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A unifying generator for cardioid modelling in circular statistics
Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2021.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2022
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| _version_ | 1867613560033509376 |
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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 | © 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 | Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2021. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/83803 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:38:04.955Z |
| 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:2263/83803 A unifying generator for cardioid modelling in circular statistics Bekker, Andriette, 1958- delenevanwyk7@gmail.com Arashi, Mohammad Ferreira, Johan Van Wyk, Delene Martine UCTD Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2021. One of the most important distributions in the circular world is the cardioid distribution. This distribution, however, suffers limitations for multimodal or asymmetric occurrences in circular data. This study addresses this shortfall by developing a flexible cardioid generated class that can capture inherent skewness and multimodality that data might present. This class is obtained by expressing the density in a general form by making use of a measurable function termed as generator. Some of the existing extensions of the cardioid distribution is shown to be special cases of this class of cardioid-generator distribution, and flexible behaviour of the proposed class in terms of skewness and multimodality is graphically demonstrated. Special cases of new and existing models of the newly proposed class are compared by making use of simulation studies and data sets. The newly proposed cardioid-t distribution proved a worthy addition to the class of symmetric models, outperforming well known circular distributions in two of the real data applications presented here. Introducing a more flexible cardioid generated class opens new insights for the cardioid model and equips the practitioner with a modified set of tools towards uncovering the intricate world of directional statistics. This work was based on research supported in part by the National Research Foundation (NRF) of South Africa, SARChI Research Chair UID: 71199; Ref.: SRUG190308422768 grant No. 120839, STATOMET at the Department of Statistics at the University of Pretoria, and DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa. Statistics MSc (Advanced Data Analytics) Unrestricted 2022-02-11T08:14:57Z 2022-02-11T08:14:57Z 2022 2021 Mini Dissertation * A2022 http://hdl.handle.net/2263/83803 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 | UCTD A unifying generator for cardioid modelling in circular statistics |
| title | A unifying generator for cardioid modelling in circular statistics |
| title_full | A unifying generator for cardioid modelling in circular statistics |
| title_fullStr | A unifying generator for cardioid modelling in circular statistics |
| title_full_unstemmed | A unifying generator for cardioid modelling in circular statistics |
| title_short | A unifying generator for cardioid modelling in circular statistics |
| title_sort | unifying generator for cardioid modelling in circular statistics |
| topic | UCTD |
| url | http://hdl.handle.net/2263/83803 |