Heavy-Tail Phenomena

by Resnick, Sidney I.

• ISBN13: 9780387242729
• ISBN10: 0387242724
• Format: Hardcover
• Copyright: 2006-12-30
• Publisher: Springer Nature

Summary

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.

Author Biography

Sidney Resnick is a Professor at Cornell University.

Table of Contents

Introduction	p. 1
Crash course I : regular variation	p. 17
Crash course II : weak convergence; implications for heavy-tail analysis	p. 39
Dipping a toe in the statistical water	p. 73
The Poisson process	p. 119
Multivariate regular variation and the Poisson transform	p. 167
Weak convergence and the Poisson process	p. 211
Applied probability models and heavy tails	p. 253
Additional statistics topics	p. 291
Notation and conventions	p. 359
Software	p. 363
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