Numerical computation of rectangular bivariate and trivariate normal and t probabilities

Authors:
Alan Genz
Affiliations:
Department of Mathematics, Washington State University, Pullman, WA 99164-3113, USA. alangenz@wsu.edu
Venue:
Statistics and Computing
Year:
2004

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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.