Heavy-Tail Phenomena: Probabilistic and Statistical Modeling

This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. Heavy tails are characteristic of many phenomena where the probability of a single huge value impacts heavily. Record-breaking insurance losses, financial-log returns, files sizes stored on a server, transmission rates of files are all examples of heavy-tailed phenomena.

Key features:

* Unique text devoted to heavy-tails

* Emphasizes both probability modeling and statistical methods for fitting models. Most treatments focus on one or the other but not both

* Presents broad applicability of heavy-tails to the fields of data networks, finance (e.g., value-at- risk), insurance, and hydrology

* Clear, efficient and coherent exposition, balancing theory and actual data to show the applicability and limitations of certain methods

* Examines in detail the mathematical properties of the methodologies as well as their implementation in Splus or R statistical languages

* Exposition driven by numerous examples and exercises

Prerequisites for the reader include a prior course in shastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use (or at least to learn) a statistics package such as R or Splus. This work will serve second-year graduate students and researchers in the areas of applied mathematics, statistics, operations research, electrical engineering, and economics.