Extremes and Related Properties of Random Sequences and Processes

  • M. R. Leadbetter
  • Georg Lindgren
  • Holger Rootzén

Part of the Springer Series in Statistics book series (SSS)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Classical Theory of Extremes

    1. Front Matter
      Pages 1-2
    2. M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 3-30
    3. M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 31-48
  3. Extremal Properties of Dependent Sequences

    1. Front Matter
      Pages 49-50
    2. M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 51-78
    3. M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 79-100
    4. M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 101-122
    5. M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 123-141
  4. Extreme Values in Continuous Time

    1. Front Matter
      Pages 143-144
    2. M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 145-162
    3. M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 163-172
    4. M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 173-190
    5. M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 191-204
    6. M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 205-215
    7. M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 216-242
    8. M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 243-263
  5. Applications of Extreme Value Theory

    1. Front Matter
      Pages 265-265
    2. M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 267-277
    3. M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 278-304

About this book

Introduction

Classical Extreme Value Theory-the asymptotic distributional theory for maxima of independent, identically distributed random variables-may be regarded as roughly half a century old, even though its roots reach further back into mathematical antiquity. During this period of time it has found significant application-exemplified best perhaps by the book Statistics of Extremes by E. J. Gumbel-as well as a rather complete theoretical development. More recently, beginning with the work of G. S. Watson, S. M. Berman, R. M. Loynes, and H. Cramer, there has been a developing interest in the extension of the theory to include, first, dependent sequences and then continuous parameter stationary processes. The early activity proceeded in two directions-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.

Keywords

Extremum Maxima Properties Random variable Stochastischer Prozess Zufallsfolge statistics

Authors and affiliations

  • M. R. Leadbetter
    • 1
  • Georg Lindgren
    • 2
  • Holger Rootzén
    • 3
  1. 1.Department of StatisticsThe University of North CarolinaChapel HillUSA
  2. 2.Department of Mathematical StatisticsUniversity of LundLundSweden
  3. 3.Institute of Mathematical StatisticsUniversity of CopenhagenCopenhagen øDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-5449-2
  • Copyright Information Springer-Verlag New York 1983
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-5451-5
  • Online ISBN 978-1-4612-5449-2
  • Series Print ISSN 0172-7397
  • About this book