Examining tail index estimators in new Pareto distribution: Monte Carlo simulations and income data applications
An evolved form of Pareto distribution, the new Pareto-type distribution, offers an alternative model for data with heavy-tailed characteristics. This investigation examines and discusses fourteen diverse estimators for the tail index of the new Pareto-type, including estimators such as maximum like...
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/112192/ http://psasir.upm.edu.my/id/eprint/112192/1/112192.pdf |
| _version_ | 1848865879535648768 |
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| author | Mohd Safari, Muhammad Aslam Masseran, Nurulkamal Haron, Mohd Azmi |
| author_facet | Mohd Safari, Muhammad Aslam Masseran, Nurulkamal Haron, Mohd Azmi |
| author_sort | Mohd Safari, Muhammad Aslam |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | An evolved form of Pareto distribution, the new Pareto-type distribution, offers an alternative model for data with heavy-tailed characteristics. This investigation examines and discusses fourteen diverse estimators for the tail index of the new Pareto-type, including estimators such as maximum likelihood, method of moments, maximum product of spacing, its modified version, ordinary least squares, weighted least squares, percentile, Kolmogorov-Smirnov, Anderson-Darling, its modified version, Cramér-von Mises, and Zhang's variants of the previous three. Using Monte Carlo simulations, the effectiveness of these estimators is compared both with and without the presence of outliers. The findings show that, without outliers, the maximum product of spacing, its modified version, and maximum likelihood are the most effective estimators. In contrast, with outliers present, the top performers are Cramér-von Mises, ordinary least squares, and weighted least squares. The study further introduces a graphical method called the new Pareto-type quantile plot for validating the new Pareto-type assumptions and outlines a stepwise process to identify the optimal threshold for this distribution. Concluding the study, the new Pareto-type distribution is employed to model the high-end household income data from Italy and Malaysia, leveraging all the methodologies proposed. |
| first_indexed | 2025-11-15T14:11:43Z |
| format | Article |
| id | upm-112192 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:11:43Z |
| publishDate | 2024 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1121922024-09-25T01:42:07Z http://psasir.upm.edu.my/id/eprint/112192/ Examining tail index estimators in new Pareto distribution: Monte Carlo simulations and income data applications Mohd Safari, Muhammad Aslam Masseran, Nurulkamal Haron, Mohd Azmi An evolved form of Pareto distribution, the new Pareto-type distribution, offers an alternative model for data with heavy-tailed characteristics. This investigation examines and discusses fourteen diverse estimators for the tail index of the new Pareto-type, including estimators such as maximum likelihood, method of moments, maximum product of spacing, its modified version, ordinary least squares, weighted least squares, percentile, Kolmogorov-Smirnov, Anderson-Darling, its modified version, Cramér-von Mises, and Zhang's variants of the previous three. Using Monte Carlo simulations, the effectiveness of these estimators is compared both with and without the presence of outliers. The findings show that, without outliers, the maximum product of spacing, its modified version, and maximum likelihood are the most effective estimators. In contrast, with outliers present, the top performers are Cramér-von Mises, ordinary least squares, and weighted least squares. The study further introduces a graphical method called the new Pareto-type quantile plot for validating the new Pareto-type assumptions and outlines a stepwise process to identify the optimal threshold for this distribution. Concluding the study, the new Pareto-type distribution is employed to model the high-end household income data from Italy and Malaysia, leveraging all the methodologies proposed. Penerbit Universiti Kebangsaan Malaysia 2024 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/112192/1/112192.pdf Mohd Safari, Muhammad Aslam and Masseran, Nurulkamal and Haron, Mohd Azmi (2024) Examining tail index estimators in new Pareto distribution: Monte Carlo simulations and income data applications. Sains Malaysiana, 53 (2). pp. 461-476. ISSN 0126-6039; EISSN: 2735-0118 https://www.ukm.my/jsm/pdf_files/SM-PDF-53-2-2024/18.pdf 10.17576/jsm-2024-5302-18 |
| spellingShingle | Mohd Safari, Muhammad Aslam Masseran, Nurulkamal Haron, Mohd Azmi Examining tail index estimators in new Pareto distribution: Monte Carlo simulations and income data applications |
| title | Examining tail index estimators in new Pareto distribution: Monte Carlo simulations and income data applications |
| title_full | Examining tail index estimators in new Pareto distribution: Monte Carlo simulations and income data applications |
| title_fullStr | Examining tail index estimators in new Pareto distribution: Monte Carlo simulations and income data applications |
| title_full_unstemmed | Examining tail index estimators in new Pareto distribution: Monte Carlo simulations and income data applications |
| title_short | Examining tail index estimators in new Pareto distribution: Monte Carlo simulations and income data applications |
| title_sort | examining tail index estimators in new pareto distribution: monte carlo simulations and income data applications |
| url | http://psasir.upm.edu.my/id/eprint/112192/ http://psasir.upm.edu.my/id/eprint/112192/ http://psasir.upm.edu.my/id/eprint/112192/ http://psasir.upm.edu.my/id/eprint/112192/1/112192.pdf |