Some non-standard statistical dependence problems

dc.contributor.advisorKoen, Chris
dc.contributor.authorBere, Alphonce
dc.date.accessioned2016-04-05T13:56:25Z
dc.date.accessioned2024-05-14T10:11:27Z
dc.date.available2016-04-05T13:56:25Z
dc.date.available2024-05-14T10:11:27Z
dc.date.issued2016
dc.descriptionPhilosophiae Doctor - PhDen_US
dc.description.abstractThe major result of this thesis is the development of a framework for the application of pair-mixtures of copulas to model asymmetric dependencies in bivariate data. The main motivation is the inadequacy of mixtures of bivariate Gaussian models which are commonly fitted to data. Mixtures of rotated single parameter Archimedean and Gaussian copulas are fitted to real data sets. The method of maximum likelihood is used for parameter estimation. Goodness-of-fit tests performed on the models giving the highest log-likelihood values show that the models fit the data well. We use mixtures of univariate Gaussian models and mixtures of regression models to investigate the existence of bimodality in the distribution of the widths of autocorrelation functions in a sample of 119 gamma-ray bursts. Contrary to previous findings, our results do not reveal any evidence of bimodality. We extend a study by Genest et al. (2012) of the power and significance levels of tests of copula symmetry, to two copula models which have not been considered previously. Our results confirm that for small sample sizes, these tests fail to maintain their 5% significance level and that the Cramer-von Mises-type statistics are the most powerful.en_US
dc.identifier.urihttps://hdl.handle.net/10566/14935
dc.language.isoenen_US
dc.publisherUniversity of the Western Capeen_US
dc.rights.holderUniversity of the Western Capeen_US
dc.subjectGamma-ray burstsen_US
dc.subjectKonusen_US
dc.subjectCopulas (Mathematical statistics)en_US
dc.subjectGaussian mixture modelen_US
dc.titleSome non-standard statistical dependence problemsen_US

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