Resnick S.I. Heavy-tail phenomena: probabilistic and statistical modeling

New York: Springer, 2007. — 412 p.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 featuresUnique 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 stochastic 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.