摘要：Let X' = (X 1 ,X 2 , ... ,X k ) have the multivariate normal distribution f(X) = MVN(μ, ∑σ 2 ) where ∑ is a known positive definite matrix, and σ 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 = ∫ A f(X) dX. If σ 2 is known, then without loss of generality, set μ = 0, σ =1 and let ∑ 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.
