An Alternative to the Log-Skew-Normal Distribution: Properties, Inference, and an Application to Air Pollutant Concentrations

Jaime Arrué, Reinaldo Boris Arellano-Valle, Osvaldo Venegas (), Heleno Bolfarine and Héctor W. Gómez
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Jaime Arrué: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
Reinaldo Boris Arellano-Valle: Departamento de Estadística, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago 7820436, Chile
Osvaldo Venegas: Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile
Heleno Bolfarine: Departamento de Estatítica, IME, Universidade de São Paulo, São Paulo 05508-090, Brazil
Héctor W. Gómez: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile

Mathematics, 2022, vol. 10, issue 22, 1-14

Abstract: In this study, we consider an alternative to the log-skew-normal distribution. It is called the modified log-skew-normal distribution and introduces greater flexibility in the skewness and kurtosis parameters. We first study several of the main probabilistic properties of the new distribution, such as the computation of its moments and the non-existence of the moment-generating function. Parameter estimation by the maximum likelihood approach is also studied. This approach presents an overestimation problem in the shape parameter, which in some cases, can even be infinite. However, as we demonstrate, this problem is solved by adapting bias reduction using Firth’s approach. We also show that the modified log-skew-normal model likewise inherits the non-singularity of the Fisher information matrix of the untransformed model, when the shape parameter is null. Finally, we apply the modified log-skew-normal model to a real example related to pollution data.

Keywords: log-normal distribution; non-singular information matrix; modified likelihood; modified score; bias prevention (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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