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A functional approach to distribution modelling : the spliced generalised normal distribution
Dissertation (MCom (Mathematical Statistics))--University of Pretoria, 2019.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2023
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| _version_ | 1867613727417696256 |
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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 | © 2021 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 | Dissertation (MCom (Mathematical Statistics))--University of Pretoria, 2019. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/93827 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:40:44.617Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| 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:2263/93827 A functional approach to distribution modelling : the spliced generalised normal distribution Bekker, Andriette, 1958- Arashi, Mohammad Naderi, M. matthias@dilectum.co.za Wagener, Matthias UCTD Generalized normal Normality Kurtosis Inferential statistics Bitcoin Dissertation (MCom (Mathematical Statistics))--University of Pretoria, 2019. A new body and tail generalisation of the normal distribution is introduced, the spliced generalised normal (SGN). A special case of the SGN, the tail-adjusted normal distribution, is further generalised with two-piece scaling to accommodate di erent combinations of skewness and tail weight in data. The two-piece scaled tail-adjusted normal (TPTAN) is thoroughly studied with the derivations of various statistical properties such as the probability density function, cumulative distribution function, quantile function, moments, and Fischer information. The applicability of the SGN distribution is demonstrated by the application of the TPTAN to light and heavy-tailed data sets. The small and large sample performance of the TPTAN is investigated with an extensive simulation study. The methods of estimation include maximum likelihood and Kolmogorov-Smirnov estimation. The goodness of t is evaluated by likelihood criteria and hypothesis tests such as Akaike information criterion, Bayesian information criterion, consistent Akaike information criterion, Hannan-Quinn information criterion, and the KS and Bayes factor tests. National Research Foundation of South Africa (SARChI Research Chair- UID: 71199 Statistics MCom (Mathematical Statistics) Unrestricted Faculty of Economic And Management Sciences 2023-12-19T14:10:09Z 2023-12-19T14:10:09Z 2020-04 2019 Dissertation * A2020 http://hdl.handle.net/2263/93827 en © 2021 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 Generalized normal Normality Kurtosis Inferential statistics Bitcoin A functional approach to distribution modelling : the spliced generalised normal distribution |
| title | A functional approach to distribution modelling : the spliced generalised normal distribution |
| title_full | A functional approach to distribution modelling : the spliced generalised normal distribution |
| title_fullStr | A functional approach to distribution modelling : the spliced generalised normal distribution |
| title_full_unstemmed | A functional approach to distribution modelling : the spliced generalised normal distribution |
| title_short | A functional approach to distribution modelling : the spliced generalised normal distribution |
| title_sort | functional approach to distribution modelling the spliced generalised normal distribution |
| topic | UCTD Generalized normal Normality Kurtosis Inferential statistics Bitcoin |
| url | http://hdl.handle.net/2263/93827 |