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Product of independent generalised gamma random variables
Dissertation (MSc (Mathematical Statistics))--University of Pretoria, 2016.
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| Format: | Thesis |
| Language: | English |
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2026
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| _version_ | 1867613534255316992 |
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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 |
| description | Dissertation (MSc (Mathematical Statistics))--University of Pretoria, 2016. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/110137 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:40.523Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2026 |
| publishDateRange | 2026 |
| publishDateSort | 2026 |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/110137 Product of independent generalised gamma random variables Bekker, Andriette, 1958- vrbilankulu@gmail.com Marques, F. Bilankulu, Vusi Raphael Generalised gamma Approximation Near exact Product Characteristic function Dissertation (MSc (Mathematical Statistics))--University of Pretoria, 2016. The generalised gamma distribution has received much attention due to its áexibility and also for having some well-known distributions as special cases. This study originates from a statistic deÖned 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 characteristic 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 statistic. In the process, a new áexible 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 between 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. Statistics MSc (Mathematical Statistics) 2026-05-15T17:26:24Z 2026-05-15T17:26:24Z 16/12/12 2016 Dissertation http://hdl.handle.net/2263/110137 en application/pdf |
| spellingShingle | Generalised gamma Approximation Near exact Product Characteristic function 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 | Generalised gamma Approximation Near exact Product Characteristic function |
| url | http://hdl.handle.net/2263/110137 |