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Contaminated models of reparameterised versions of the Dirichlet-multinomial distribution
Mini Dissertation
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2026
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| access_status_str | Open Access |
| author2 | Makgai, Seite |
| author_browse | Makgai, Seite |
| author_facet | Makgai, Seite |
| collection | Thesis |
| dc_rights_str_mv | © 2024 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Mini Dissertation |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/108074 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:24.077Z |
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| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2026 |
| publishDateRange | 2026 |
| publishDateSort | 2026 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/108074 Contaminated models of reparameterised versions of the Dirichlet-multinomial distribution Makgai, Seite u20439530@tuks.co.za Bekker, Andriette Van Heerden, Ockert Johannes Contaminated Models Dirichlet-multinomial Outliers Overdispersion Reparameterisation Mini Dissertation The Dirichlet-Multinomial (DM) distribution is often used for the modelling of multivariate count data, which has been applied in diverse areas such as microbiome studies, genetics, and ecological analysis. Despite its wide use, the distribution lacks easily interpretable parameters and the ability to account for outliers. In this study, we propose a novel reconstruction/perspective of the DM distribution: namely, reparameterisation of the DM distribution, which will be utilised to develop contaminated versions. Two reparameterisations are considered: the first in terms of the mode and a parameter referred to as the pseudo-variance and the second in terms of the mean and another pseudo-variance parameter. Such reparameterisations improve interpretability and allow the further construction of contaminated models that are robust to outliers. We consider properties such as the derived probability mass functions and moments for the proposed models. Simulation studies evaluate these models under varying scenarios, comparing estimation accuracy, bias, and computational performance. The relevance of the proposed models is illustrated via a microbiome data application. The developments from this study enhance the flexibility of the DM distribution and reinforce its usefulness for analyzing modern complex datasets in the biological and statistical sciences. None Statistics MSc in Advanced Data Analytics Restricted Faculty of Natural and Agricultural Sciences None 2026-02-11T07:18:43Z 2026-02-11T07:18:43Z 2025 2025 Mini Dissertation * M2026 http://hdl.handle.net/2263/108074 10.25403/UPresearchdata.31303864 en © 2024 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | Contaminated Models Dirichlet-multinomial Outliers Overdispersion Reparameterisation Contaminated models of reparameterised versions of the Dirichlet-multinomial distribution |
| title | Contaminated models of reparameterised versions of the Dirichlet-multinomial distribution |
| title_full | Contaminated models of reparameterised versions of the Dirichlet-multinomial distribution |
| title_fullStr | Contaminated models of reparameterised versions of the Dirichlet-multinomial distribution |
| title_full_unstemmed | Contaminated models of reparameterised versions of the Dirichlet-multinomial distribution |
| title_short | Contaminated models of reparameterised versions of the Dirichlet-multinomial distribution |
| title_sort | contaminated models of reparameterised versions of the dirichlet multinomial distribution |
| topic | Contaminated Models Dirichlet-multinomial Outliers Overdispersion Reparameterisation |
| url | http://hdl.handle.net/2263/108074 |