[PDF] Heavy-tail phenomena: probabilistic and statistical modeling Sidney I. Resnick

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 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.