Laws of Small Numbers: Extremes and Rare Events - Softcover

Falk, Michael; Hüsler, Jürg; Reiss, Rolf-Dieter

Softcover

ISBN 10: 3764324163 ISBN 13: 9783764324162

Publisher: Birkhäuser Basel, 2005

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

Book Description

2nd edition

From the Back Cover

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. In this third edition, the dramatic change of focus of extreme value theory has been taken into account: from concentrating on maxima of observations it has shifted to large observations, defined as exceedances over high thresholds. One emphasis of the present third edition lies on multivariate generalized Pareto distributions, their representations, properties such as their peaks-over-threshold stability, simulation, testing and estimation. Reviews of the 2nd edition: "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." David Stirzaker, Bulletin of the London Mathematical Society "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." Holger Drees, Metrika

Edition details

• Publisher: Birkhäuser Basel
• Publication date: 2005
• Language: English
• ISBN 10: 3764324163
• ISBN 13: 9783764324162
• Binding: Paperback
• Edition number: 2
• Number of pages: 376