Improved Tolerance Factors for Multivariate Normal Distributions

摘要

In this article, an improved method of computing tolerance factors for multivariate normal distributions is proposed. The method involves an approximation and simulation, and is more accurate than the several approximate methods considered in Krishnamoorthy and Mathew (1999). The accuracies of the tolerance regions are evaluated using Monte Carlo simulation. Simulation study shows that the new approach is very satisfactory even for small samples. Tolerance factors based on the proposed approach are tabulated for the dimension of the normal distribution p = 2(1)10, and various sample sizes ranging from 2p + 1 to 1000.