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Closed-Form Estimation for the Pareto Distribution Based on Logarithmic Moments | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 6، شماره 2، مهر 2026، صفحه 159-182 اصل مقاله (499.98 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2026.91047.1253 | ||
| نویسندگان | ||
| Zahra Karimiezmareh* 1؛ Ghazal Elahi2 | ||
| 1Department of Statistics, Faculty of Statistics, Mathematics and Computer, Allameh Tabataba’i University Tehran, Iran | ||
| 2Department of Statistics, Faculty of Statistics, Mathematics and Computer, Allameh Tabataba’i University, Tehran, Iran | ||
| چکیده | ||
| The Pareto distribution is a cornerstone for modeling heavy-tailed phenomena in fields like economics, finance, and risk management. While maximum likelihood (ML) estimation is prevalent, its estimators lack closed-form expressions, requiring iterative numerical methods. This paper introduces closed-form estimators for the Pareto distribution using the method of logarithmic moments. The proposed estimators are computationally simple and eliminate convergence issues associated with ML. We derive their large-sample properties, establishing consistency. For comparative purposes, L-moments estimators for the Pareto distribution are also considered. A comprehensive simulation study demonstrates that the proposed logarithmic moments estimators perform competitively with ML for heavy-tailed distributions. Moreover, an empirical application to real-world fire insurance claims data confirms the practical advantages of the proposed method, where it achieves a better fit compared to ML. The combination of closed-form simplicity, competitive performance in heavy-tailed settings, and computational efficiency makes the proposed estimators a powerful and practical alternative for rapid data analysis, pedagogical purposes, and applications with limited computational resources. | ||
| کلیدواژهها | ||
| Pareto Distribution؛ Logarithmic Moments؛ Closed-Form Estimators؛ Asymptotic Properties | ||
| مراجع | ||
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