Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model
In categorical data analysis, the $2\times 2$ contingency tables are commonly used to assess the association between groups and responses, this is achieved by using some measures of association, such as the contingency coefficient, odds ratio, risk relative, etc. In a Bayesian approach, the risk rat...
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| Language: | English |
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Académie des sciences
2023-09-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.469/ |
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| author | Andrade, Jose A. A. Rathie, Pushpa |
| author_facet | Andrade, Jose A. A. Rathie, Pushpa |
| author_sort | Andrade, Jose A. A. |
| collection | DOAJ |
| description | In categorical data analysis, the $2\times 2$ contingency tables are commonly used to assess the association between groups and responses, this is achieved by using some measures of association, such as the contingency coefficient, odds ratio, risk relative, etc. In a Bayesian approach, the risk ratio is modeled according to a Beta-Binomial model, which has exact posterior distribution, due to the conjugacy property of the model. In this work, we provide the exact posterior distribution of the relative risk for the non-conjugate Kumaraswamy–Binomial model. The results are based on special functions and we give exact expressions for the posterior density, moments, and cumulative distribution. An example illustrates the theory. |
| format | Article |
| id | doaj-art-e8820b8450ac4704b210b75287a590d9 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-e8820b8450ac4704b210b75287a590d92025-02-07T11:09:17ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-09-01361G61063106910.5802/crmath.46910.5802/crmath.469Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial modelAndrade, Jose A. A.0Rathie, Pushpa1Department of Statistics and Applied Mathematics, Federal University of Ceara, 60455-670, Fortaleza-Ce, BrazilDepartment of Statistics, University of Brasilia, 70910-900, Brasilia-DF, BrazilIn categorical data analysis, the $2\times 2$ contingency tables are commonly used to assess the association between groups and responses, this is achieved by using some measures of association, such as the contingency coefficient, odds ratio, risk relative, etc. In a Bayesian approach, the risk ratio is modeled according to a Beta-Binomial model, which has exact posterior distribution, due to the conjugacy property of the model. In this work, we provide the exact posterior distribution of the relative risk for the non-conjugate Kumaraswamy–Binomial model. The results are based on special functions and we give exact expressions for the posterior density, moments, and cumulative distribution. An example illustrates the theory.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.469/ |
| spellingShingle | Andrade, Jose A. A. Rathie, Pushpa Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model Comptes Rendus. Mathématique |
| title | Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model |
| title_full | Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model |
| title_fullStr | Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model |
| title_full_unstemmed | Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model |
| title_short | Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model |
| title_sort | exact posterior distribution of risk ratio in the kumaraswamy binomial model |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.469/ |
| work_keys_str_mv | AT andradejoseaa exactposteriordistributionofriskratiointhekumaraswamybinomialmodel AT rathiepushpa exactposteriordistributionofriskratiointhekumaraswamybinomialmodel |