Heavy-Tail Phenomena: Probabilistic and Statistical Modeling

Resnick S.I.0387450246, 0387242724

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 exercisesPrerequisites 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.