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

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datacite.alternateIdentifier.citationMATHEMATICS,Vol.10,,2022
datacite.alternateIdentifier.doi10.3390/math10224336
datacite.creatorArrue, Jaime
datacite.creatorArellano Valle, Reinaldo Boris
datacite.creatorVenegas, Osvaldo
datacite.creatorBolfarine, Heleno
datacite.creatorGomez, Hector W.
datacite.date2022
datacite.subject.englishlog-normal distribution
datacite.subject.englishnon-singular information matrix
datacite.subject.englishmodified likelihood
datacite.subject.englishmodified score
datacite.subject.englishbias prevention
datacite.titleAn Alternative to the Log-Skew-Normal Distribution: Properties, Inference, and an Application to Air Pollutant Concentrations
dc.date.accessioned2023-06-08T15:48:08Z
dc.date.available2023-06-08T15:48:08Z
dc.description.abstractIn 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.
dc.identifier.urihttps://repositoriodigital.uct.cl/handle/10925/5233
dc.language.isoen
dc.publisherMDPI
dc.sourceMATHEMATICS
oaire.resourceTypeArticle
uct.indizacionSCI
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