Lognormal processes are important from a theoretical perspective. We reexamine the problem of whether it is better to take natural log or not? If not, how to identify the probability density function is still an important problem. The assertion that taking natural log is closer to normality is not supported by the simulation and empirical data. The probabilistic neural network contains the entire set of training cases, and is therefore space-consuming and slow to execute. In addition, there is an inverse problem in PNNs, i.e.. we may obtain the same sum of square errors from different density functions. We therefore propose a screening mechanism based on characteristics oriented fuzzy rules in the Hopfield neural network to simplify the estimation process and avoid the inverse problem. From the characteristics oriented fuzzy HNN, we obtain that the best fitting of the data is the Weibull distribution. (C) 2008 Elsevier Ltd. All rights reserved.