Statistics and Computing

, Volume 14, Issue 3, pp 251–260 | Cite as

Numerical computation of rectangular bivariate and trivariate normal and t probabilities

  • Alan Genz
Article

Abstract

Algorithms for the computation of bivariate and trivariate normal and t probabilities for rectangles are reviewed. The algorithms use numerical integration to approximate transformed probability distribution integrals. A generalization of Plackett's formula is derived for bivariate and trivariate t probabilities. New methods are described for the numerical computation of bivariate and trivariate t probabilities. Test results are provided, along with recommendations for the most efficient algorithms for single and double precision computations.

distribution bivariate normal trivariate normal bivariate t trivariate t Plackett formula 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Alan Genz
    • 1
  1. 1.Department of MathematicsWashington State UniversityPullmanUSA

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