The distribution of the maximum likelihood-ratio statistic used for testing a normal sample for three outliers

We study the exact distribution of the likelihood-ratio statistic used for testing a normal sample for three upper (lower) outliers. We obtain recursive relationships for the integral distribution function of this statistic. We apply the obtained relationships for calculating critical values of the likelihood-ratio statistic which appear to be close to critical values of this statistic simulated by the Monte Carlo method. We give an example of the joint use of the likelihood-ratio statistic for testing a sample for more than one outlier.