Heavy-Tail Phenomena, 2007 Probabilistic and Statistical Modeling Springer Series in Operations Research and Financial Engineering Series

Langue : Anglais

Auteur : Resnick Sidney I.

Couverture de l’ouvrage Heavy-Tail Phenomena

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This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. It is uniquely devoted to heavy-tails 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 second-year graduate students and researchers in the areas of applied mathematics, statistics, operations research, electrical engineering, and economics.

Crash Courses.- Crash Course I: Regular Variation.- Crash Course II: Weak Convergence; Implications for Heavy-Tail Analysis.- Statistics.- Dipping a Toe in the Statistical Water.- Probability.- The Poisson Process.- Multivariate Regular Variation and the Poisson Transform.- Weak Convergence and the Poisson Process.- Applied Probability Models and Heavy Tails.- More Statistics.- Additional Statistics Topics.- Appendices.- Notation and Conventions.- Software.

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