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Advances in Pólya-Aeppli distributions and applications
Thesis (PhD)--University of Pretoria, 2025.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2025
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| _version_ | 1867613571335061504 |
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| access_status_str | Open Access |
| author2 | Ehlers, René |
| author_browse | Ehlers, René |
| author_facet | Ehlers, René |
| 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 | Thesis (PhD)--University of Pretoria, 2025. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/103690 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:38:15.902Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| 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:2263/103690 Advances in Pólya-Aeppli distributions and applications Ehlers, René u29090777@tuks.co.za Bekker, Andriëtte Geldenhuys, Claire UCTD Sustainable Development Goals (SDGs) Bivariate distributions Count data Laguerre polynomials Multivariate distributions Overdispersion Pólya-Aeppli distributions Zero-and-one inflation Zero-inflation Thesis (PhD)--University of Pretoria, 2025. Count data are frequently encountered in fields such as biomedicine, social sciences, economics, and ecological research. However, count data often exhibit overdispersion, which can compromise the accuracy of model parameter estimates. This thesis introduces new bivariate and multivariate Pólya-Aeppli distributions that offer greater flexibility for modelling overdispersed count data, including scenarios involving zero- and zero-and-one inflation. This study presents a significant advantage through the formulation of probability mass functions and their associated distributional properties using Laguerre polynomials. This approach effectively addresses existing limitations in current methodologies, thereby enhancing the applicability and relevance of the distributions to real-world data. The methodology is validated through comprehensive simulation studies and applications to real datasets, showcasing its effectiveness and superiority compared to various existing approaches or models. National Research Foundation of South Africa (Grant ref. CPRR160403161466 nr. 105840) Statistics PhD (Mathematical Statistics) Restricted Faculty of Natural and Agricultural Sciences None 2025-07-30T07:54:14Z 2025-07-30T07:54:14Z 2025-09-01 2025-07-30 Thesis * S2025 http://hdl.handle.net/2263/103690 https://doi.org/10.1002/jae.3950010104, https://doi.org/10.1080/10920277.2007.10597487, https://doi.org/10.2307/3001656, https://doi.org/10.1080/00401706.1972.10488881 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 application/pdf University of Pretoria |
| spellingShingle | UCTD Sustainable Development Goals (SDGs) Bivariate distributions Count data Laguerre polynomials Multivariate distributions Overdispersion Pólya-Aeppli distributions Zero-and-one inflation Zero-inflation Advances in Pólya-Aeppli distributions and applications |
| title | Advances in Pólya-Aeppli distributions and applications |
| title_full | Advances in Pólya-Aeppli distributions and applications |
| title_fullStr | Advances in Pólya-Aeppli distributions and applications |
| title_full_unstemmed | Advances in Pólya-Aeppli distributions and applications |
| title_short | Advances in Pólya-Aeppli distributions and applications |
| title_sort | advances in polya aeppli distributions and applications |
| topic | UCTD Sustainable Development Goals (SDGs) Bivariate distributions Count data Laguerre polynomials Multivariate distributions Overdispersion Pólya-Aeppli distributions Zero-and-one inflation Zero-inflation |
| url | http://hdl.handle.net/2263/103690 https://doi.org/10.1002/jae.3950010104, https://doi.org/10.1080/10920277.2007.10597487, https://doi.org/10.2307/3001656, https://doi.org/10.1080/00401706.1972.10488881 |