Computation of tolerance ellipses for bivariate and trivariate normal populations

Abstract

We consider the computation of the critical constants c of a p-content -confidence tolerance ellipse for bivariate and trivariate normal populations which are probably the most used multivariate normal distributions in applications. There are only approximation methods available in the statistical literature for computing c. Without knowing the accurate value of c, it is impossible to assess the accuracy of the approximation methods. In this paper, a new method is given to compute c. Although the method is also based on Monte-Carlo simulation, it allows c to be computed as accurate as required if the number of simulation replications is sufficiently large. The R codes provided allow easy implementation of the method. Furthermore, the method allows the accuracy of the available approximation methods for bivariate and trivariate normal distributions to be assessed.