Asymptotic Approximations for Probability Integrals

  • Authors
  • Karl Wilhelm Breitung
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1592)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Karl Wilhelm Breitung
    Pages 1-8
  3. Karl Wilhelm Breitung
    Pages 9-33
  4. Karl Wilhelm Breitung
    Pages 34-44
  5. Karl Wilhelm Breitung
    Pages 45-50
  6. Karl Wilhelm Breitung
    Pages 51-84
  7. Karl Wilhelm Breitung
    Pages 85-105
  8. Karl Wilhelm Breitung
    Pages 106-120
  9. Karl Wilhelm Breitung
    Pages 121-134
  10. Back Matter
    Pages 135-149

About this book

Introduction

This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists. A collection of results of the Laplace methods is given. Such methods are useful for example in reliability, statistics, theoretical physics and information theory. An important special case is the approximation of multidimensional normal integrals. Here the relation between the differential geometry of the boundary of the integration domain and the asymptotic probability content is derived. One of the most important applications of these methods is in structural reliability. Engineers working in this field will find here a complete outline of asymptotic approximation methods for failure probability integrals.

Keywords

Asymptotic approximation Extreme Values Gaussian distribution Laplace method Normal distribution geometry statistics

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0073538
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-58617-3
  • Online ISBN 978-3-540-49033-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book