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Laws of Small Numbers: Extremes and Rare Events

  • Michael Falk
  • Rolf-Dieter Reiss
  • Jürg Hüsler

Table of contents

  1. Front Matter
    Pages i-xiii
  2. The IID Case: Functional Laws of Small Numbers

    1. Front Matter
      Pages 1-1
    2. Michael Falk, Rolf-Dieter Reiss, Jürg Hüsler
      Pages 3-22
    3. Michael Falk, Rolf-Dieter Reiss, Jürg Hüsler
      Pages 23-74
    4. Michael Falk, Rolf-Dieter Reiss, Jürg Hüsler
      Pages 75-103
  3. The IID Case: Multivariate Extremes

    1. Front Matter
      Pages 105-105
    2. Michael Falk, Rolf-Dieter Reiss, Jürg Hüsler
      Pages 107-130
    3. Michael Falk, Rolf-Dieter Reiss, Jürg Hüsler
      Pages 131-159
    4. Michael Falk, Rolf-Dieter Reiss, Jürg Hüsler
      Pages 161-202
    5. Michael Falk, Rolf-Dieter Reiss, Jürg Hüsler
      Pages 203-232
  4. Non IID Observations

    1. Front Matter
      Pages 233-233
    2. Michael Falk, Rolf-Dieter Reiss, Jürg Hüsler
      Pages 235-248
    3. Michael Falk, Rolf-Dieter Reiss, Jürg Hüsler
      Pages 249-271
    4. Michael Falk, Rolf-Dieter Reiss, Jürg Hüsler
      Pages 273-296
    5. Michael Falk, Rolf-Dieter Reiss, Jürg Hüsler
      Pages 297-327
    6. Michael Falk, Rolf-Dieter Reiss, Jürg Hüsler
      Pages 329-345
  5. Back Matter
    Pages 347-378

About this book

Introduction

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.

Keywords

Gaussian process Maxima probability probability theory statistics

Authors and affiliations

  • Michael Falk
    • 1
  • Rolf-Dieter Reiss
    • 2
  • Jürg Hüsler
    • 3
  1. 1.Institute of Applied Mathematics and StatisticsUniversity of WürzburgWürzburgGermany
  2. 2.Department of MathematicsUniversity of SiegenSiegenGermany
  3. 3.Department of Mathematical Statistics and Actuarial ScienceUniversity of BerneBernSwitzerland

Bibliographic information