Overview
Third edition of the successful seminar book, with special consideration of the recent change of focus of extreme value theory Focus on large observations defined as exceedances over high thresholds Emphasis on multivariate generalized Pareto distributions
Includes supplementary material: sn.pub/extras
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Table of contents (12 chapters)
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Front Matter
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The IID Case: Functional Laws of Small Numbers
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Front Matter
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The IID Case: Multivariate Extremes
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Front Matter
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Non-IID Observations
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Front Matter
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Back Matter
Keywords
About this book
Reviews
From the reviews of the third edition:
Review Janet Hefferman, Journal of Applied Statistics The authors claim that the book is aimed at graduate students and researchers with basic knowledge of probability theory. This claim seems slightly misleading, the material instead being written at a research level, and I suspect generally impenetrable to readers without some previous specialist knowledge of the area. Being almost exclusively theoretical in nature, the book is likely to be of little interest or indeed practical use to an applied statistician. However the book offers a useful addition to the literature of the probabilistic theory of extremes as it consolidates recent developments in the field. Review Holger Drees, Metrika The book is completed by an extensive bibliography with almost 400 references and the usual indices. Indeed, this is a big improvement over the first edition where the references were given in each section separately. The readability is further improved by a considerable number of new plots to visualize examples. Unfortunately, a distorting technical error has crept in Sect. 1.2: on page 8 the first sentence ends abruptly in the middle and nine lines which should be printed here are instead given on page 14, where they interrupt another sentence in a similar manner. In summary, Laws of Small Numbers can be highly recommended to everyone who is looking for a smooth introduction to Poisson approximations in EVT and other fields of probability theory and statistics. In particular, it offers an interesting view on multivariate EVT and on EVT for non-iid observations, which is not presented in a similar way in any other textbook. Review David Stirzaker, Bulletin of the London Mathematical Society In brief, it is clear that this will surely be a valuable resource for anyone involved in, or seeking to master, the more mathematical features of this field.
“Chapters outline the mathematical development of the basic ideas and their extensions and applications. … The material is well presented, with clear explanations and illustrations. For a graduate student with a good background in probability theory, I believe that this book can provide a strong foundation for research into a fascinating area.” (Martin Crowder, International Statistical Review, Vol. 79 (3), 2011)
Authors and Affiliations
Bibliographic Information
Book Title: Laws of Small Numbers: Extremes and Rare Events
Authors: Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss
DOI: https://doi.org/10.1007/978-3-0348-0009-9
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel AG 2011
Softcover ISBN: 978-3-0348-0008-2Published: 15 October 2010
eBook ISBN: 978-3-0348-0009-9Published: 07 October 2010
Edition Number: 3
Number of Pages: XVI, 509
Additional Information: Originally published as volume 23 in the series: DMV Seminar
Topics: Probability Theory and Stochastic Processes, Statistical Theory and Methods