Estimating 𝐿-Functionals for Heavy-Tailed Distributions and Application
𝐿-functionals summarize numerous statistical parameters and actuarial risk measures. Their sample estimators are linear combinations of order statistics (𝐿-statistics). There exists a class of heavy-tailed distributions for which the asymptotic normality of these estimators cannot be obtained by cla...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2010/707146 |
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| _version_ | 1832554523369930752 |
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| author | Abdelhakim Necir Djamel Meraghni |
| author_facet | Abdelhakim Necir Djamel Meraghni |
| author_sort | Abdelhakim Necir |
| collection | DOAJ |
| description | 𝐿-functionals summarize numerous statistical parameters and actuarial risk
measures. Their sample estimators are linear combinations of order statistics
(𝐿-statistics). There exists a class of heavy-tailed distributions for which the
asymptotic normality of these estimators cannot be obtained by classical results.
In this paper we propose, by means of extreme value theory, alternative
estimators for 𝐿-functionals and establish their asymptotic normality. Our
results may be applied to estimate the trimmed 𝐿-moments and financial risk
measures for heavy-tailed distributions. |
| format | Article |
| id | doaj-art-cda7f16e6e03451b94b042c2f094a87b |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-cda7f16e6e03451b94b042c2f094a87b2025-02-03T05:51:18ZengWileyJournal of Probability and Statistics1687-952X1687-95382010-01-01201010.1155/2010/707146707146Estimating 𝐿-Functionals for Heavy-Tailed Distributions and ApplicationAbdelhakim Necir0Djamel Meraghni1Laboratory of Applied Mathematics, Mohamed Khider University of Biskra, 07000 Biskra, AlgeriaLaboratory of Applied Mathematics, Mohamed Khider University of Biskra, 07000 Biskra, Algeria𝐿-functionals summarize numerous statistical parameters and actuarial risk measures. Their sample estimators are linear combinations of order statistics (𝐿-statistics). There exists a class of heavy-tailed distributions for which the asymptotic normality of these estimators cannot be obtained by classical results. In this paper we propose, by means of extreme value theory, alternative estimators for 𝐿-functionals and establish their asymptotic normality. Our results may be applied to estimate the trimmed 𝐿-moments and financial risk measures for heavy-tailed distributions.http://dx.doi.org/10.1155/2010/707146 |
| spellingShingle | Abdelhakim Necir Djamel Meraghni Estimating 𝐿-Functionals for Heavy-Tailed Distributions and Application Journal of Probability and Statistics |
| title | Estimating 𝐿-Functionals for Heavy-Tailed Distributions and Application |
| title_full | Estimating 𝐿-Functionals for Heavy-Tailed Distributions and Application |
| title_fullStr | Estimating 𝐿-Functionals for Heavy-Tailed Distributions and Application |
| title_full_unstemmed | Estimating 𝐿-Functionals for Heavy-Tailed Distributions and Application |
| title_short | Estimating 𝐿-Functionals for Heavy-Tailed Distributions and Application |
| title_sort | estimating 𝐿 functionals for heavy tailed distributions and application |
| url | http://dx.doi.org/10.1155/2010/707146 |
| work_keys_str_mv | AT abdelhakimnecir estimatinglfunctionalsforheavytaileddistributionsandapplication AT djamelmeraghni estimatinglfunctionalsforheavytaileddistributionsandapplication |