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dc.contributor.authorSun, Julian
dc.date.accessioned2018-09-11T19:34:26Z
dc.date.available2018-09-11T19:34:26Z
dc.date.issued2018-08-11
dc.identifier.urihttps://hdl.handle.net/1813/58726
dc.description.abstractExtreme events are frequently observed in nature and in human activities; they tend to have severe and often negative impact. For this reason they are wellstudied, and the underlying body of work is usually referred to as extreme value theory. The theory often deals with the behavior in the tail of probability distributions or data sets. A key notation is that of heavy-tailed probability distributions. Univariate heavy-tailed distributions exhibit interesting mathematical properties practical for modelling purposes. However, many types of univariate heavy-tailed distributions do not have natural multivariate extensions. Another area of interest in extreme value theory is that of the clustering of extremes in stationary sequences. Inference of cluster sizes tends to be difficult, partly due to the scarcity of data. Clustering also introduces heavy serial dependence in extremal observations, which in turn influences statistical analysis. This thesis seeks to address the aforementioned problems and difficulties. Key contributions include: a multivariate model for a particular class of heavy-tailed distributions, the subexponential distributions, that allows for the approximation of ruin probabilities; a multilevel approach to extremal inference that partially addresses the issue of data scarcity and that improves the variance of extremal estimators; and an algorithmic method to reduce of serial dependence in extremal inferenceen_US
dc.language.isoen_USen_US
dc.subjectextreme valueen_US
dc.subjectheavy tailsen_US
dc.subjectextremal indexen_US
dc.subjectsubexponentialen_US
dc.titleModelling and Inference for Extremal Eventsen_US
dc.typedissertation or thesisen_US


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