A Fortran 90 Program for Evaluation of Multivariate Normal and Multivariate t Integrals Over Convex Regions

Let X' = (X_1,X_2, ... ,X_k) have the multivariate normal distribution f(X) = MVN(mu, sumsigma^2) where sum is a known positive definite matrix, and sigma^2 is a constant. There are many problems in statistics which require the evaluation of f(x) over some convex region A. That is P = integral _A f(X) dX. If sigma^2 is known, then without loss of generality, set mu = 0, sigma =1 and let sum be the correlation matrix. For the case where the region A is rectangular, the problem has been addressed by many authors. They include Gupta (1963), Milton (1972), Schervish (1984), Deak (1986), Wang and Kennedy (1990,1992), Olson and Weissfeld (1991), Drezner (1992) and Genz (1992,1993). However, regions of integration for many statistical applications, for example multiple comparisons, are not rectangular.