Characteristic function and moment generating function of multivariate folded normal distribution

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dc.contributor.authorBenko, Matejcs
dc.contributor.authorHübnerová, Zuzanacs
dc.contributor.authorWitkovský, Viktorcs
dc.coverage.issue4cs
dc.coverage.volume66cs
dc.date.issued2025-05-10cs
dc.description.abstractIn this study, we derive the characteristic function of the multivariate folded normal distribution, a distribution that arises when the magnitudes-but not the signs-of a normally distributed random vector are of interest. The folded normal distribution is widely applicable across various fields. Thus, obtaining an analytical expression for its characteristic function is pivotal in understanding its fundamental properties. Moreover, this allows one to facilitate numerical evaluations of complex distributions involving linear combinations of absolute values of dependent normal variables. The derivation is based on a novel expression of the moment generating function, formulated using the cumulative distribution function of the multivariate normal distribution. To validate our findings, we present two examples using our MATLAB implementation. We compare the characteristic function for the sum of the absolute values of elements of a multivariate normal vector with the simulated empirical counterpart. Additionally, we derive the second mixed moment of the bivariate folded normal distribution from the moment generating function, demonstrating its agreement with known theoretical expressions.en
dc.formattextcs
dc.format.extent1-23cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationSTATISTICAL PAPERS. 2025, vol. 66, issue 4, p. 1-23.en
dc.identifier.doi10.1007/s00362-025-01711-zcs
dc.identifier.issn0932-5026cs
dc.identifier.orcid0009-0005-8311-6301cs
dc.identifier.orcid0000-0001-5772-2125cs
dc.identifier.other198334cs
dc.identifier.researcheridKRR-9263-2024cs
dc.identifier.researcheridAGD-6573-2022cs
dc.identifier.scopus59179399000cs
dc.identifier.scopus55927063100cs
dc.identifier.urihttp://hdl.handle.net/11012/255198
dc.language.isoencs
dc.publisherSpringer Naturecs
dc.relation.ispartofSTATISTICAL PAPERScs
dc.relation.urihttps://link.springer.com/article/10.1007/s00362-025-01711-zcs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/0932-5026/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectAbsolute valueen
dc.subjectCharacteristic functionen
dc.subjectFolded normal distributionen
dc.subjectMoment generating functionen
dc.subjectMultivariate normal distributionen
dc.subjectOwen's normal integralen
dc.titleCharacteristic function and moment generating function of multivariate folded normal distributionen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-198334en
sync.item.dbtypeVAVen
sync.item.insts2025.07.18 07:56:38en
sync.item.modts2025.07.18 07:33:39en
thesis.grantorVysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematikycs
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