Discriminating between gamma and generalized exponential distributions

Recently the two-parameter generalized exponential distribution was introduced by the authors. It is observed that a generalized exponential distribution has several properties which are quite similar to a gamma distribution. It is also observed that a generalized exponential distribution can be used quite effectively in many situations where a skewed distribution is needed. In this paper, we use the ratio of the maximized likelihoods in choosing between a generalized exponential distribution and a gamma distribution. We obtain asymptotic distributions of the logarithm of the ratio of the maximized likelihoods under null hypotheses and use them to determine the sample size needed to discriminate between two overlapping families of distributions for a user specified probability of correct selection and a tolerance limit.