Near-exact distributions for the likelihood ratio test statistic to test equality of several variance-covariance matrices in elliptically contoured distributions

The exact distribution of the likelihood ratio test statistic to test the equalityof several variance-covariance matrices has a non-manageable form.On the other hand, the existing asymptotic approximations do not exhibit the necessary precision for many applications. For these reasons, the development of near-exact approximations to the distribution of this statistic, arising from a different method of approximating distributions,emerges as a desirable goal. These distributions, while being manageable are much closer to the exact distribution than the usual asymptotic distributions and opposite to these, are also asymptotic for increasing number of variables and matrices involved. Computational modules to implement the near-exact distributions are made available on a web-site.