Numerical Computation of
Bivariate and Trivariate Normal 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 probabilities are described. The algorithms use numerical integration to approximate transformed normal integrals. A five point Gauss rule is shown to be sufficient for single precision accuracy for the bivariate normal algorithm. The trivariate normal algorithm uses the bivariate algorithm in combination with adaptive integration. Double precision algorithms are also described.
Key Words: bivariate normal, trivariate normal, Gaussian quadrature