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Hypersphere candidates emanating from the Dirichlet and its extension
Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2024.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2024
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| _version_ | 1867613517423575040 |
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| access_status_str | Open Access |
| author2 | Makgai, Seitebaleng |
| author_browse | Makgai, Seitebaleng |
| author_facet | Makgai, Seitebaleng |
| collection | Thesis |
| dc_rights_str_mv | © 2023 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 (MSc (Advanced Data Analytics))--University of Pretoria, 2024. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/97052 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:24.530Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| 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:2263/97052 Hypersphere candidates emanating from the Dirichlet and its extension Makgai, Seitebaleng u18243020@tuks.co.za Bekker, Andriette, 1958- Leshilo, Ramadimetje Lethabo Compositional datasets Dirichlet type III distribution Hypersphere Spherical- Dirichlet distribution Square-root transformation table UCTD Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2024. Compositional datasets consist of observations that are proportional and are subject to non-negativity and unit-sum constraints. These datasets arise naturally in a multiplicity of fields such as agriculture, archaeology, economics, geology, health sciences, and psychology. There is a strong footprint in the literature on the Dirichlet distribution for modelling compositional datasets, followed by several generalizations of the Dirichlet distribution, with more flexible structures. In this study, we consider a transformation of two Dirichlet-type random variables W1,W2, . . . ,Wm by applying the square-root transformation Xi = √Wi for i = 1, 2, . . . , m. With this square-root transformation, we propose and develop a new distribution that is defined on the positive orthant of the hypersphere, that accommodates both positive and negative covariance structure. This novel model is a flexible offering to the spherical-Dirichlet models. We perform several simulation studies for the proposed model. The maximum likelihood is used for parameter estimation. Two applications of the models to biological and archaeological compositional datasets are presented, to illustrate the flexibility of the proposed model. Energy Mobility Education Trust (EMET) Statistics MSc (Advanced Data Analytics) Unrestricted Faculty of Natural and Agricultural Sciences SDG-03: Good health and well-being SDG-15: Life on land 2024-07-16T11:53:56Z 2024-07-16T11:53:56Z 2024-09 2024-07 Mini Dissertation * S2024 http://hdl.handle.net/2263/97052 DOI: https://doi.org/10.25403/UPresearchdata.26309959.v1 https://doi.org/10.25403/UPresearchdata.26309959 en © 2023 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 | Compositional datasets Dirichlet type III distribution Hypersphere Spherical- Dirichlet distribution Square-root transformation table UCTD Hypersphere candidates emanating from the Dirichlet and its extension |
| title | Hypersphere candidates emanating from the Dirichlet and its extension |
| title_full | Hypersphere candidates emanating from the Dirichlet and its extension |
| title_fullStr | Hypersphere candidates emanating from the Dirichlet and its extension |
| title_full_unstemmed | Hypersphere candidates emanating from the Dirichlet and its extension |
| title_short | Hypersphere candidates emanating from the Dirichlet and its extension |
| title_sort | hypersphere candidates emanating from the dirichlet and its extension |
| topic | Compositional datasets Dirichlet type III distribution Hypersphere Spherical- Dirichlet distribution Square-root transformation table UCTD |
| url | http://hdl.handle.net/2263/97052 https://doi.org/10.25403/UPresearchdata.26309959 |