Laws of Small Numbers: Extremes and Rare Events,3 Edition - ISBN:3034800088

Laws of Small Numbers: Extremes and Rare Events,3 Edition

Date: 15 April 2011, 10:50

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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
Summary: extremes with software and applications
Rating: 5
This book provides a nice introduction to the mathematical theory of rare events and extreme values. It takes the point process approach to rare events using the empirical point process defined by the crossing of a high or low level to employ an approximate Poisson process. This approach has broad applicability and the authors use it to consider rare and extreme events for stochastic processes including Gaussian processes, Poisson point processes, extreme value models and nonparametric regression.
This book is noteworthy for its mix of theory and application and for the introduction of the software XTREMES. Chapter 6 is devoted to explaining how to analyze data for extremes using the software XTREMES. A diskette is included with the text with version 1.2 of XTREMES that is an interactive program that can run on MS-DOS operated computers. The text is very much up-to-date on the theoretical developments as of 1994.

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