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Laws of Small Numbers: Extremes and Rare Events

  • Michael Falk
  • Jürg Hüsler
  • Rolf-Dieter Reiss

Table of contents

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

    1. Front Matter
      Pages 1-1
    2. Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss
      Pages 3-23
    3. Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss
      Pages 25-101
    4. Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss
      Pages 103-131
  3. The IID Case: Multivariate Extremes

    1. Front Matter
      Pages 133-133
    2. Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss
      Pages 135-169
    3. Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss
      Pages 171-257
    4. Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss
      Pages 259-309
    5. Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss
      Pages 311-340
  4. Non-IID Observations

    1. Front Matter
      Pages 341-341
    2. Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss
      Pages 343-356
    3. Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss
      Pages 357-380
    4. Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss
      Pages 381-418
    5. Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss
      Pages 419-454
    6. Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss
      Pages 455-471
  5. Back Matter
    Pages 473-509

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. 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

Keywords

Gaussian process Maxima Peak probability theory statistics

Authors and affiliations

  • Michael Falk
    • 1
  • Jürg Hüsler
    • 2
  • Rolf-Dieter Reiss
    • 3
  1. 1.Lehrstuhl für StatistikInstitut für MathematikWürzburgGermany
  2. 2.Inst. Mathematische Statistik und, VersicherungslehreUniversität BernBernSwitzerland
  3. 3.FB 6 MathematikUniversität SiegenSiegenGermany

Bibliographic information

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