Heavy-Tail Phenomena Probabilistic and Statistical Modeling [Paperback]

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.

This 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.

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.place on personal bookshelves of many applied probabilists. (Ilya S. Molchanov, Mathematical Reviews, Issue 2008 j)

This is a survey of the mathematical, probabilistic and statistical tools used in heavy-tail analysis as well as some examples of their use. & This book could be used very conveniently for a Masters-level course in point processes or regular variation; theoretical concepts are introduced in a pedagogical way, and several exercises accompany each chapter. Researchers in applied probability or statistics will also benefit from readinglF