The saddle-point method and its application to the hill estimator

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dc.contributor.advisorDe Wet, Tertiusen_ZA
dc.contributor.authorBuitendag, Svenen_ZA
dc.contributor.otherStellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics & Actuarial Science.en_ZA
dc.date.accessioned2016-12-22T13:10:20Z
dc.date.available2016-12-22T13:10:20Z
dc.date.issued2016-12
dc.descriptionThesis (MCom)--Stellenbosch University, 2016.
dc.description.abstractENGLISH 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.en_ZA
dc.description.abstractAFRIKAANSE 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.af_ZA
dc.description.versionMasters
dc.format.extent109 pages ; illustrations, includes annexures
dc.identifier.urihttp://hdl.handle.net/10019.1/100057
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch University
dc.rights.holderStellenbosch University
dc.subjectSaddle point method (Numerical analysis)en_ZA
dc.subjectHill estimatoren_ZA
dc.subjectMethod of steepest descent (Numerical analysis)en_ZA
dc.subjectEdgeworth expansionsen_ZA
dc.subjectExtreme value theoryen_ZA
dc.subjectUCTD
dc.titleThe saddle-point method and its application to the hill estimatoren_ZA
dc.typeThesisen_ZA
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Masters Degrees (Statistics and Actuarial Science)