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From Beta to Dirichlet Frontiers
Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2019.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2022
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| _version_ | 1867613723202420736 |
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| access_status_str | Open Access |
| author2 | Bekker, Andriette, 1958- |
| author_browse | Bekker, Andriette, 1958- |
| author_facet | Bekker, Andriette, 1958- |
| collection | Thesis |
| dc_rights_str_mv | © 2021 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 | Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2019. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/85894 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:40:40.528Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| 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:2263/85894 From Beta to Dirichlet Frontiers Bekker, Andriette, 1958- seite.makgai@up.ac.za Arashi, Mohammad Visagie, Jaco Makgai, Seitebaleng Littah UCTD Beta-generated Coverage probability Dirichlet distribution Empirical cumulative distribution function Kolmogorov-Smirnov distance Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2019. In this study, two classes of multivariate distributions are proposed as extensions of the well known univariate class of beta-generated distributions. This extension from the univariate to the multivari- ate domain addresses the need of flexible multivariate distributions that can model a wide range of multivariate data sets where outliers are present. The first class is constructed by embedding the cumulative distribution functions (cdf) of univariate baseline distributions within the probability den- sity function (pdf) of the Dirichlet type I distribution. The second class is constructed through an interesting view of embedding the cdf of a multivariate distribution within the pdf of the univariate beta distribution. Each class presents their own unique properties such as specific parameter require- ments and dependence structures for distributions belonging to these classes. An example of a newly developed distribution for each class is investigated, where the value and performance of the models are illustrated using real data sets and simulation studies. The method of maximum likelihood is used for parameter estimation; and measures such as the Kolmogorov-Smirnov distance is implemented as a performance based measure for competing models. A new model testing technique is also introduced to evaluate the performance of the multivariate models. Possible extensions of these classes of distributions are discussed for future research. Mathematics and Applied Mathematics PhD (Mathematical Statistics) Unrestricted 2022-06-22T07:16:09Z 2022-06-22T07:16:09Z 2020 2019 Thesis * A2020 https://repository.up.ac.za/handle/2263/85894 en © 2021 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 | UCTD Beta-generated Coverage probability Dirichlet distribution Empirical cumulative distribution function Kolmogorov-Smirnov distance From Beta to Dirichlet Frontiers |
| title | From Beta to Dirichlet Frontiers |
| title_full | From Beta to Dirichlet Frontiers |
| title_fullStr | From Beta to Dirichlet Frontiers |
| title_full_unstemmed | From Beta to Dirichlet Frontiers |
| title_short | From Beta to Dirichlet Frontiers |
| title_sort | from beta to dirichlet frontiers |
| topic | UCTD Beta-generated Coverage probability Dirichlet distribution Empirical cumulative distribution function Kolmogorov-Smirnov distance |
| url | https://repository.up.ac.za/handle/2263/85894 |