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Numerical computation of rectangular bivariate and trivariate normal and t probabilities

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.

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Genz, A. Numerical computation of rectangular bivariate and trivariate normal and t probabilities. Statistics and Computing 14, 251–260 (2004). https://doi.org/10.1023/B:STCO.0000035304.20635.31

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  • DOI: https://doi.org/10.1023/B:STCO.0000035304.20635.31

  • distribution
  • bivariate normal
  • trivariate normal
  • bivariate t
  • trivariate t
  • Plackett formula