Estimating Risk of Extreme and Catastrophic Events under Interval Uncertainty

Authors

Nitaya Buntao
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

3-2011

Comments

Technical Report: UTEP-CS-11-12

Abstract

In many application areas, we encounter heavy-taildistributions -- for example, such distributions are ubiquitousin financial applications. These distributions are oftendescribed by Pareto law. There exist techniques for estimatingthe parameters of such the corresponding Pareto distributionsbased on the sample x₁, ..., x_n. In practice, we oftenonly know the values x_i with interval uncertainty. In thispaper, we show how to estimate the parameters of the Paretodistribution under such uncertainty and how to describe deviationand dependence for general heavy-tailed distributions.