A New Multimodal Modification of the Skew Family of Distributions: Properties and Applications to Medical and Environmental Data

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dc.contributor.authorReyes, Jimmy
dc.contributor.authorRojas, Mario A.
dc.contributor.authorCortés, Pedro L.
dc.contributor.authorArrué, Jaime
dc.date.accessioned2026-04-06T13:20:26Z
dc.date.available2026-04-06T13:20:26Z
dc.date.issued2024
dc.description.abstractThe skew distribution has the characteristic of appropriately modeling asymmetric unimodal data. However, in practice, there are several cases in which the data present more than one mode. In the literature, it is possible to find a large number of authors who have studied extensions based on the skew distribution to model this type of data. In this article, a new family is introduced,consisting of a multimodal modification to the family of skew distributions. Using the methodology of the weighted version of a function, we perform the product of the density function of a family of skew distributions with a polynomial of degree 4, thus obtaining a more flexible model that allows modeling data sets, whose distribution contains at most three modes. The density function, some properties, moments, skewness coefficients, and kurtosis of this new family are presented. This study focuses on the particular cases of skew-normal and Laplace distributions, although it can be applied to any other distribution. A simulation study was carried out, to study the behavior of the model parameter estimates. Illustrations with real data, referring to medicine and environmental data, show the practical performance of the proposed model in the two particular cases presented.
dc.description.sponsorshipSemillero UA 2022.
dc.identifier.doi10.3390/sym16091224
dc.identifier.issn2073-8994
dc.identifier.urihttps://repositorioabierto.uantof.cl/handle/uantof/680
dc.language.isoen
dc.publisherMDPI
dc.rightsAttribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.sourceSymmetry
dc.subjectskew distribution
dc.subjectmultimodal
dc.subjectmoments
dc.subjectcoefficient of asymmetry
dc.subjectcoefficient of kurtosis
dc.subjectmaximum likelihood estimate
dc.subjectmoment estimate
dc.subjectacceptance and rejection method
dc.subjectskew Laplace
dc.titleA New Multimodal Modification of the Skew Family of Distributions: Properties and Applications to Medical and Environmental Data
dc.typeArticle
oaire.citation.issue9
oaire.citation.volume16
organization.identifier.rorhttps://ror.org/04eyc6d95
organization.legalNameUniversidad de Antofagasta
uantof.identificator.departmentDepartamento de Estadística y Ciencia de Datos
uantof.identificator.facultyFacultad de Ciencias Básicas
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