Department of Statistics, The Ohio State University
Chotey Lal & Mohra Devi Rustagi Memorial Lecture
STATISTICS OF EXTREMES, WITH APPLICATIONS IN ENVIRONMENTAL
SCIENCE, INSURANCE AND FINANCE
RICHARD L SMITH
UNIVERSITY OF NORTH CAROLINA
3:30PM - Tuesday, April 30th, 2002
Room 170, Eighteenth Avenue Bldg. (EA 170)
ABSTRACT
There are many areas of the application of statistics where
the main interest lies in the probabilities of extreme events
rather than more conventional statistics such as means and
variances. Examples include many areas of environmental science,
such as floods, hurricanes and extreme environmental pollution;
insurance, where there is a long history of statistical
techniques to assess the probabilities of very large claims; and
mathematical finance, where there has been increasing interest in
topics such as Value at Risk, which are concerned with extreme
fluctations in the markets.
This lecture will survey the use of Extreme Value Theory as a
class of techniques to solve these problems. Beginning with the
classical limit theorems of Fisher-Tippett and Gnedenko, we shall
consider modern statistical methods based on threshold
exceedances, and extensions including multivariate extremes and
the use of Bayesian hierarchical models. A variety of examples
will illustrate the rich possibilities for applications of these
techniques.
