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A mixture model approach to extreme value analysis of heavy tailed processes
Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2023.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2024
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| _version_ | 1867613519395946496 |
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| access_status_str | Open Access |
| author2 | Maribe, Gaonyalelwe |
| author_browse | Maribe, Gaonyalelwe |
| author_facet | Maribe, Gaonyalelwe |
| 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, 2023. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/94472 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:26.341Z |
| 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:2263/94472 A mixture model approach to extreme value analysis of heavy tailed processes Maribe, Gaonyalelwe lizosanqela@gmail.com Kanfer, Frans Millard, Sollie Sanqela, Lizo UCTD Extreme value theory Mixture model Bernstein polynomial Extended generalized Pareto distribution Semiparametric Sustainable development goals (SDGs) SDG-09: Industry, innovation and infrastructure Natural and Agricultural Sciences theses SDG-09 SDG-13: Climate action Natural and Agricultural Sciences theses SDG-13 Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2023. Extreme value theory (EVT) encompasses statistical tools for modelling extreme events, which are defined in the peaks-over-threshold methodology as excesses over a certain high threshold. The estimation of this threshold is a crucial problem and an ongoing area of research in EVT. This dissertation investigates extreme value mixture models which bypass threshold selection. In particular, we focus on the Extended Generalised Pareto Distribution (EGPD). This is a model for the full range of data characterised by the presence of extreme values. We consider the non-parametric EGPD based on a Bernstein polynomial approximation. The ability of the EGPD to estimate the extreme value index (EVI) is investigated for distributions in the Frechet, Gumbel and Weibull domains through a simulation study. Model performance is measured in terms of bias and mean squared error. We also carry out a case study on rainfall data to illustrate how the EGPD fits as a distribution for the full range of data. The case study also includes quantile estimation. We further propose substituting the Pareto distribution, in place of the GPD, as the tail model of the EGPD in the case of heavy-tailed data. We give the mathematical background of this new model and show that it is a member of the EGPD family and is thus in compliance with EVT. We compare this new model's bias and mean squared error in EVI estimation to the old EGPD through a simulation study. Furthermore, the simulation study is extended to include other estimators for Frechet-type data. Moreover, a case study is carried out on the Belgian Secura Re data. Statistics MSc (Advanced Data Analytics) Restricted Faculty of Natural and Agricultural Sciences 2024-02-12T09:18:48Z 2024-02-12T09:18:48Z 2024-04 2023-12-07 Mini Dissertation * A2024 http://hdl.handle.net/2263/94472 10.25403/UPresearchdata.25196390 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 | UCTD Extreme value theory Mixture model Bernstein polynomial Extended generalized Pareto distribution Semiparametric Sustainable development goals (SDGs) SDG-09: Industry, innovation and infrastructure Natural and Agricultural Sciences theses SDG-09 SDG-13: Climate action Natural and Agricultural Sciences theses SDG-13 A mixture model approach to extreme value analysis of heavy tailed processes |
| title | A mixture model approach to extreme value analysis of heavy tailed processes |
| title_full | A mixture model approach to extreme value analysis of heavy tailed processes |
| title_fullStr | A mixture model approach to extreme value analysis of heavy tailed processes |
| title_full_unstemmed | A mixture model approach to extreme value analysis of heavy tailed processes |
| title_short | A mixture model approach to extreme value analysis of heavy tailed processes |
| title_sort | mixture model approach to extreme value analysis of heavy tailed processes |
| topic | UCTD Extreme value theory Mixture model Bernstein polynomial Extended generalized Pareto distribution Semiparametric Sustainable development goals (SDGs) SDG-09: Industry, innovation and infrastructure Natural and Agricultural Sciences theses SDG-09 SDG-13: Climate action Natural and Agricultural Sciences theses SDG-13 |
| url | http://hdl.handle.net/2263/94472 |