Novel closed-form point estimators for the beta distribution
In this paper, we propose and investigate novel closed-form point estimators for the beta distribution. The estimators of the first type are a modified version of Pearson's method of moments. The underlying idea is to involve the sufficient statistics, i.e., log-moments in the moment estimation...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-11-01
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| Series: | Statistical Theory and Related Fields |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/24754269.2024.2419360 |
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| _version_ | 1846172704657375232 |
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| author | Piao Chen Xun Xiao |
| author_facet | Piao Chen Xun Xiao |
| author_sort | Piao Chen |
| collection | DOAJ |
| description | In this paper, we propose and investigate novel closed-form point estimators for the beta distribution. The estimators of the first type are a modified version of Pearson's method of moments. The underlying idea is to involve the sufficient statistics, i.e., log-moments in the moment estimation equations and solve the mixed type of moment equations simultaneously. The estimators of the second type are based on an approximation to Fisher's likelihood principle. The idea is to solve two score equations derived from the log-likelihood function of generalized beta distributions. Both two resulted estimators are in closed forms, strongly consistent and asymptotically normal. In addition, through theoretical analyses and extensive simulations, the proposed estimators are shown to perform very close to the maximum likelihood estimators in both small and large samples, and they significantly outperform the method of moment estimators. |
| format | Article |
| id | doaj-art-ee6c6a4edefc45fdaf4bb9f24925fece |
| institution | Kabale University |
| issn | 2475-4269 2475-4277 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Statistical Theory and Related Fields |
| spelling | doaj-art-ee6c6a4edefc45fdaf4bb9f24925fece2024-11-09T10:02:00ZengTaylor & Francis GroupStatistical Theory and Related Fields2475-42692475-42772024-11-0111710.1080/24754269.2024.2419360Novel closed-form point estimators for the beta distributionPiao Chen0Xun Xiao1State Key Laboratory of Biobased Transportation Fuel Technology, ZJUI Institute, Zhejiang University, Haining, People's Republic of ChinaDepartment of Mathematics and Statistics, University of Otago, Dunedin, New ZealandIn this paper, we propose and investigate novel closed-form point estimators for the beta distribution. The estimators of the first type are a modified version of Pearson's method of moments. The underlying idea is to involve the sufficient statistics, i.e., log-moments in the moment estimation equations and solve the mixed type of moment equations simultaneously. The estimators of the second type are based on an approximation to Fisher's likelihood principle. The idea is to solve two score equations derived from the log-likelihood function of generalized beta distributions. Both two resulted estimators are in closed forms, strongly consistent and asymptotically normal. In addition, through theoretical analyses and extensive simulations, the proposed estimators are shown to perform very close to the maximum likelihood estimators in both small and large samples, and they significantly outperform the method of moment estimators.https://www.tandfonline.com/doi/10.1080/24754269.2024.2419360Asymptotic efficiencyconsistencyestimation equationlog-momentscore equation |
| spellingShingle | Piao Chen Xun Xiao Novel closed-form point estimators for the beta distribution Statistical Theory and Related Fields Asymptotic efficiency consistency estimation equation log-moment score equation |
| title | Novel closed-form point estimators for the beta distribution |
| title_full | Novel closed-form point estimators for the beta distribution |
| title_fullStr | Novel closed-form point estimators for the beta distribution |
| title_full_unstemmed | Novel closed-form point estimators for the beta distribution |
| title_short | Novel closed-form point estimators for the beta distribution |
| title_sort | novel closed form point estimators for the beta distribution |
| topic | Asymptotic efficiency consistency estimation equation log-moment score equation |
| url | https://www.tandfonline.com/doi/10.1080/24754269.2024.2419360 |
| work_keys_str_mv | AT piaochen novelclosedformpointestimatorsforthebetadistribution AT xunxiao novelclosedformpointestimatorsforthebetadistribution |