Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
The saddle-point method and its application to the hill estimator
Thesis (MCom)--Stellenbosch University, 2016.
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | en_ZA |
| Published: |
Stellenbosch : Stellenbosch University
2016
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613845920415744 |
|---|---|
| access_status_str | Open Access |
| author | Buitendag, Sven |
| author2 | De Wet, Tertius |
| author_browse | Buitendag, Sven De Wet, Tertius |
| author_facet | De Wet, Tertius Buitendag, Sven |
| author_sort | Buitendag, Sven |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MCom)--Stellenbosch University, 2016. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/100057 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:42:37.450Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/100057 The saddle-point method and its application to the hill estimator Buitendag, Sven De Wet, Tertius Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics & Actuarial Science. Saddle point method (Numerical analysis) Hill estimator Method of steepest descent (Numerical analysis) Edgeworth expansions Extreme value theory UCTD Thesis (MCom)--Stellenbosch University, 2016. ENGLISH SUMMARY : The saddle-point approximation is a highly accurate approximation of the distribution of a random variable. It was originally derived as an approximation in situations where a parameter takes on large values. However, due to its high accuracy and good behaviour in a variety of applications not involving such a parameter, it has been generalized and applied to the distribution of any random variable with a well-behaved cumulant generating function. In this thesis the theory underlying the saddle-point approximation will be discussed and illustrated with an application to approximate the distribution of the Hill estimator in extreme value theory. AFRIKAANSE OPSOMMING : Die saalpunt-benadering is 'n hoogs noukeurige benadering van die verdeling van 'n stochastiese veranderlike. Dit is oorspronklik afgelei as 'n benadering in gevalle waar 'n parameter groot waardes aanneem. Nietemin, na aanleiding van sy hoogs akkurate aard en goeie gedrag in 'n verskeidenheid van toepassings wat nie betrekking het op so 'n parameter nie, is dit veralgemeen en toegepas op die verdeling van enige stochastiese veranderlike met 'n kumulantvoortbringende funksie wat goeie gedrag toon. In hierdie tesis sal die teorie onderliggend aan die saalpunt-benadering bespreek en gellustreer word met 'n toepassing om die verdeling van die Hill-beramer te benader. Masters 2016-12-22T13:10:20Z 2016-12-22T13:10:20Z 2016-12 Thesis http://hdl.handle.net/10019.1/100057 en_ZA Stellenbosch University 109 pages ; illustrations, includes annexures application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Saddle point method (Numerical analysis) Hill estimator Method of steepest descent (Numerical analysis) Edgeworth expansions Extreme value theory UCTD Buitendag, Sven The saddle-point method and its application to the hill estimator |
| title | The saddle-point method and its application to the hill estimator |
| title_full | The saddle-point method and its application to the hill estimator |
| title_fullStr | The saddle-point method and its application to the hill estimator |
| title_full_unstemmed | The saddle-point method and its application to the hill estimator |
| title_short | The saddle-point method and its application to the hill estimator |
| title_sort | saddle point method and its application to the hill estimator |
| topic | Saddle point method (Numerical analysis) Hill estimator Method of steepest descent (Numerical analysis) Edgeworth expansions Extreme value theory UCTD |
| url | http://hdl.handle.net/10019.1/100057 |
| work_keys_str_mv | AT buitendagsven thesaddlepointmethodanditsapplicationtothehillestimator AT buitendagsven saddlepointmethodanditsapplicationtothehillestimator |