Approximate ellipsoidal tolerance regions for multivariate normal populations

For the approximate computation of an ellipsoidal tolerance region for multivariate normal distributions, an approximation due to Liu et al. (2008) for the cdf of a positive linear combination of independent non-central chisquare random variables is used, along with Monte Carlo simulation. Such a computational approach is originally due to Krishnamoorthy and Mondal (2006, 2008), and the present work provides an improvement.