Publication Date


Document Type


First Advisor

Polansky, Alan M.

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

Department of Mathematical Sciences


In an increasingly connected global environment, “high-impact, low-probability" (HILP)

events can have devastating consequences and result in large insurance losses with a heavy-

tailed distribution. Examples of such events include Hurricane Katrina, the Deepwater

Horizon oil disaster and the Japanese nuclear crisis and tsunami. According to the 2012

Blackett Review of HILP Risks from the UK Government Office for Science, the

identification of low-probability risks, and the subsequent development of mitigation plans,

is complicated by their rare or conjectural nature, and their potential for causing impacts

beyond everyday experience. Extremal mixture models and more generally extreme value

analysis help assess HILP risks. In this dissertation, we introduce various classes of heavy-

tailed distributions before moving on to mixture models. In particular, we are interested in

the mixture of a heavy-tailed distribution and a light-tailed distribution. Estimation of the

mixture distribution is based on the expectation-maximization (EM) algorithm and model

selection is achieved using information criteria. Our results indicate that one of the

components of our mixture may provide us with a good model for modeling nonnegative,

heavy-tailed data.


97 pages




Northern Illinois University

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