Laws of Small Numbers: Extremes and Rare Events - Couverture souple

Couverture souple

ISBN 10 : 3764350717 ISBN 13 : 9783764350710

Editeur : Birkhauser Verlag AG, 1994

Synopsis

Laws of small numbers concern rare events, i.e., events having but a small probability of occurrence. It is reasonable to describe such events as truncated empirical point processes, and a point process of rare events can be approximated by a Poisson process. This approach is applied to the following topics: extremes and rare events of stochastic processes, with special emphasis given to Gaussian processes; Poisson point processes; statistics in extreme value models; and nonparametric regression analysis. This book comes with the statistical software system XTREMES, version 1.2, an interactive menu-driven system which runs on IBM-compatible PCs under MS-DOS and is designed for dealing with various questions in extreme value analysis. The beginner should appreciate the introduction to the fields mentioned above, and the expert the comprehensive account of recent results and developments.

A propos du livre

Présentation de l'éditeur

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

Détails de l'édition

• Éditeur: Birkhauser Verlag AG
• Date d'édition: 1994
• Langue: anglais
• ISBN 10: 3764350717
• ISBN 13: 9783764350710
• Reliure: Broché
• Nombre de pages: 293
• Éditeur: Falk Michael, Etc.
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible