04439nam a22005775i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001900172050001600191072001600207072001700223072002300240082001400263100003200277245011500309264004600424300003400470336002600504337002600530338003600556347002400592490008100616505048000697520194101177650001703118650002503135650002903160650002503189650002503214650002403239650001903263650001603282650001703298650004903315650003603364650003303400650004503433650005403478710003403532773002003566776003603586830008103622856004803703912001403751999001903765952007703784978-0-387-45024-7DE-He21320180115171407.0cr nn 008mamaa100301s2007 xxu| s |||| 0|eng d a97803874502479978-0-387-45024-77 a10.1007/978-0-387-45024-72doi 4aQA273.A1-274.9 4aQA274-274.9 7aPBT2bicssc 7aPBWL2bicssc 7aMAT0290002bisacsh04a519.22231 aResnick, Sidney I.eauthor.10aHeavy-Tail Phenomenah[electronic resource] :bProbabilistic and Statistical Modeling /cby Sidney I. Resnick. 1aNew York, NY :bSpringer New York,c2007. aXIX, 404 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aSpringer Series in Operations Research and Financial Engineering,x1431-85980 aCrash 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. aThis 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). 0aMathematics. 0aApplied mathematics. 0aEngineering mathematics. 0aMathematical models. 0aOperations research. 0aManagement science. 0aProbabilities. 0aStatistics.14aMathematics.24aProbability Theory and Stochastic Processes.24aStatistical Theory and Methods.24aApplications of Mathematics.24aOperations Research, Management Science.24aMathematical Modeling and Industrial Mathematics.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387242729 0aSpringer Series in Operations Research and Financial Engineering,x1431-859840uhttp://dx.doi.org/10.1007/978-0-387-45024-7 aZDB-2-SMA c369499d369499 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK