Abstract
In this paper, an exact distribution of the likelihood ratio criterion for testing the equality of p two-parameter exponential distributions is obtained for unequal sample sizes in a computational form. A useful asymptotic expansion of the distribution is also obtained up to the order of n-4 with the second term of the order of n-3 and so can be used to obtain accurate approximations to the critical values of the test statistic even for comparatively small values of n where n is the combined sample size. In fact the first term alone which is a single beta distribution provides a powerful approximation for moderately large values of n.