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

Abstract

In this paper we consider the model selection / discrimination among the three important lifetime distributions. All these three distributions have been used quite e®ectively to analyze lifetime data in the reliability analysis. 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 di®erent sample sizes and for di®erent 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 speci¯ed protection level.