Laws of Small Numbers: Extremes and Rare Events / Edition 2

Laws of Small Numbers: Extremes and Rare Events / Edition 2

by Michael Falk, Rolf-Dieter Reiss, J rg H sler
     
 

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ISBN-10: 3764324163

ISBN-13: 9783764324162

Pub. Date: 09/11/2008

Publisher: Springer-Verlag New York, LLC

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

Overview

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 on about 130 additional pages.

Part II, which has been added in the second edition, discusses recent developments in multivariate extreme value theory. Particularly notable is a new spectral decomposition of multivariate distributions in univariate ones which makes multivariate questions more accessible in theory and practice. One of the most innovative and fruitful topics during the last decades was the introduction of generalized Pareto distributions in the univariate extreme value theory. Such a statistical modelling of extremes is now systematically developed in the multivariate framework.

Product Details

ISBN-13:
9783764324162
Publisher:
Springer-Verlag New York, LLC
Publication date:
09/11/2008
Edition description:
REV
Pages:
396
Product dimensions:
9.21(w) x 6.14(h) x 0.81(d)

Table of Contents

Preface to the Third Edition.- Preface to the Second Edition.- Preface to the First Edition.- Part I. The IID Case: Functional Laws Of Small Numbers.- 1 Functional Laws of Small Numbers.- 2 Extreme Value Theory.- 3 Estimation of Conditional Curves.- Part II. The IID Case: Multivariate Extremes.- 4 Basic Theory of Multivariate Maxima.- 5 Multivariate Generalized Pareto Distributions.- 6 The Pickands Approach in the Bivariate Case.- 7 Multivariate Extremes: Supplementary Concepts and Results.- Part III. Non-IID Observations.- 8 Introduction to the Non-IID Case.- 9 Extremes of Random Sequences.- 10 Extremes of Gaussian Processes.- 11 Extensions for Rare Events.- 12 Statistics of Extremes.- Author Index.- Subject Index.- Bibliography.

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