A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto Distribution
Estimation based on probability-weighted moments is a well-established method and an excellent alternative to the classic method of moments or the maximum likelihood method, especially for small sample sizes. In this research, we developed a new class of estimators for the parameters of the Pareto t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/5/1076 |
| _version_ | 1797614873763381248 |
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| author | Frederico Caeiro Ayana Mateus |
| author_facet | Frederico Caeiro Ayana Mateus |
| author_sort | Frederico Caeiro |
| collection | DOAJ |
| description | Estimation based on probability-weighted moments is a well-established method and an excellent alternative to the classic method of moments or the maximum likelihood method, especially for small sample sizes. In this research, we developed a new class of estimators for the parameters of the Pareto type I distribution. A generalization of the probability-weighted moments approach is the foundation for this new class of estimators. It has the advantage of being valid in the entire parameter space of the Pareto distribution. We established the asymptotic normality of the new estimators and applied them to simulated and real datasets in order to illustrate their finite sample behavior. The results of comparisons with the most used estimation methods were also analyzed. |
| first_indexed | 2024-03-11T07:18:26Z |
| format | Article |
| id | doaj.art-428c7229cc2a47098c4f05f02ec60791 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T07:18:26Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-428c7229cc2a47098c4f05f02ec607912023-11-17T08:07:51ZengMDPI AGMathematics2227-73902023-02-01115107610.3390/math11051076A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto DistributionFrederico Caeiro0Ayana Mateus1NOVA School of Science and Technology (FCT NOVA) and CMA, Campus de Caparica, NOVA University Lisbon, 2829-516 Caparica, PortugalNOVA School of Science and Technology (FCT NOVA) and CMA, Campus de Caparica, NOVA University Lisbon, 2829-516 Caparica, PortugalEstimation based on probability-weighted moments is a well-established method and an excellent alternative to the classic method of moments or the maximum likelihood method, especially for small sample sizes. In this research, we developed a new class of estimators for the parameters of the Pareto type I distribution. A generalization of the probability-weighted moments approach is the foundation for this new class of estimators. It has the advantage of being valid in the entire parameter space of the Pareto distribution. We established the asymptotic normality of the new estimators and applied them to simulated and real datasets in order to illustrate their finite sample behavior. The results of comparisons with the most used estimation methods were also analyzed.https://www.mdpi.com/2227-7390/11/5/1076asymptotic distributionPareto distributionparameter estimationprobability-weighted moment |
| spellingShingle | Frederico Caeiro Ayana Mateus A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto Distribution Mathematics asymptotic distribution Pareto distribution parameter estimation probability-weighted moment |
| title | A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto Distribution |
| title_full | A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto Distribution |
| title_fullStr | A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto Distribution |
| title_full_unstemmed | A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto Distribution |
| title_short | A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto Distribution |
| title_sort | new class of generalized probability weighted moment estimators for the pareto distribution |
| topic | asymptotic distribution Pareto distribution parameter estimation probability-weighted moment |
| url | https://www.mdpi.com/2227-7390/11/5/1076 |
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