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Asymmetric generalizations of symmetric univariate probability distributions obtained through quantile splicing
Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2020.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2021
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| _version_ | 1867613693183787008 |
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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 | Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2020. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/78371 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:40:11.720Z |
| 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:2263/78371 Asymmetric generalizations of symmetric univariate probability distributions obtained through quantile splicing Van Staden, Paul J. Brenda.omachar@up.ac.za King, Robert Arthur Ravencroft Mac'Oduol, Brenda Vuguza UCTD Thesis (PhD (Mathematical Statistics))--University of Pretoria, 2020. This thesis develops a skewing methodology for the formulation of two-piece families of distri- butions that can be defined through their cumulative distribution functions (CDFs), probability density functions (PDFs) or quantile functions. The advantage of this methodology is that the families of distributions constructed have skewness-invariant measures of kurtosis, allowing for the independent analysis of the skewness and kurtosis of a distribution. The central contribution of this thesis is in the development of the quantile function of the two-piece family of distributions. This quantile function is constructed through the use of the quantile functions of half distributions developed from symmetric univariate distributions (henceforth referred to as the parent distribution). This quantile function is the used to derive a general formula for the rth order L-moments of the two-piece family of distributions. The results of these L-moments will be in terms of the L-moments of both the parent distribution and the half distribution. The parameters of this new family of distributions can be estimated through the method of L-moments since closed form expressions exist for the L-moments and subsequently the estimators. The results from the skewing methodology as well as from the formula for the rth order L-moments will be applied to well-known symmetric univariate distributions. These include the arcsine, uniform, cosine, normal, logistic, hyperbolic secant and Student’s t(2) distributions, which do not have a shape parameter, as well as the quantile-based Tukey lamba distribution which has a kurtosis parameter. STATOMET DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) Statistics PhD (Mathematical Statistics) Unrestricted 2021-02-10T06:47:17Z 2021-02-10T06:47:17Z 2021-05-05 2020 Thesis Mac'Oduol, BV 2020, Asymmetric generalizations of symmetric univariate probability distributions obtained through quantile splicing, University of Pretoria, Pretoria. A2021 http://hdl.handle.net/2263/78371 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 Asymmetric generalizations of symmetric univariate probability distributions obtained through quantile splicing |
| title | Asymmetric generalizations of symmetric univariate probability distributions obtained through quantile splicing |
| title_full | Asymmetric generalizations of symmetric univariate probability distributions obtained through quantile splicing |
| title_fullStr | Asymmetric generalizations of symmetric univariate probability distributions obtained through quantile splicing |
| title_full_unstemmed | Asymmetric generalizations of symmetric univariate probability distributions obtained through quantile splicing |
| title_short | Asymmetric generalizations of symmetric univariate probability distributions obtained through quantile splicing |
| title_sort | asymmetric generalizations of symmetric univariate probability distributions obtained through quantile splicing |
| topic | UCTD |
| url | http://hdl.handle.net/2263/78371 |