A Sieve model for extreme values

Abstract

From the class of extreme value distributions, we focus on the set of heavy-tailed distributions which produce low-frequency, high-cost events. The regular Pareto distribution is the basic model of choice, being the simplest heavy-tailed distribution. Real data suggest that modifications of the Pareto distribution may be a better fit; an alternative model is the truncated Pareto distribution (TPD). For further study, this paper proposed a TPD Sieve class of distributions. The properties and estimation on the Sieve class are also discussed. We fit the models to the largest Black Sea bass caught in Buzzard's Bay, MA, USA and the costliest Atlantic hurricanes from 1900 to 2005. Using measures of model adequacy, the TPD Sieve model is generally found to be the best-fitting model.

Keywords:

• extreme value theory
• heavy-tailed distributions
• power law
• Pareto distribution
• truncated Pareto distribution
• Sieve class of distributions
• Black Sea bass
• conservation biology
• hurricanes

AMS 2010 Subject Classifications::

• primary: 62G30
• secondary: 62G32

Acknowledgements

We express our appreciation for the very useful comments of the referee and editor, which helped to improve the paper. This research is supported by the Natural Sciences and Engineering Research Council of Canada.