Abstract

This paper compares methods for the numerical computation of multivariate t-probabilities for hyper-rectangular integration regions. Methods based on acceptance-rejection, spherical-radial transformations and separation-of-variables transformations are considered. Tests using randomly chosen problems show that the most efficient numerical methods use a transformation developed by Genz (1992) for multivariate normal probabilities. These methods allow moderately accurate multivariate t-probabilities to be quickly computed for problems with as many as twenty variables. Methods for the non-central multivariate t-distribution are also described.

Key Words: multivariate t-distribution, non-central distribution, numerical integration, statistical computation.