TY - BOOK
AU - Resnick,Sidney I.
ED - SpringerLink (Online service)
TI - Heavy-Tail Phenomena: Probabilistic and Statistical Modeling
T2 - Springer Series in Operations Research and Financial Engineering,
SN - 9780387450247
AV - QA273.A1-274.9
U1 - 519.2 23
PY - 2007///
CY - New York, NY
PB - Springer New York
KW - Mathematics
KW - Applied mathematics
KW - Engineering mathematics
KW - Mathematical models
KW - Operations research
KW - Management science
KW - Probabilities
KW - Statistics
KW - Probability Theory and Stochastic Processes
KW - Statistical Theory and Methods
KW - Applications of Mathematics
KW - Operations Research, Management Science
KW - Mathematical Modeling and Industrial Mathematics
N1 - 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
N2 - 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 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 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 Stochastic Processes (ISBN: 0817635912) and Extreme Values, Regular Variation, and Point Processes (ISBN: 0387964819)
UR - http://dx.doi.org/10.1007/978-0-387-45024-7
ER -