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Geometric skew-Cauchy distribution as an alternative to the skew-normal and geometric skew-normal distributions
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_ | 1867613493063057408 |
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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 | © 2019 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:2263/83345 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:01.063Z |
| 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:2263/83345 Geometric skew-Cauchy distribution as an alternative to the skew-normal and geometric skew-normal distributions Ehlers, René xan97der@gmail.com Bekker, Andriette, Heaney, Xander Statistics Distribution Theory Distributions Multimodal distributions Data Analytics Data Science skewed data UCTD Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2021. The skew-normal distribution was popularised by Azzalini [4] to model skewed data. However, the skew-normal distribution is always unimodal. Kundu [24] recently presented the geometric skew-normal distribution by considering a geometric compounding sum of normal random variables. This distribution is more flexible than the skew-normal distribution since it can be multimodal. In this dissertation we present a new distribution namely the geometric skew-Cauchy distribution. The idea follows a similar approach to that of Kundu's. The difference, however, is that we consider a geometric compounding sum of Cauchy random variables. The inclusion of a simulation and application chapter demonstrates the practical use of this new distribution. It turns out that the geometric skew-Cauchy distribution is also more flexible than the skew-normal distribution. It is concluded that this new distribution can be used as an alternative to the geometric skew-normal distribution since both distributions can be multimodal. The advantage over the geometric skew-normal distribution, is the ability of the geometric skew-Cauchy distribution to model fatter-tailed data. National Research Foundation (NRF) of South Africa, Reference: SRUG190308422768 grant No. 120839; Academic Statistics Funding Instrument grant No. 127946; SARChI Research Chair UID71199. Statistics MSc (Advanced Data Analytics) Unrestricted 2022-01-18T08:01:03Z 2022-01-18T08:01:03Z 2022-05-06 2021 Mini Dissertation * A2022 http://hdl.handle.net/2263/83345 DOI: 10.25403/UPresearchdata.18319196 en © 2019 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 | Statistics Distribution Theory Distributions Multimodal distributions Data Analytics Data Science skewed data UCTD Geometric skew-Cauchy distribution as an alternative to the skew-normal and geometric skew-normal distributions |
| title | Geometric skew-Cauchy distribution as an alternative to the skew-normal and geometric skew-normal distributions |
| title_full | Geometric skew-Cauchy distribution as an alternative to the skew-normal and geometric skew-normal distributions |
| title_fullStr | Geometric skew-Cauchy distribution as an alternative to the skew-normal and geometric skew-normal distributions |
| title_full_unstemmed | Geometric skew-Cauchy distribution as an alternative to the skew-normal and geometric skew-normal distributions |
| title_short | Geometric skew-Cauchy distribution as an alternative to the skew-normal and geometric skew-normal distributions |
| title_sort | geometric skew cauchy distribution as an alternative to the skew normal and geometric skew normal distributions |
| topic | Statistics Distribution Theory Distributions Multimodal distributions Data Analytics Data Science skewed data UCTD |
| url | http://hdl.handle.net/2263/83345 |