A Fortran 90 Program for Evaluation of Multivariate Normal and Multivariate t Integral over Convex Regions. The Fortran 90 program MVI3.FOR (which combines and extends two previous programs, MVI and MVIB) can be used to evaluate multivariate normal or multivariate-t integrals over any region which is bounded by hyperplanes (and thus convex). Three decimal accuracies may be obtained in seconds for 20 dimensional integrals using a 486 processor. The original programs MVI and MVIB could be used only if the convex region contained the origin. The present program MVI3 has no such limitation. However, if the region does not contain the origin, MVI3 uses “crude Monte Carlo” for the evaluation. In addition, the user of the program may elect to do the evaluation using “crude Monte Carlo” even when the convex region contains the origin.

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  1. Genz, Alan: MCQMC methods for multivariate statistical distributions (2008)