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AuthorFalk, Michael. author
TitleLaws of Small Numbers: Extremes and Rare Events [electronic resource] / by Michael Falk, Rolf-Dieter Reiss, Jรผrg Hรผsler
ImprintBasel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2004
Edition Second, revised and extended edition
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Descript XIII, 378 p. 12 illus. online resource


Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book was strengthened in the second edition by incorporating various new results on about 130 additional pages. Part II, which has been added in the second edition, discusses recent developments in multivariate extreme value theory. Particularly notable is a new spectral decomposition of multivariate distributions in univariate ones which makes multivariate questions more accessible in theory and practice. One of the most innovative and fruitful topics during the last decades was the introduction of generalized Pareto distributions in the univariate extreme value theory. Such a statistical modelling of extremes is now systematically developed in the multivariate framework


I. The IID Case: Functional Laws of Small Numbers -- 1 Functional Laws of Small Numbers -- 2 Extreme Value Theory -- 3 Estimation of Conditional Curves -- II. The IID Case: Multivariate Extremes -- 4 Basic Theory of Multivariate Maxima -- 5 Multivariate Extremes: The Pickands Approach -- 6 The Pickands Approach in the Bivariate Case -- 7 Multivariate Extremes: Supplementary Concepts and Results -- III. Non IID Observations -- 8 Introduction to the Non IID Case -- 9 Extremes of Random Sequences -- 10 Extremes of Gaussian Processes -- 11 Extensions for Rare Events -- 12 Statistics of Extremes -- Author Index

Mathematics Probabilities Statistics Mathematics Probability Theory and Stochastic Processes Statistical Theory and Methods


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