two parameters are estimated by using three distinct parameter estimation methods. The goodness of fit measure used in choosing the best estimation method is the Mean Square Error (MSE) value. The smallest MSE is the best method. A simulation study is carried out as well as the case study of the data on the number of Gross National Income (GNI) per capita in Southeast Asian countries in 2019. The estimation and simulation results indicate that the best estimation method in estimating the parameters of the Pareto distribution is the Maximum Likelihood in terms of MSE value.

Keywords: Pareto distribution, Moment Method, Maximum Likelihood IMethod, Bayesian Method

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Arnold, B. C. (2015). Pareto Distribution Second Edition. Boca Raton: CRC Press.

Bain, L. J., & Engelhardt, M. (1992). Introduction to Probability and Mathematical Statistics: Second Edition. USA: Brooks/Cole.

Casella, G., & Berger, R. L. (2002). Statistical Inference, Second Edition. USA: Thomson Learning.

Chotikapanich, D. (2008). Modelling Income Distribution and Lorenz Curves. New York: Springer.

Hogg, R. V., McKean, J. W., & Craig, A. T. (2005). Introduction to Mathematical Statistics: Sixth Edition. USA: Pearson Prentice Hall.

Kleiber, C., & Kotz, S. (2003). Statistical Size Distributions in Economics and Acturial Sciences. New Jersey: John Wiley & Sons International.

Montgomery, D. C., & Runger, G. C. (2014). Applied Statistics and Probability for Engineers. USA: John Wiley & Sons.

Pangestu, M. A., & Eliyah, S. (2018, Maret 25). Scribd. Retrieved April 4, 2020, from

Quandt, R. E. (1964). Old and New Methods of Estimation and the Pareto Distribution. Research Memorandum No. 70, 55-82.

Ridiani, F. (n.d.). Pendugaan Parameter Distribusi Beta dengan Metode Momen dan Metode Maksimum Likelihood. Jurnal Matematika UNAND, Vol. 3 No. 2 Hal. 23-28.

Rosenkrantz, W. (2009). Introduction to Probability and Statistics for Science, Engineering, and Finance. USA: CRC Press.

Sahoo, P. (2008). Probability and Mathematical Statistics. Louisville: University of Louisville.

Setiya, P., Kumar, V., & Pande, M. K. (2016). Bayesian Estimation of Scale Parameter of Pareto Type I Distribution by Two Different Methods. Thailand Statistician, 47-62.

Sudjana. (1986). Metoda Statistika Edisi ke IV. Bandung: Tarsito.

Tiro, M. A. (2015). Dasar-Dasar Statistika Edisi Keempat. Makassar: Andira Publisher.

Tiro, M. A., Sukarna, & Aswi. (2014). Pengantar Teori Peluang. Makassar: Andira Publisher.

Warsono, Gustavia, E., Kurniasari, D., Amanto, & Antonio, Y. (2019). On the Comparison of the Methods of Parameter Estimation for Pareto Distribution. Journal of Physics: Conference Series.

Will, K. (2008, April 3). Advantages of Method of Moments Estimators. Retrieved April 19, 2020, from TAMU Stat:

Yanuar, F., Saputri, C., & Devianto, D. (2020). Bayesian Inference for Pareto Distribution with Prior Conjugate and Prior Non Conjugate. Jurnal Matematika, Statistika & Komputasi, 382-390

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