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The quantile-based generalised Rayleigh distribution
Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2020.
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| Other Authors: | |
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2021
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| _version_ | 1867613633297514496 |
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| access_status_str | Open Access |
| author2 | Van Staden, Paul J. |
| author_browse | Van Staden, Paul J. |
| author_facet | Van Staden, Paul J. |
| 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, 2020. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/78262 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:39:14.996Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| 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:2263/78262 The quantile-based generalised Rayleigh distribution Van Staden, Paul J. u14350778@tuks.co.za Wragg, Trystan UCTD Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2020. The Rayleigh distribution is a special case of different families of distributions, one of these being the Weibull distribution. This mini-dissertation considers the development of a new distributional family, the quantile-based generalized Rayleigh distribution, henceforth denoted GRD. The Rayleigh distribution acts as the parent distribution that will be used in the construction of the GRD. That is, the quantile function of the GRD is obtained by taking the weighted sum of the quantile function of the Rayleigh distribution and the quantile function of the reflected Rayleigh distribution. Compared to the Rayleigh distribution, the GRD is more flexible in terms of distributional shape in that, depending on the value of its shape parameter, it can be negatively skewed, symmetric or positively skewed. The GRD furthermore possesses the advantageous property of skewness-invariant measures of kurtosis. The GRD is characterized through its L-moments. These measures are used to describe the location, spread and shape of this distribution. Quantile-based measures of location, spread and shape are also considered in this mini-dissertation. Using method of L-moments estimation, closed- form expressions for the estimators of the unknown parameters of the GRD are derived and the GRD is then fitted to two observed data sets. Statistics MSc (Advanced Data Analytics) Restricted 2021-02-04T12:52:19Z 2021-02-04T12:52:19Z 2021 2020 Mini Dissertation * A2021 http://hdl.handle.net/2263/78262 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 | UCTD The quantile-based generalised Rayleigh distribution |
| title | The quantile-based generalised Rayleigh distribution |
| title_full | The quantile-based generalised Rayleigh distribution |
| title_fullStr | The quantile-based generalised Rayleigh distribution |
| title_full_unstemmed | The quantile-based generalised Rayleigh distribution |
| title_short | The quantile-based generalised Rayleigh distribution |
| title_sort | quantile based generalised rayleigh distribution |
| topic | UCTD |
| url | http://hdl.handle.net/2263/78262 |