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Overview
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 phenomena where there is a significant probability of a single huge value impacting system behavior. Record-breaking insurance losses, financial returns, sizes of files stored on a server, transmission rates of files are all examples of heavy-tailed phenomena.
Key features:
Unique text devoted to heavy-tails.
The treatment of heavy tails is largely dimensionless.
The text gives attention to both probability modeling and statistical methods for fitting models. Most other books focus on one or the other but not both.
The book emphasizes the broad applicability of heavy-tails to the fields of finance (e.g., value-at- risk), data networks, insurance.
The presentation is clear, efficient and coherent and, balances theory and data analysis to show the applicability and limitations of certain methods.
Several chapters examine in detail the mathematical properties of the methodologies as well as their implementation in the Splus or R statistical languages.
The exposition is driven by numerous examples and exercises.
Prerequisites for the reader include a prior course in shastic 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 operations research, statistics, applied mathematics, electrical engineering, financial engineering, networking and economics.
Sidney Resnick is a Professor at Cornell University and has written several well-known bestsellers: A Probability Path (ISBN: 081764055X), Adventures in Shastic Processes (ISBN: 0817635912) and Extreme Values, Regular Variation, and Point Processes (ISBN: 0387964819).
Synopsis
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.