Smoothed Dirichlet Distribution
Abstract When the cells are ordinal in the multinomial distribution, i.e., when cells have a natural ordering, guaranteeing that the borrowing information among neighboring cells makes sense conceptually. In this paper, we introduce a novel probability distribution for borrowing information among ne...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Springer
2023-09-01
|
| Series: | Journal of Statistical Theory and Applications (JSTA) |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/s44199-023-00062-8 |
| _version_ | 1797413835803459584 |
|---|---|
| author | Lahiru Wickramasinghe Alexandre Leblanc Saman Muthukumarana |
| author_facet | Lahiru Wickramasinghe Alexandre Leblanc Saman Muthukumarana |
| author_sort | Lahiru Wickramasinghe |
| collection | DOAJ |
| description | Abstract When the cells are ordinal in the multinomial distribution, i.e., when cells have a natural ordering, guaranteeing that the borrowing information among neighboring cells makes sense conceptually. In this paper, we introduce a novel probability distribution for borrowing information among neighboring cells in order to provide reliable estimates for cell probabilities. The proposed smoothed Dirichlet distribution forces the probabilities of neighboring cells to be closer to each other than under the standard Dirichlet distribution. Basic properties of the proposed distribution, including normalizing constant, moments, and marginal distributions, are developed. Sample generation of smoothed Dirichlet distribution is discussed using the acceptance-rejection algorithm. We demonstrate the performance of the proposed smoothed Dirichlet distribution using 2018 Major League Baseball (MLB) batters data. |
| first_indexed | 2024-03-09T05:24:43Z |
| format | Article |
| id | doaj.art-ceede5ff4fb045e286d82751d1e0e23a |
| institution | Directory Open Access Journal |
| issn | 2214-1766 |
| language | English |
| last_indexed | 2024-03-09T05:24:43Z |
| publishDate | 2023-09-01 |
| publisher | Springer |
| record_format | Article |
| series | Journal of Statistical Theory and Applications (JSTA) |
| spelling | doaj.art-ceede5ff4fb045e286d82751d1e0e23a2023-12-03T12:38:25ZengSpringerJournal of Statistical Theory and Applications (JSTA)2214-17662023-09-0122423726110.1007/s44199-023-00062-8Smoothed Dirichlet DistributionLahiru Wickramasinghe0Alexandre Leblanc1Saman Muthukumarana2Department of Mathematics and Statistics, University of WinnipegDepartment of Statistics, University of ManitobaDepartment of Statistics, University of ManitobaAbstract When the cells are ordinal in the multinomial distribution, i.e., when cells have a natural ordering, guaranteeing that the borrowing information among neighboring cells makes sense conceptually. In this paper, we introduce a novel probability distribution for borrowing information among neighboring cells in order to provide reliable estimates for cell probabilities. The proposed smoothed Dirichlet distribution forces the probabilities of neighboring cells to be closer to each other than under the standard Dirichlet distribution. Basic properties of the proposed distribution, including normalizing constant, moments, and marginal distributions, are developed. Sample generation of smoothed Dirichlet distribution is discussed using the acceptance-rejection algorithm. We demonstrate the performance of the proposed smoothed Dirichlet distribution using 2018 Major League Baseball (MLB) batters data.https://doi.org/10.1007/s44199-023-00062-8Dirichlet distributionMultinomial distribution, Bayesian |
| spellingShingle | Lahiru Wickramasinghe Alexandre Leblanc Saman Muthukumarana Smoothed Dirichlet Distribution Journal of Statistical Theory and Applications (JSTA) Dirichlet distribution Multinomial distribution, Bayesian |
| title | Smoothed Dirichlet Distribution |
| title_full | Smoothed Dirichlet Distribution |
| title_fullStr | Smoothed Dirichlet Distribution |
| title_full_unstemmed | Smoothed Dirichlet Distribution |
| title_short | Smoothed Dirichlet Distribution |
| title_sort | smoothed dirichlet distribution |
| topic | Dirichlet distribution Multinomial distribution, Bayesian |
| url | https://doi.org/10.1007/s44199-023-00062-8 |
| work_keys_str_mv | AT lahiruwickramasinghe smootheddirichletdistribution AT alexandreleblanc smootheddirichletdistribution AT samanmuthukumarana smootheddirichletdistribution |