Polansky, Alan M.
Ph.D. (Doctor of Philosophy)
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,
Dovoedo, Philippe Kponbogan, "Maximum Likelihood Estimation for a Heavy-Tailed Mixture Distribution" (2019). Graduate Research Theses & Dissertations. 6983.
Northern Illinois University
Rights Statement 2
NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.