Asymmetric Kernels for Boundary Modification in Distribution Function Estimation
Kernel-type estimators are popular in density and distribution function estimation. However, they suffer from boundary effects. In order to modify this drawback, this study has proposed two new kernel estimators for the cumulative distribution function based on two asymmetric kernels including the...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2021-12-01
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| Series: | Revstat Statistical Journal |
| Subjects: | |
| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/350 |
| _version_ | 1817998329270763520 |
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| author | Habib Allah Mombeni Behzad Mansouri MohammadReza Akhoond |
| author_facet | Habib Allah Mombeni Behzad Mansouri MohammadReza Akhoond |
| author_sort | Habib Allah Mombeni |
| collection | DOAJ |
| description |
Kernel-type estimators are popular in density and distribution function estimation. However, they suffer from boundary effects. In order to modify this drawback, this study has proposed two new kernel estimators for the cumulative distribution function based on two asymmetric kernels including the Birnbaum–Saunders kernel and the Weibull kernel. We show the asymptotic convergence of our proposed estimators in boundary as well as interior design points. We illustrate the performance of our proposed estimators using a numerical study and show that our proposed estimators outperform the other commonly used methods. The illustration of our proposed estimators to a real data set indicates that they provide better estimates than those of the formerly-known methodologies.
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| first_indexed | 2024-04-14T02:51:38Z |
| format | Article |
| id | doaj.art-8c96d198b0284cbb9e9d345059a25a2e |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-14T02:51:38Z |
| publishDate | 2021-12-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-8c96d198b0284cbb9e9d345059a25a2e2022-12-22T02:16:16ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712021-12-0119410.57805/revstat.v19i4.350Asymmetric Kernels for Boundary Modification in Distribution Function EstimationHabib Allah Mombeni 0Behzad Mansouri 1MohammadReza Akhoond 2Shahid Chamran University of AhvazShahid Chamran University of AhvazShahid Chamran University of Ahvaz Kernel-type estimators are popular in density and distribution function estimation. However, they suffer from boundary effects. In order to modify this drawback, this study has proposed two new kernel estimators for the cumulative distribution function based on two asymmetric kernels including the Birnbaum–Saunders kernel and the Weibull kernel. We show the asymptotic convergence of our proposed estimators in boundary as well as interior design points. We illustrate the performance of our proposed estimators using a numerical study and show that our proposed estimators outperform the other commonly used methods. The illustration of our proposed estimators to a real data set indicates that they provide better estimates than those of the formerly-known methodologies. https://revstat.ine.pt/index.php/REVSTAT/article/view/350cumulative distribution functionboundary effectskernel-type estimatorsasymmetric kernels |
| spellingShingle | Habib Allah Mombeni Behzad Mansouri MohammadReza Akhoond Asymmetric Kernels for Boundary Modification in Distribution Function Estimation Revstat Statistical Journal cumulative distribution function boundary effects kernel-type estimators asymmetric kernels |
| title | Asymmetric Kernels for Boundary Modification in Distribution Function Estimation |
| title_full | Asymmetric Kernels for Boundary Modification in Distribution Function Estimation |
| title_fullStr | Asymmetric Kernels for Boundary Modification in Distribution Function Estimation |
| title_full_unstemmed | Asymmetric Kernels for Boundary Modification in Distribution Function Estimation |
| title_short | Asymmetric Kernels for Boundary Modification in Distribution Function Estimation |
| title_sort | asymmetric kernels for boundary modification in distribution function estimation |
| topic | cumulative distribution function boundary effects kernel-type estimators asymmetric kernels |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/350 |
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