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Approximating the distribution of the product of two normally distributed random variables

2020Journal article Open access
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dc.contributor.authorSeijas-Macias, J. Antonio
dc.contributor.authorOliveira, Amilcar
dc.contributor.authorOliveira, Teresa A.
dc.contributor.authorLeiva, Victor
dc.date.accessioned2021-05-11T12:38:26Z
dc.date.available2021-05-11T12:38:26Z
dc.date.issued2020
dc.description.abstractThe distribution of the product of two normally distributed random variables has been an open problem from the early years in the XXth century. First approaches tried to determinate the mathematical and statistical properties of the distribution of such a product using different types of functions. Recently, an improvement in computational techniques has performed new approaches for calculating related integrals by using numerical integration. Another approach is to adopt any other distribution to approximate the probability density function of this product. The skew-normal distribution is a generalization of the normal distribution which considers skewness making it flexible. In this work, we approximate the distribution of the product of two normally distributed random variables using a type of skew-normal distribution. The influence of the parameters of the two normal distributions on the approximation is explored. When one of the normally distributed variables has an inverse coefficient of variation greater than one, our approximation performs better than when both normally distributed variables have inverse coefficients of variation less than one. A graphical analysis visually shows the superiority of our approach in relation to other approaches proposed in the literature on the topic.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.doi10.3390/sym12081201pt_PT
dc.identifier.issn2073-8994
dc.identifier.urihttp://hdl.handle.net/10400.2/10713
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherMDPIpt_PT
dc.relationCentre of Statistics and its Applications
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/pt_PT
dc.subjectExtended skew-normal distributionpt_PT
dc.subjectkurtosispt_PT
dc.subjectMomentspt_PT
dc.subjectR softwarept_PT
dc.subjectSkewnesspt_PT
dc.titleApproximating the distribution 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/UIDB%2F00006%2F2020/PT
oaire.citation.conferencePlaceBasel, Switzerlandpt_PT
oaire.citation.issue8pt_PT
oaire.citation.startPage1201pt_PT
oaire.citation.titleSymmetrypt_PT
oaire.citation.volume12pt_PT
oaire.fundingStream6817 - DCRRNI ID
person.familyNameSeijas-Macias
person.familyNameOliveira
person.familyNameOliveira
person.familyNameLeiva-Sanchez
person.givenNameJ. Antonio
person.givenNameAmilcar
person.givenNameTeresa A.
person.givenNameVictor
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.orcid0000-0003-4755-3270
person.identifier.ridJ-3077-2019
person.identifier.scopus-author-id57194105655
person.identifier.scopus-author-id55675222550
person.identifier.scopus-author-id54403540300
person.identifier.scopus-author-id22953630400
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
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