Heavy Tail Phenomena: Probabilistic and Statistical Modeling

Sidney I. Resnick, "Heavy-Tail Phenomena: Probabilistic and Statistical Modeling"

Springer; 1 edition (December 1, 2006) | ISBN:0387242724 | 406 pages | PDF | 3,2 Mb

This comprehensive textgives an interestingand useful blendof the mathematical, probabilistic and statistical tools used in heavy-tail analysis.Heavy tails are characteristic of manyphenomena 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 ofheavy-tailed phenomena.

Key features:

* Uniquetext devoted to heavy-tails

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

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

* Clear, efficient and coherent exposition, balancingtheory 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 inSplus 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.