Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model

Jose A. A. Andrade; Pushpa Rathie

doi:10.5802/crmath.469

Statistiques

Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model

Jose A. A. Andrade ¹ ; Pushpa Rathie ²

¹ Department of Statistics and Applied Mathematics, Federal University of Ceara, 60455-670, Fortaleza-Ce, Brazil
² Department of Statistics, University of Brasilia, 70910-900, Brasilia-DF, Brazil

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1063-1069.

Résumé

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.

Reçu le : 2022-11-12
Accepté le : 2023-01-29
Publié le : 2023-09-07

DOI : 10.5802/crmath.469

Classification : 62C10

Affiliations des auteurs :

Jose A. A. Andrade ¹ ; Pushpa Rathie ²

¹ Department of Statistics and Applied Mathematics, Federal University of Ceara, 60455-670, Fortaleza-Ce, Brazil
² Department of Statistics, University of Brasilia, 70910-900, Brasilia-DF, Brazil

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Jose A. A. Andrade and Pushpa Rathie},
     title = {Exact {Posterior} distribution of risk ratio in the {Kumaraswamy{\textendash}Binomial} model},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1063--1069},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.469},
     language = {en},
}

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Jose A. A. Andrade; Pushpa Rathie. Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1063-1069. doi : 10.5802/crmath.469. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.469/

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