Numerical Computation of Rectangular
Bivariate and Trivariate Normal and t Probabilities

Alan Genz
Department of Mathematics
Washington State University
Pullman, WA 99164-3113, USA
alangenz@wsu.edu

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.
Key Words: distribution, bivariate normal, trivariate normal, bivariate t , trivariate t, Plackett formula