Monte Carlo pp 13-144 | Cite as

Estimating Volume and Count

  • George S. Fishman
Part of the Springer Series in Operations Research book series (ORFE)


This chapter introduces the reader to fundamental issues that arise when applying the Monte Carlo method to solving a commonly encountered problem in numerical computation. In its most basic form the problem is to evaluate the volume of a bounded region in multi-dimensional euclidean space. The more general problem is to evaluate the integral of a function on such a region. The Monte Carlo method often offers a competitive and sometimes the only useful solution to the problem. The appeal of the Monte Carlo method arises when the shape of the region of interest makes solution by analytical methods impossible and, in the case of the more general function integration, when little is known about the smoothness and variational properties of the integrand, or what is known precludes the applications of alternative numerical evaluation techniques.


Sampling Plan Error Criterion Percent Confidence Interval CoNFIDENCE Interval Normal Sample Size 
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • George S. Fishman
    • 1
  1. 1.Department of Operations ResearchUniversity of North CarolinaChapel HillUSA

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