Discriminating Between the Log-Normal and Log-Logistic Distributions

Abstract

Log-normal and log-logistic distributions are often used to analyze lifetime data. For certain ranges of the parameters, the shape of the probability density functions or the hazard functions can be very similar in nature. It might be very difficult to discriminate between the two distribution functions. In this article, we consider the discrimination procedure between the two distribution functions. We use the ratio of maximized likelihood for discrimination purposes. The asymptotic properties of the proposed criterion are investigated. It is observed that the asymptotic distributions are independent of the unknown parameters. The asymptotic distributions are used to determine the minimum sample size needed to discriminate between these two distribution functions for a user specified probability of correct selection. We perform some simulation experiments to see how the asymptotic results work for small sizes. For illustrative purpose, two data sets are analyzed.