Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Advances and considerations of Dirichlet with an emphasis on entropy
Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2022.
Saved in:
| Other Authors: | |
|---|---|
| Format: | Thesis |
| Language: | English |
| Published: |
University of Pretoria
2023
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613575722303488 |
|---|---|
| access_status_str | Open Access |
| author2 | Ferreira, Johan T. |
| author_browse | Ferreira, Johan T. |
| author_facet | Ferreira, Johan T. |
| collection | Thesis |
| dc_rights_str_mv | © 2022 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, 2022. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/89134 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:38:19.968Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| 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:2263/89134 Advances and considerations of Dirichlet with an emphasis on entropy Ferreira, Johan T. tcnita@gmail.com Botha, Tanita Double flexible Entropy Flexible Generator Noncentral Power sum function Unit simplex UCTD Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2022. The Dirichlet distribution is a cornerstone probabilistic consideration when working with data on the unit simplex. This thesis studies advances of several Dirichlet generalizations such as the Dirichlet generator, noncentral Dirichlet (including meaningful reparameterizations) and two particular finite mixtures of the Dirichlet distribution. Key statistical characteristics of these Dirichlet generalizations are studied together with data fitting examples to highlight the methodological- and computational advantages that these considerations offer. Subsequently, these Dirichlet generalizations are considered in a Bayes framework as priors conjugate to a multinomial likelihood with K distinct classes. An emphasis on entropy follows to determine closed-form estimators for the Tsallis-, generalized Mathai-, and Abe entropies subject to these Dirichlet considerations as priors. These estimators are particularly convenient following from complete product moments of the derived posterior distributions to access the underlying probabilities of the K-dimensional classes, p. These entropies are incorporated within an explorative estimation approach using real economic data and a prior selection method is illustrated to suggest a suitable prior for the consideration of the practitioner. The contributions of this thesis to fundamental multivariate statistical theory as well as the information-theoretic environment (via considered entropies) are meaningful and substantiated. Statistics PhD (Mathematical Statistics) Unrestricted 2023-02-03T10:49:15Z 2023-02-03T10:49:15Z 2023-04 2022 Thesis * A2023 https://repository.up.ac.za/handle/2263/89134 Disclaimer en © 2022 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 | Double flexible Entropy Flexible Generator Noncentral Power sum function Unit simplex UCTD Advances and considerations of Dirichlet with an emphasis on entropy |
| title | Advances and considerations of Dirichlet with an emphasis on entropy |
| title_full | Advances and considerations of Dirichlet with an emphasis on entropy |
| title_fullStr | Advances and considerations of Dirichlet with an emphasis on entropy |
| title_full_unstemmed | Advances and considerations of Dirichlet with an emphasis on entropy |
| title_short | Advances and considerations of Dirichlet with an emphasis on entropy |
| title_sort | advances and considerations of dirichlet with an emphasis on entropy |
| topic | Double flexible Entropy Flexible Generator Noncentral Power sum function Unit simplex UCTD |
| url | https://repository.up.ac.za/handle/2263/89134 |