Table of contents
About this book
Introduction
Keywords
Bibliographic information
 Book Title Laws of Small Numbers: Extremes and Rare Events

Authors
Michael Falk
Jürg Hüsler
RolfDieter Reiss
 DOI https://doi.org/10.1007/9783034800099
 Copyright Information Springer Basel AG 2011
 Publisher Name Springer, Basel
 eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
 Softcover ISBN 9783034800082
 eBook ISBN 9783034800099
 Edition Number 3
 Number of Pages XVI, 509
 Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
 Additional Information Originally published as volume 23 in the series: DMV Seminar

Topics
Probability Theory and Stochastic Processes
Statistical Theory and Methods
 Buy this book on publisher's site
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 noniid 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)