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Types of Asymptotic Approximations for Normal Probability Integrals

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Stochastic Programming

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 423))

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Abstract

For many problems in reliability and optimization it is necessary to calculate the probabilities of large deviations of normal random vectors. Using the structure of the normal probability density it is possible to derive simple asymptotic approximations for such integrals. Here three types of such approximations are described: approximations for the logarithm of the probabilities, approximations for the probabilities and asymptotic expansions for them.

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Author information

Authors and Affiliations

  1. Schellingstr. 21, D-80799, München, Germany

    K. Breitung

Authors
  1. K. Breitung
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Editor information

Editors and Affiliations

  1. Fk. LRT, Universität der Bundeswehr Müchen, D-85577, Neubiberg/München, Germany

    Kurt Marti

  2. Institut für Operations Research, Universität Zürich, Moussonstr. 15, CH-8044, Zürich, Switzerland

    Peter Kall

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© 1995 Springer-Verlag Berlin Heidelberg

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Breitung, K. (1995). Types of Asymptotic Approximations for Normal Probability Integrals. In: Marti, K., Kall, P. (eds) Stochastic Programming. Lecture Notes in Economics and Mathematical Systems, vol 423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-88272-2_1

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  • DOI: https://doi.org/10.1007/978-3-642-88272-2_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58996-9

  • Online ISBN: 978-3-642-88272-2

  • eBook Packages: Springer Book Archive

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