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

 dc.contributor.advisor De Wet, Tertius en_ZA dc.contributor.author Buitendag, Sven en_ZA dc.contributor.other Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics & Actuarial Science. en_ZA dc.date.accessioned 2016-12-22T13:10:20Z dc.date.available 2016-12-22T13:10:20Z dc.date.issued 2016-12 dc.identifier.uri http://hdl.handle.net/10019.1/100057 dc.description Thesis (MCom)--Stellenbosch University, 2016. dc.description.abstract 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. en_ZA dc.description.abstract 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. af_ZA dc.format.extent 109 pages ; illustrations, includes annexures dc.language.iso en_ZA en_ZA dc.publisher Stellenbosch : Stellenbosch University dc.subject Saddle point method (Numerical analysis) en_ZA dc.subject Hill estimator en_ZA dc.subject Method of steepest descent (Numerical analysis) en_ZA dc.subject Edgeworth expansions en_ZA dc.subject Extreme value theory en_ZA dc.subject UCTD dc.title The saddle-point method and its application to the hill estimator en_ZA dc.type Thesis en_ZA dc.description.version Masters dc.rights.holder Stellenbosch University
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