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Product of independent generalised gamma random variables
Mini Dissertation (MSc (Mathematical Statistics))--University of Pretoria, 2016.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2023
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| _version_ | 1867613507657138176 |
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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 | Mini Dissertation (MSc (Mathematical Statistics))--University of Pretoria, 2016. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/93805 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:15.129Z |
| 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:2263/93805 Product of independent generalised gamma random variables Bekker, Andriette, 1958- Marques, Filipe Bilankulu, Vusi Raphael UCTD Gamma random variables Mini Dissertation (MSc (Mathematical Statistics))--University of Pretoria, 2016. The generalised gamma distribution has received much attention due to its exibility and also for having some well-known distributions as special cases. This study originates from a statistic de ned as the ratio of products of independent generalised gamma random variables and shows that it can be represented as the product of independent generalised gamma random variables with some re-parametrisation. By decomposing the character- istic function of the negative logarithm of the statistic and then using the distribution of the di¤erence of two independent generalized integer gamma random variables as a basis, accurate and computationally appealing near-exact distributions are derived for the statis- tic. In the process, a new exible parameter is introduced in the near-exact distributions which allows to control the degree of precision of these approximations. Furthermore, the performance of the near-exact distributions is assessed using a measure of proximity be- tween cumulative distribution functions; also, by comparison with the exact distribution, empirical distribution and with an approximation developed using a di¤erent method and which can only be applied in some particular cases. National Research Foundation (NRF) STATOMET Statistics MSc (Mathematical Statistics) Unrestricted Faculty of Natural and Agricultural Sciences 2023-12-19T09:03:16Z 2023-12-19T09:03:16Z 2017 2016-10 Mini Dissertation * A2017 http://hdl.handle.net/2263/93805 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 Gamma random variables Product of independent generalised gamma random variables |
| title | Product of independent generalised gamma random variables |
| title_full | Product of independent generalised gamma random variables |
| title_fullStr | Product of independent generalised gamma random variables |
| title_full_unstemmed | Product of independent generalised gamma random variables |
| title_short | Product of independent generalised gamma random variables |
| title_sort | product of independent generalised gamma random variables |
| topic | UCTD Gamma random variables |
| url | http://hdl.handle.net/2263/93805 |