E-Bayesian Estimation of Hierarchical Poisson-Gamma Model on the Basis of Restricted and Unrestricted Parameter Spaces
In this study, we use the idea of the hierarchical model (HM) to estimate an unknown parameter of the hierarchical Poisson-Gamma model using the E-Bayesian (E-B) theory. We propose the idea of hierarchical probability function instead of the traditional hierarchical prior density function. We aim to...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2023/8767200 |
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| author | Azeem Iqbal Laila A. Al-Essa Muhammad Yousaf Shad Fuad S. Alduais Mansour F. Yassen Muhammad Ahmad Raza |
| author_facet | Azeem Iqbal Laila A. Al-Essa Muhammad Yousaf Shad Fuad S. Alduais Mansour F. Yassen Muhammad Ahmad Raza |
| author_sort | Azeem Iqbal |
| collection | DOAJ |
| description | In this study, we use the idea of the hierarchical model (HM) to estimate an unknown parameter of the hierarchical Poisson-Gamma model using the E-Bayesian (E-B) theory. We propose the idea of hierarchical probability function instead of the traditional hierarchical prior density function. We aim to infer E-B estimates with respect to the conjugate Gamma prior distribution along with the E-posterior risks on the basis of different symmetric and asymmetric loss functions (LFs) under restricted and unrestricted parameter spaces using uniform hyperprior. Whereas, E-B estimators are compared with maximum likelihood estimators (MLEs) using mean squared error (MSE). Monte Carlo simulations are prosecuted to study the efficiency of E-B estimators empirically. It is shown that the LFs under a restricted parameter space dominate to estimate the parameter of the hierarchical Poisson-Gamma model. It is also found that the E-B estimators are more precise than MLEs, and Stein’s LF has the least E-PR. Moreover, the application of outcomes to a real-life example has been made for analysis, comparison, and motivation. |
| format | Article |
| id | doaj-art-4dbc151a9c4e4cbcba8d55db5d54da4c |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-4dbc151a9c4e4cbcba8d55db5d54da4c2025-08-20T03:36:22ZengWileyComplexity1099-05262023-01-01202310.1155/2023/8767200E-Bayesian Estimation of Hierarchical Poisson-Gamma Model on the Basis of Restricted and Unrestricted Parameter SpacesAzeem Iqbal0Laila A. Al-Essa1Muhammad Yousaf Shad2Fuad S. Alduais3Mansour F. Yassen4Muhammad Ahmad Raza5Higher Education DepartmentDepartment of Mathematical SciencesDepartment of StatisticsDepartment of MathematicsDepartment of MathematicsFederal Urdu University of Arts Science and TechnologyIn this study, we use the idea of the hierarchical model (HM) to estimate an unknown parameter of the hierarchical Poisson-Gamma model using the E-Bayesian (E-B) theory. We propose the idea of hierarchical probability function instead of the traditional hierarchical prior density function. We aim to infer E-B estimates with respect to the conjugate Gamma prior distribution along with the E-posterior risks on the basis of different symmetric and asymmetric loss functions (LFs) under restricted and unrestricted parameter spaces using uniform hyperprior. Whereas, E-B estimators are compared with maximum likelihood estimators (MLEs) using mean squared error (MSE). Monte Carlo simulations are prosecuted to study the efficiency of E-B estimators empirically. It is shown that the LFs under a restricted parameter space dominate to estimate the parameter of the hierarchical Poisson-Gamma model. It is also found that the E-B estimators are more precise than MLEs, and Stein’s LF has the least E-PR. Moreover, the application of outcomes to a real-life example has been made for analysis, comparison, and motivation.http://dx.doi.org/10.1155/2023/8767200 |
| spellingShingle | Azeem Iqbal Laila A. Al-Essa Muhammad Yousaf Shad Fuad S. Alduais Mansour F. Yassen Muhammad Ahmad Raza E-Bayesian Estimation of Hierarchical Poisson-Gamma Model on the Basis of Restricted and Unrestricted Parameter Spaces Complexity |
| title | E-Bayesian Estimation of Hierarchical Poisson-Gamma Model on the Basis of Restricted and Unrestricted Parameter Spaces |
| title_full | E-Bayesian Estimation of Hierarchical Poisson-Gamma Model on the Basis of Restricted and Unrestricted Parameter Spaces |
| title_fullStr | E-Bayesian Estimation of Hierarchical Poisson-Gamma Model on the Basis of Restricted and Unrestricted Parameter Spaces |
| title_full_unstemmed | E-Bayesian Estimation of Hierarchical Poisson-Gamma Model on the Basis of Restricted and Unrestricted Parameter Spaces |
| title_short | E-Bayesian Estimation of Hierarchical Poisson-Gamma Model on the Basis of Restricted and Unrestricted Parameter Spaces |
| title_sort | e bayesian estimation of hierarchical poisson gamma model on the basis of restricted and unrestricted parameter spaces |
| url | http://dx.doi.org/10.1155/2023/8767200 |
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