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Poisson and compound Poisson approximation
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
2005 (English)In: An introduction to Stein's method / [ed] A.D. Barbour, Louis H.Y. Chen, Singapore: Singapore University Press , 2005, 61-113 p.Chapter in book (Other academic)
Abstract [en]

A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. Traditional approaches, for example using Fourier analysis, become awkward to carry through in situations in which dependence plays an important part, whereas Stein's method can often still be applied to great effect. In addition, the method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the distribution to be approximated; it can equally well be normal, or Poisson, or that of the whole path of a random process, though the techniques have so far been worked out in much more detail for the classical approximation theorems. This volume of lecture notes provides a detailed introduction to the theory and application of Stein's method, in a form suitable for graduate students who want to acquaint themselves with the method. It includes chapters treating normal, Poisson and compound Poisson approximation, approximation by Poisson processes, and approximation by an arbitrary distribution, written by experts in the different fields. The lectures take the reader from the very basics of Stein's method to the limits of current knowledge.

Place, publisher, year, edition, pages
Singapore: Singapore University Press , 2005. 61-113 p.
Series
Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, 4
Keyword [en]
sannolikhetslära, approximationer
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-35067Local ID: 24785ISBN: 981-256-280-X (print)ISBN: 981-256-330-X (print)ISBN: 978-9-8125-6330-9 (print)OAI: oai:DiVA.org:liu-35067DiVA: diva2:255915
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-10-11Bibliographically approved

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find book at a swedish library/hitta boken i ett svenskt bibliotekläs utdrag

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Erhardsson, Torkel

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf