Maximum lq-likelihood estimator of the heavy-tailed distribution parameter
Studying the extreme value theory (EVT) involves multiple main objectives, among them the estimation of the tail index parameter. Some estimation methods are used to estimate the tail index parameter like maximum likelihood estimation (MLE). Additionally, the Hill estimator is one type of maximum li...
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| Format: | Article |
| Language: | English |
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Croatian Statistical Association
2024-01-01
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| Series: | Croatian Review of Economic, Business and Social Statistics |
| Subjects: | |
| Online Access: | https://hrcak.srce.hr/file/466649 |
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| _version_ | 1850221383634649088 |
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| author | Mohammed Ridha Kouider Nesrine Idiou Samia Toumi Fatah Benatia |
| author_facet | Mohammed Ridha Kouider Nesrine Idiou Samia Toumi Fatah Benatia |
| author_sort | Mohammed Ridha Kouider |
| collection | DOAJ |
| description | Studying the extreme value theory (EVT) involves multiple main objectives, among them the estimation of the tail index parameter. Some estimation methods are used to estimate the tail index parameter like maximum likelihood estimation (MLE). Additionally, the Hill estimator is one type of maximum likelihood estimator, which is a more robust with a large sample than a small sample. This research proposes the construction of an alternative estimator for the parameter of the heavy-tailed distribution using the maximum lq-likelihood estimation (MLqE) approach in order to adapt the ML and Hill estimator with the small sample. Furthermore, the maximum lq-likelihood estimator asymptotic normality is established. Moreover, several simulation studies in order to compare the MLq estimator with the ML estimators are provided. In the excesses over high suitable threshold values the number of the largest observation k will lead to an efficient estimate of the Hill estimator. For this, selection of k in the Hill estimator was investigated using the method of the quantile type 8 which is effective with the hydrology data. The performance of the Hill estimator and the lq-Hill estimator is subsequently compared by employing real relies with the distribution of hydrology data. |
| format | Article |
| id | doaj-art-036f37463d474cbfa00cff36dcee3616 |
| institution | OA Journals |
| issn | 1849-8531 2459-5616 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Croatian Statistical Association |
| record_format | Article |
| series | Croatian Review of Economic, Business and Social Statistics |
| spelling | doaj-art-036f37463d474cbfa00cff36dcee36162025-08-20T02:06:44ZengCroatian Statistical AssociationCroatian Review of Economic, Business and Social Statistics1849-85312459-56162024-01-01102294810.62366/crebss.2024.2.003Maximum lq-likelihood estimator of the heavy-tailed distribution parameterMohammed Ridha Kouider0Nesrine Idiou1Samia Toumi2Fatah Benatia3Mohamed Khider University of Biskra, AlgeriaSalah Boubnider University of Constantine 3, AlgeriaMohamed Khider University of Biskra, AlgeriaMohamed Khider University of Biskra, AlgeriaStudying the extreme value theory (EVT) involves multiple main objectives, among them the estimation of the tail index parameter. Some estimation methods are used to estimate the tail index parameter like maximum likelihood estimation (MLE). Additionally, the Hill estimator is one type of maximum likelihood estimator, which is a more robust with a large sample than a small sample. This research proposes the construction of an alternative estimator for the parameter of the heavy-tailed distribution using the maximum lq-likelihood estimation (MLqE) approach in order to adapt the ML and Hill estimator with the small sample. Furthermore, the maximum lq-likelihood estimator asymptotic normality is established. Moreover, several simulation studies in order to compare the MLq estimator with the ML estimators are provided. In the excesses over high suitable threshold values the number of the largest observation k will lead to an efficient estimate of the Hill estimator. For this, selection of k in the Hill estimator was investigated using the method of the quantile type 8 which is effective with the hydrology data. The performance of the Hill estimator and the lq-Hill estimator is subsequently compared by employing real relies with the distribution of hydrology data.https://hrcak.srce.hr/file/466649excesses over thresholdextreme value indexheavy-tailed distributionmaximum lq-likelihood estimator |
| spellingShingle | Mohammed Ridha Kouider Nesrine Idiou Samia Toumi Fatah Benatia Maximum lq-likelihood estimator of the heavy-tailed distribution parameter Croatian Review of Economic, Business and Social Statistics excesses over threshold extreme value index heavy-tailed distribution maximum lq-likelihood estimator |
| title | Maximum lq-likelihood estimator of the heavy-tailed distribution parameter |
| title_full | Maximum lq-likelihood estimator of the heavy-tailed distribution parameter |
| title_fullStr | Maximum lq-likelihood estimator of the heavy-tailed distribution parameter |
| title_full_unstemmed | Maximum lq-likelihood estimator of the heavy-tailed distribution parameter |
| title_short | Maximum lq-likelihood estimator of the heavy-tailed distribution parameter |
| title_sort | maximum lq likelihood estimator of the heavy tailed distribution parameter |
| topic | excesses over threshold extreme value index heavy-tailed distribution maximum lq-likelihood estimator |
| url | https://hrcak.srce.hr/file/466649 |
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