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The skewness and kurtosis of the product of two normally distributed random variables

2021-04-14Journal article Restricted access
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datacite.subject.sdg04:Educação de Qualidadept_PT
datacite.subject.sdg08:Trabalho Digno e Crescimento Económicopt_PT
dc.contributor.authorSeijas-Macias, J. Antonio
dc.contributor.authorOliveira, Amilcar
dc.contributor.authorOliveira, Teresa
dc.date.accessioned2023-07-31T10:17:54Z
dc.date.available2023-07-31T10:17:54Z
dc.date.issued2021-04-14
dc.description.abstractThe analysis of the product of two normally distributed variables does not seem to follow any known distribution. Fortunately, the moment-generating function is available and we can calculate the statistics of the product distribution: mean, variance, the skewness and kurtosis (excess of kurtosis). In this work, we have considered the role played by the parameters of the two normal distributions’ factors (mean and variance) on the values of the skewness and kurtosis of the product. Ranges of variation are defined for kurtosis and the skewness. The determination of the evolution of the skewness and kurtosis values of the product can be used to establish the normality of the product and how to modelize its distribution. Finally, the Pearson Inequality is proved for the skewness and kurtosis of the product of two normal random variables.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationAntonio Seijas-Macias, Amílcar Oliveira & Teresa A. Oliveira (2023) The skewness and kurtosis of the product of two normally distributed random variables, Communications in Statistics - Theory and Methods, 52:1, 80-93, DOI: 10.1080/03610926.2021.1909734pt_PT
dc.identifier.doi10.1080/03610926.2021.1909734pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.2/14660
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherTaylor & Francis Onlinept_PT
dc.relationCentre of Statistics and its Applications
dc.subjectMoment generating functionpt_PT
dc.subjectPearson’s inequalitypt_PT
dc.subjectMomentspt_PT
dc.titleThe skewness and kurtosis of the product of two normally distributed random variablespt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleCentre of Statistics and its Applications
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMAT%2F00006%2F2019/PT
oaire.citation.endPage93pt_PT
oaire.citation.startPage80pt_PT
oaire.citation.titleCommunications in Statistics - Theory and Methodspt_PT
oaire.citation.volume52pt_PT
oaire.fundingStream6817 - DCRRNI ID
person.familyNameSeijas-Macias
person.familyNameOliveira
person.familyNameOliveira
person.givenNameJ. Antonio
person.givenNameAmilcar
person.givenNameTeresa Azinheira
person.identifier1155497
person.identifier.ciencia-id3717-BC82-53C2
person.identifier.ciencia-id7110-61B4-B87F
person.identifier.ciencia-id8814-A54B-12DE
person.identifier.orcid0000-0002-6056-3257
person.identifier.orcid0000-0001-5500-7742
person.identifier.orcid0000-0003-3283-9946
person.identifier.ridJ-3077-2019
person.identifier.scopus-author-id57194105655
person.identifier.scopus-author-id55675222550
person.identifier.scopus-author-id54403540300
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsrestrictedAccesspt_PT
rcaap.typearticlept_PT
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relation.isAuthorOfPublication1c873476-22fd-4331-8286-ff5576ac3b0c
relation.isAuthorOfPublication82b3cd70-88cc-4d31-b4b0-4705f8496c67
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