Skip to main content
SpringerLink
Log in

Approximation of Multivariate Probability Integrals

  • Reference work entry
Book cover Encyclopedia of Optimization

Article Outline

Keywords

Upper Bounds

Monte-Carlo Simulation Algorithm

One- and Two-Dimensional Marginal Distribution Functions

Examples

Remarks

See also

References

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 2,500.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 2,499.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bonferroni CE (1937) Teoria statistica delle classi e calcolo delle probabilita. Volume in onordi Riccardo Dalla Volta:1–62

    Google Scholar 

  2. Deák I (1980) Three digit accurate multiple normal probabilities. Numerische Math 35:369–380

    MATH  Google Scholar 

  3. Gassmann H (1988) Conditional probability and conditional expectation of a random vector. In: Ermoliev Y, Wets RJ-B (eds) Numerical Techniques for Stochastic Optimization. Springer, Berlin, pp 237–254

    Google Scholar 

  4. Genz A (1993) Comparison of methods for the computation of multivariate normal probabilities. Computing Sci and Statist 25:400–405

    Google Scholar 

  5. Hunter D (1976) Bounds for the probability of a union. J Appl Probab 13:597–603

    MathSciNet  MATH  Google Scholar 

  6. IMSL (1977) Library 1 reference manual. Internat. Math. Statist. Library

    Google Scholar 

  7. Kall P, Mayer J (1995) Computer support for modeling in stochastic linear programming. In: Marti K, Kall P (eds) Stochastic Programming: Numerical Methods and Techn. Applications. Springer, Berlin, pp 54–70

    Google Scholar 

  8. Kennedy WJ Jr, Gentle JE (1980) Statistical computing. M. Dekker, New York

    MATH  Google Scholar 

  9. Kruskal JB (1956) On the shortest spanning subtree of a graph and the travelling salesman problem. Proc Amer Math Soc 7:48–50

    MathSciNet  Google Scholar 

  10. Mayer J (1988) Probabilistic constrained programming: A reduced gradient algorithm implemented on PC. Working Papers IIASA WP-88-39

    Google Scholar 

  11. Prékopa A (1995) Stochastic programming. Akad. Kiadó and Kluwer, Budapest–Dordrecht

    Google Scholar 

  12. Prékopa A, Szántai T (1978) A new multivariate gamma distribution and its fitting to empirical streamflow data. Water Resources Res 14:19–24

    Google Scholar 

  13. Szántai T (1985) Numerical evaluation of probabilities concerning multivariate probability distributions. Thesis Candidate Degree Hungarian Acad Sci (in Hungarian)

    Google Scholar 

  14. Szántai T (1986) Evaluation of a special multivariate gamma distribution function. Math Program Stud 27:1–16

    MATH  Google Scholar 

  15. Szántai T (1988) A computer code for solution of probabilistic‐constrained stochastic programming problems. In: Ermoliev Y, Wets RJ-B (eds) Numerical Techniques for Stochastic Optimization. Springer, Berlin, pp 229–235

    Google Scholar 

  16. Szántai T: Improved bounds and simulation procedures on the value of multivariate normal probability distribution functions. Ann Oper Res (to appear) Special Issue: Research in Stochastic Programming (Selected refereed papers from the VII Internat. Conf. Stochastic Programming, Aug. 10–14, Univ. British Columbia, Vancouver, Canada).

    Google Scholar 

  17. Takács L (1955) On the general probability theorem. Comm Dept Math Physics Hungarian Acad Sci 5:467–476 (In Hungarian.)

    MATH  Google Scholar 

  18. Worsley KJ (1982) An improved Bonferroni inequality and applications. Biometrika 69:297–302

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technical University, Budapest, Hungary

    Tamás Szántai

Authors
  1. Tamás Szántai
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Szántai, T. (2008). Approximation of Multivariate Probability Integrals . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_14

Download citation

Publish with us

Policies and ethics

Search

Navigation