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HeavyTail Phenomena: Probabilistic and Statistical Modeling (Springer Series in Operations Research and Financial Enginee)by Sidney I. Resnick
Synopses & ReviewsPublisher Comments:This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavytail analysis. Heavy tails are characteristic of phenomena where there is a significant probability of a single huge value impacting system behavior. Recordbreaking insurance losses, financial returns, sizes of files stored on a server, transmission rates of files are all examples of heavytailed phenomena. Key features: Unique text devoted to heavytails. 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 heavytails to the fields of finance (e.g., valueat 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 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 secondyear 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 wellknown bestsellers: A Probability Path (
Synopsis:This text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavytail analysis. It is uniquely devoted to heavytails and emphasizes both probability modeling and statistical methods for fitting models.
Synopsis:This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavytail analysis. It is uniquely devoted to heavytails and emphasizes both probability modeling and statistical methods for fitting models. 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 a statistics package. This work will serve secondyear graduate students and researchers in the areas of applied mathematics, statistics, operations research, electrical engineering, and economics.
Table of ContentsIntroduction. Part 1. Crash Courses. Crash Course I: Regular Variation. Crash Course II: Weak Convergence; Implications for Heavy Tail Analysis. Part II. Statistics. Dipping a Toe in the Statistical Water. Part III. Probability. The Poisson Process. Multivariate Regular Variation and the Poisson Transform. Weak Convergence and the Poisson Process. Applied Probability Models and Heavy Tails. Part IV. More Statistics.Additional Statistics Topics. Part V. Appendices. Notation and Conventions. Software Routines. Index.
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