Model selection among log-normal, Weibull, Gamma and generalized exponential distributions

Abstract

We conduct discrimination among four important life distributions — Log-Normal distribution, Weibull distribution, Gamma distribution and Generalized Exponential distribution. In this paper, we have assumed that the data is coming from either of these four distributions. For the purpose of analyzing lifetime data in the field of reliability analysis, these distributions have been extensively used. Even though adequate amount of research work has been done which focuses on discriminating between two or three distributions, enough work has not been done in choosing among more than three distributions. We have used three goodness of fit tests, namely, KS test, AIC test and BIC test to choose the best fitting model. The task of choosing the right model becomes difficult when we have to discriminate among closely fitting models. We have used probability of correct selection to further validate the results of the discrimination process. The probability of correct selection is calculated using asymptotic distributions. For illustration, we have analyzed two real life data sets.