Laws of Small Numbers: Extremes and Rare Events: v. 23 (Oberwolfach Seminars) - Softcover

Falk, Michael

Softcover

ISBN 10: 3764324163 ISBN 13: 9783764324162

Publisher: Birkhäuser Basel, 2008

Synopsis

Since the publication of the first edition of this seminar book, the theory and applications of extremes and rare events have seen increasing interest. "Laws of Small Numbers" gives a mathematically oriented development of the theory of rare events underlying various applications. The new edition incorporates numerous new results on about 130 additional pages. Part II, added in the second edition, discusses recent developments in multivariate extreme value theory.

About this title

Review

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)

Book Description

2nd edition

Edition details

• Publisher: Birkhäuser Basel
• Publication date: 2008
• Language: English
• ISBN 10: 3764324163
• ISBN 13: 9783764324162
• Binding: Paperback
• Edition number: 2
• Number of pages: 396