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Modeling of generalized families of probability distribution in the quantile statistical universe
Thesis (PhD)--University of Pretoria, 2013.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2014
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| _version_ | 1867613647633645568 |
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| access_status_str | Open Access |
| author2 | Boraine, H. |
| author_browse | Boraine, H. |
| author_facet | Boraine, H. |
| collection | Thesis |
| dc_rights_str_mv | © 2013 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)--University of Pretoria, 2013. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/40265 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:39:28.478Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| 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:2263/40265 Modeling of generalized families of probability distribution in the quantile statistical universe Boraine, H. paul.vanstaden@up.ac.za King, Robert Arthur Ravencroft Van Staden, Paul Jacobus Generalized lambda distribution L-moment Quantile function Skewness-invariant measure of kurtosis UCTD Thesis (PhD)--University of Pretoria, 2013. This thesis develops a methodology for the construction of generalized families of probability distributions in the quantile statistical universe, that is, distributions specified in terms of their quantile functions. The main benefit of the proposed methodology is that it generates quantile-based distributions with skewness-invariant measures of kurtosis. The skewness and kurtosis can therefore be identified and analyzed separately. The key contribution of this thesis is the development of a new type of the generalized lambda distribution (GLD), using the quantile function of the generalized Pareto distribution as the basic building block (in the literature each different type of the GLD is incorrectly referred to as a parameterization of the GLD – in this thesis the term type is used). The parameters of this new type can, contrary to existing types, easily be estimated with method of L-moments estimation, since closed-form expressions are available for the estimators as well as for their asymptotic standard errors. The parameter space and the shape properties of the new type are discussed in detail, including its characterization through L-moments. A simple estimation algorithm is presented and utilization of the new type in terms of data fitting and approximation of probability distributions is illustrated. gm2014 Statistics unrestricted 2014-06-17T13:08:11Z 2014-06-17T13:08:11Z 2014-04-15 2013 Thesis Van Staden, PJ 2013, Modeling of generalized families of probability distribution in the quantile statistical universe, PhD thesis, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/40265> D14/4/87/gm http://hdl.handle.net/2263/40265 en © 2013 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 | Generalized lambda distribution L-moment Quantile function Skewness-invariant measure of kurtosis UCTD Modeling of generalized families of probability distribution in the quantile statistical universe |
| title | Modeling of generalized families of probability distribution in the quantile statistical universe |
| title_full | Modeling of generalized families of probability distribution in the quantile statistical universe |
| title_fullStr | Modeling of generalized families of probability distribution in the quantile statistical universe |
| title_full_unstemmed | Modeling of generalized families of probability distribution in the quantile statistical universe |
| title_short | Modeling of generalized families of probability distribution in the quantile statistical universe |
| title_sort | modeling of generalized families of probability distribution in the quantile statistical universe |
| topic | Generalized lambda distribution L-moment Quantile function Skewness-invariant measure of kurtosis UCTD |
| url | http://hdl.handle.net/2263/40265 |