Estimation of the Tail Index of Pareto-Type Distributions Using Regularisation
In this paper, we introduce reduced-bias estimators for the estimation of the tail index of Pareto-type distributions. This is achieved through the use of a regularised weighted least squares with an exponential regression model for log-spacings of top-order statistics. The asymptotic properties of...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/5064875 |
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| author | E. Ocran R. Minkah G. Kallah-Dagadu K. Doku-Amponsah |
| author_facet | E. Ocran R. Minkah G. Kallah-Dagadu K. Doku-Amponsah |
| author_sort | E. Ocran |
| collection | DOAJ |
| description | In this paper, we introduce reduced-bias estimators for the estimation of the tail index of Pareto-type distributions. This is achieved through the use of a regularised weighted least squares with an exponential regression model for log-spacings of top-order statistics. The asymptotic properties of the proposed estimators are investigated analytically and found to be asymptotically unbiased, asymptotically consistent, and asymptotically normally distributed. Also, the finite sample behaviour of the estimators are studied through a simulation study The proposed estimators were found to yield low bias and mean square errors. In addition, the proposed estimators are illustrated through the estimation of the tail index of the underlying distribution of claims from the insurance industry. |
| format | Article |
| id | doaj-art-6c8014fc40c94f418e43f46386a61256 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-6c8014fc40c94f418e43f46386a612562025-02-03T01:22:43ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/5064875Estimation of the Tail Index of Pareto-Type Distributions Using RegularisationE. Ocran0R. Minkah1G. Kallah-Dagadu2K. Doku-Amponsah3Department of Statistics and Actuarial ScienceDepartment of Statistics and Actuarial ScienceDepartment of Statistics and Actuarial ScienceDepartment of Statistics and Actuarial ScienceIn this paper, we introduce reduced-bias estimators for the estimation of the tail index of Pareto-type distributions. This is achieved through the use of a regularised weighted least squares with an exponential regression model for log-spacings of top-order statistics. The asymptotic properties of the proposed estimators are investigated analytically and found to be asymptotically unbiased, asymptotically consistent, and asymptotically normally distributed. Also, the finite sample behaviour of the estimators are studied through a simulation study The proposed estimators were found to yield low bias and mean square errors. In addition, the proposed estimators are illustrated through the estimation of the tail index of the underlying distribution of claims from the insurance industry.http://dx.doi.org/10.1155/2022/5064875 |
| spellingShingle | E. Ocran R. Minkah G. Kallah-Dagadu K. Doku-Amponsah Estimation of the Tail Index of Pareto-Type Distributions Using Regularisation Journal of Mathematics |
| title | Estimation of the Tail Index of Pareto-Type Distributions Using Regularisation |
| title_full | Estimation of the Tail Index of Pareto-Type Distributions Using Regularisation |
| title_fullStr | Estimation of the Tail Index of Pareto-Type Distributions Using Regularisation |
| title_full_unstemmed | Estimation of the Tail Index of Pareto-Type Distributions Using Regularisation |
| title_short | Estimation of the Tail Index of Pareto-Type Distributions Using Regularisation |
| title_sort | estimation of the tail index of pareto type distributions using regularisation |
| url | http://dx.doi.org/10.1155/2022/5064875 |
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