The log-power-normal distribution with application to air pollution

Abstract

In this article, we study an extension of the power-normal distribution to the case of the more flexible log-power-normal distribution. We find the density function and study some properties of the new distribution, deriving a general expression for its moments. Parameter estimation is implemented by using the moments and the maximum likelihood approaches. We obtain the Fisher information matrix for the new model, which is shown to be nonsingular in the vicinity of symmetry. Results of an application to air contamination data indicate good performance of the proposed model, validating a modification of Ahrens' law.