Discriminating Among the Log-Normal, Weibull, and Generalized Exponential Distributions

We consider model selection and discrimination among three important lifetime distributions. These three distributions have been used quite effectively to analyze lifetime data. We study the probability of correct selection using the maximized likelihood method, as it has been used in the literature. We further compute the asymptotic probability of correct selection, and compare the theoretical, and simulation results for different sample sizes, and for different model parameters. The results have been extended for Type-I censored data also. The theoretical, and simulation results match quite well. Two real data sets have been analyzed for illustrative purposes. We also suggest a method to determine the minimum sample size required to discriminate among the three distributions for a given probability of correct selection, and a user specified protection level.