How does one estimate the very unlikely event? Heavy Tailed probability models for extreme events

Heavy tailed models arise when examining phenomena that occur more frequently than the standard statistical models (normality, chi-squared, etc.) would predict. In many applications our focus is precisely on the “outliers” rather than upon the bulk of the data, however standard statistical methods are not available in these heavy tailed situations. Examples of heavy tailed distributions include the size distribution of files sent over the internet, high frequency financial data, insurance (and reinsurance) loss data, and income distributions, among others. Techniques for estimating the occurrence of rare events beyond the range of available data (extrapolation outside the data set) will be discussed (and is, of course, model dependent). Methods for estimating the probability of extreme events, and implementing these estimates for practical decision making is the subject of this session, and the topic area known as “extreme value theory”. This talk will give an overview of extreme value theoretic modeling, motivating two of the most commonly used heavy tailed models, (the generalized extreme value and generalized Pareto models – stable distributions constitute a third important heavy tailed model and will be discussed subsequently). We shall also discuss how and why these models arise, with asymptotic rationales justifying why they are reasonable to use, and we shall discuss what role heavy tailed models have in implementing Enterprise Risk Management.