dc.contributor.advisor De Waal, D. J. dc.contributor.author Nel, Andrehette dc.date.accessioned 2018-06-15T11:43:58Z dc.date.available 2018-06-15T11:43:58Z dc.date.issued 2007-11 dc.identifier.uri http://hdl.handle.net/11660/8416 dc.description.abstract English: The aim of this thesis is to investigate the modelling of multivariate extreme en_ZA values. Extreme value theory is becoming very popular as a statistical discipline. Not only is extreme value theory emerging in the statistical field but also in other disciplines such as engineering, financial markets and energy markets. Extreme value analysis focuses on the probability of unusual or extreme events. Extreme value theory is particularly useful in environmental applications such as the modelling of high rainfall, strong wind, etc. A lot of literature is available on the modelling of univariate extreme values. One topic of interest is the calculation of probabilities of related extreme events. To address this topic the modelling of multivariate extreme values is investigated. Various models are considered for modelling multivariate extreme values. The data set used in the thesis is the daily inflow of water, in cubic meters per second, into the Gariep Dam over a period of 29 years, from 1976 to 2006, excluding 1980 and 1982 due to large data losses. The models considered are the Multivariate Generalized Burr-Gamma distribution (Chapter 2), multivariate regression (Chapter 3), the Gumbel, Tawn and Logistic copulas (Chapter 5 and 6), and the Dirichlet mixture model (Chapter 5). The emphasis of Extreme Value Theory lies in the extreme values or events. Therefore, a threshold is chosen and only data above the threshold is modelled. Hence, specific research is done in this thesis on how to choose a threshold (Chapter 4). The preferred threshold method in this thesis is the method of the negative differential entropy of the Dirichlet process (Chapter 4). The thesis mainly considers a Bayesian approach for the estimation of parameter, although other approaches are also discussed. The last chapter, Chapter 7, gives a conclusion on the work that is covered in the thesis and recommendations for further research. dc.description.abstract Afrikaans: Die doel van die tesis is om ondersoek is te stel na die modellering van en_ZA meerveranderlike-ekstreemwaardes. Die gewildheid van ekstreemwaardeteorie as ŉ statistiese dissipline neem toe. Ekstreemwaardeteorie neem nie net toe in ŉ statistiese veld nie maar ook in ander dissiplines bv. ingenieurswese, finansiële markte en energiemarkte. Ekstreemwaarde-analise fokus op waarskynlikhede van ongewone, ekstreme gebeurtenisse wat plaasvind. Ekstreemwaardeteorie is besonders bruikbaar in toepassings omtrent omgewingsaspakte bv. hoë reënval, sterk winde ens. Baie literatuur is beskikbaar omtrent modellering van eenveranderlikeekstreemwaardes. Die onderwerp van belang is die berekening van waarskynlikhede van verwante ekstreme gebeurtenisse. Hierdie onderwerp word aangespreek deur die modellering van meerveranderlike-ekstreemwaardes te ondersoek. In hierdie tesis word verskeie modelle beskou vir die modellering van meerveranderlike-ekstreemwaardes. Die datastel wat in hierdie tesis gebruik word, is die daaglikse invloei van water in die Gariepdam, gemeet in kubieke meter per sekonde, oor ŉ periode van 29 jaar,1976 tot en met 2006, met uitsluiting van 1980 en 1982 weens onvolledige data inskrywings. Die modelle wat beskou word is die Meerveranderlike Veralgemeende Burr Gammaverdeling (Hoofstuk 2), meerveranderlike regressie (Hoofstuk 3), die Gumbel, Tawn en Logistiese kopula (Hoofstuk 5 en 6), en die Dirichletmengselmodel (Hoofstuk 5). Ekstreemwaardeteorie plaas die klem op die ekstreme waardes of gebeurtenisse, daarom word ŉ drumpelwaarde gekies en net data bokant die drumpelwaarde word gemodelleer. Spesifieke navorsing is in hierdie tesis gedoen oor hoe om ŉ drumpelwaarde te kies (Hoofstuk 4). Die voorkeur metode van hoe om die drumpelwaarde te kies is die metode van die negatiewe differensiële entropie van die Dirichletproses (Hoofstuk 4). Alhoewel ander benaderings ook bespreek word, word ŉ Bayesbenadering hoofsaaklik vir die beraming van die parameters beskou. Die laaste hoofstuk, Hoofstuk 7, gee ŉ gevolgtrekking, oor die werk wat gedoen is in die tesis, en ook verdere navorsingsaanbevelings. dc.language.iso en en_ZA dc.publisher University of the Free State en_ZA dc.subject Extreme value theory en_ZA dc.subject QQ-plots en_ZA dc.subject Threshold en_ZA dc.subject MGBG en_ZA dc.subject GPD en_ZA dc.subject Bayesian estimates en_ZA dc.subject MDI prior en_ZA dc.subject Joint estimating en_ZA dc.subject Dirichlet process en_ZA dc.subject Tail probabilities en_ZA dc.subject Extreme value copula en_ZA dc.subject Logistic copula en_ZA dc.subject Dependence structure en_ZA dc.subject Dirichlet mixture model en_ZA dc.subject Spectral distribution function en_ZA dc.subject Frechet marginals en_ZA dc.subject Thesis (Ph.D. (Mathematical Statistics))--University of the Free State, 2007 en_ZA dc.title Modelling of multivariate extreme data en_ZA dc.type Thesis en_ZA dc.rights.holder University of the Free State en_ZA
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