Discriminating between the Weibull and Power Lindley Distributions Utilizing Fisher Information

Abstract

Recently, the power Lindley distribution was proposed by Ghitany et al. (2013). It can be considered as an alternative to the Weibull distribution. In some cases, the Weibull and PL distributions provide similar data fit. In this paper, we discriminate between the Weibull and PL distributions by taking advantage of the Fisher information procedure proposed by Gupta and Kundu (2006). In addition, the Fisher information matrix is used to compute the asymptotic variance of the p^th percentile estimators including the asymptotic variances of the median and the average asymptotic variance of the percentile estimators. Furthermore, both of the asymptotic variances are useful as they can provide the further information of the Q-Q plot, especially the variation. In cases of the Weibull and PL distributions, the trends of the asymptotic variance of the pth percentile estimators are demonstrated with respect to the shape and the scale parameters. Moreover, we also analyze two datasets and compare the result between the likelihood ratio and the Fisher information procedures.