Shrinkage Methods for Estimating the Shape Parameter of the Generalized Pareto Distribution
The generalized Pareto distribution is one of the most important distributions in statistics of extremes as it has wide applications in fields such as finance, insurance, and hydrology. This study proposes two new methods for estimating the shape parameter of the generalized Pareto distribution (GPD...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/9750638 |
| _version_ | 1797545311782043648 |
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| author | Wilhemina Adoma Pels Atinuke O. Adebanji Sampson Twumasi-Ankrah Richard Minkah |
| author_facet | Wilhemina Adoma Pels Atinuke O. Adebanji Sampson Twumasi-Ankrah Richard Minkah |
| author_sort | Wilhemina Adoma Pels |
| collection | DOAJ |
| description | The generalized Pareto distribution is one of the most important distributions in statistics of extremes as it has wide applications in fields such as finance, insurance, and hydrology. This study proposes two new methods for estimating the shape parameter of the generalized Pareto distribution (GPD). The proposed methods use the shrinkage principle to adapt the existing empirical Bayesian with data-based prior and the likelihood moment method to obtain two estimators. The performance of the proposed estimators is compared with the existing estimators (i.e., maximum likelihood, likelihood moment estimators, etc.) for the shape parameter of the generalized Pareto distribution in a simulation study. The results show that the proposed estimators perform better for small to moderate number of exceedances in estimating shape parameter of the light-tailed distributions and competitive when estimating heavy-tailed distributions. The proposed estimators are illustrated with practical datasets from climate and insurance studies. |
| first_indexed | 2024-03-10T14:13:39Z |
| format | Article |
| id | doaj.art-61a2887636a248d881a2b418265803cf |
| institution | Directory Open Access Journal |
| issn | 1687-0042 |
| language | English |
| last_indexed | 2024-03-10T14:13:39Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj.art-61a2887636a248d881a2b418265803cf2023-11-21T00:00:05ZengHindawi LimitedJournal of Applied Mathematics1687-00422023-01-01202310.1155/2023/9750638Shrinkage Methods for Estimating the Shape Parameter of the Generalized Pareto DistributionWilhemina Adoma Pels0Atinuke O. Adebanji1Sampson Twumasi-Ankrah2Richard Minkah3Department of Statistics and Actuarial ScienceDepartment of Statistics and Actuarial ScienceDepartment of Statistics and Actuarial ScienceDepartment of Statistics and Actuarial ScienceThe generalized Pareto distribution is one of the most important distributions in statistics of extremes as it has wide applications in fields such as finance, insurance, and hydrology. This study proposes two new methods for estimating the shape parameter of the generalized Pareto distribution (GPD). The proposed methods use the shrinkage principle to adapt the existing empirical Bayesian with data-based prior and the likelihood moment method to obtain two estimators. The performance of the proposed estimators is compared with the existing estimators (i.e., maximum likelihood, likelihood moment estimators, etc.) for the shape parameter of the generalized Pareto distribution in a simulation study. The results show that the proposed estimators perform better for small to moderate number of exceedances in estimating shape parameter of the light-tailed distributions and competitive when estimating heavy-tailed distributions. The proposed estimators are illustrated with practical datasets from climate and insurance studies.http://dx.doi.org/10.1155/2023/9750638 |
| spellingShingle | Wilhemina Adoma Pels Atinuke O. Adebanji Sampson Twumasi-Ankrah Richard Minkah Shrinkage Methods for Estimating the Shape Parameter of the Generalized Pareto Distribution Journal of Applied Mathematics |
| title | Shrinkage Methods for Estimating the Shape Parameter of the Generalized Pareto Distribution |
| title_full | Shrinkage Methods for Estimating the Shape Parameter of the Generalized Pareto Distribution |
| title_fullStr | Shrinkage Methods for Estimating the Shape Parameter of the Generalized Pareto Distribution |
| title_full_unstemmed | Shrinkage Methods for Estimating the Shape Parameter of the Generalized Pareto Distribution |
| title_short | Shrinkage Methods for Estimating the Shape Parameter of the Generalized Pareto Distribution |
| title_sort | shrinkage methods for estimating the shape parameter of the generalized pareto distribution |
| url | http://dx.doi.org/10.1155/2023/9750638 |
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