Subroutines for computing normal probabilities of sets – computer experiences

A subroutine package, called NORSET, has been prepared, that – via Monte Carlo integration – is suitable for evaluating several types of probabilities related to the n-dimensional normal distribution. The following probabilities can be computed: the distribution function value, the probabilities of rectangles, convex polyhedra, hyperellipsoids and circular cones in case of normal distribution. Probabilities accurate to three digits can be computed in less than 0.3 sec for up to 20 dimensions and in less than 10 sec for up to 100 dimensions. The description of the subroutines, results of computer testing and experimentations together with the conclusions are presented here.