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

Authors

  • Guillermo Martínez-Flórez,

    1. Departamento de Matemáticas y Estadística, Facultad de Ciencias, Universidad de Córdoba, Córdoba, Colombia
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  • Heleno Bolfarine,

    1. Departamento de Estatítica, IME, Universidade de São Paulo, São Paulo, Brazil
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  • Héctor W. Gómez

    Corresponding author
    1. Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta, Chile
    • Correspondence to: Héctor W. Gómez, Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta, Chile. E-mail: hgomez@uantof.cl

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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. Copyright © 2014 John Wiley & Sons, Ltd.

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