Multimatricvariate and Multimatrix Variate Distributions Based on Elliptically Contoured Laws under Real Normed Division Algebras

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dc.contributor.affiliationDíaz-García J.A., Universidad Autónoma de Chihuahua, Facultad de Zootecnia y Ecología, Periférico Francisco R. Almada Km 1, Zootecnia, Chihuahua, Chihuahua, 33820, Mexico
dc.contributor.affiliationCaro-Lopera F.J., University of Medellin, Faculty of Basic Sciences, Carrera 87 No.30-65, Medellin, Colombia
dc.contributor.authorDíaz-García J.A.
dc.contributor.authorCaro-Lopera F.J.
dc.date.accessioned2025-09-08T14:23:30Z
dc.date.available2025-09-08T14:23:30Z
dc.date.issued2024
dc.descriptionThis paper proposes famillies of multimatricvariate and multimatrix variate distributions based on elliptically contoured laws in the context of real normed division algebras. The work allows to answer the following inference problems about random matrix variate distributions: 1) Modeling of two or more probabilistically dependent random variables in all possible combinations whether univariate, vector and matrix simultaneously. 2) Expected marginal distributions under independence and joint estimation of models under likelihood functions of dependent samples. 3) Definition of a likelihood function for dependent samples in the mentioned random dimensions and under real normed division algebras. The corresponding real distributions are alternative approaches to the existing univariate and vector variate copulas, with the additional advantages previously listed. An application for quaternionic algebra is illustrated by a computable dependent sample joint distribution for landmark data emerged from shape theory. © (2024), (Iranian Statistical Society). All rights reserved.
dc.identifier.doi10.22034/jirss.2025.2042155.1078
dc.identifier.instnameinstname:Universidad de Medellínspa
dc.identifier.issn17264057
dc.identifier.reponamereponame:Repositorio Institucional Universidad de Medellínspa
dc.identifier.repourlrepourl:https://repository.udem.edu.co/
dc.identifier.urihttp://hdl.handle.net/11407/9063
dc.language.isoeng
dc.publisher.facultyFacultad de Ciencias Básicasspa
dc.relation.citationendpage67
dc.relation.citationissue2
dc.relation.citationstartpage35
dc.relation.citationvolume23
dc.relation.isversionofhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-105009717543&doi=10.22034%2fjirss.2025.2042155.1078&partnerID=40&md5=d96fca409b83ff4966f4c623f9538b2a
dc.relation.referencesBekker A., Roux J. J. J., Ehlers E., Arashi M., Bimatrix variate beta type IV distribution: relation to Wilks’s statistics and bimatrix variate Kummer-beta type IV distribution, Comm. Statist. (T&M), 40, pp. 4165-4178, (2001)
dc.relation.referencesBaez J. C., The octonions, Bull. Amer. Math. Soc, 39, pp. 145-205, (2002)
dc.relation.referencesChen J. J., Novick M. R., Bayesian analysis for binomial models with generalized beta prior distributions, J. Educational Statist, 9, pp. 163-175, (1984)
dc.relation.referencesDiaz-Garcia J. A., Integral properties of zonal spherical functions, hypergeometric functions and invariant polynomials, J Iranian Statist. Soc, 13, 1, pp. 83-124, (2014)
dc.relation.referencesDiaz-Garcia J. A., Gutierrez-Jaimez R., Bimatrix variate generalised beta distributions, South African Statist. J, 44, pp. 193-208, (2010)
dc.relation.referencesDiaz-Garcia J. A., Gutierrez-Jaimez R., Complex bimatrix variate generalised beta distributions, Linear Algebra Appl, 432, 2–3, pp. 571-582, (2010)
dc.relation.referencesDiaz-Garcia J. A., Gutierrez-Jaimez R., On Wishart distribution: Some extensions, Linear Algebra Appl, 435, pp. 1296-1310, (2011)
dc.relation.referencesDiaz-Garcia J. A., Gutierrez-Jaimez R., Noncentral bimatrix variate generalised beta distributions, Metrika, 73, 3, pp. 317-333, (2011)
dc.relation.referencesDiaz-Garcia J. A., Gutierrez-Jaimez R., On Wishart distribution: Some extensions, Linear Algebra Appl, 435, pp. 1296-1310, (2011)
dc.relation.referencesDiaz-Garcia J. A., Gutierrez-Jaimez R., Matricvariate and matrix multivariate T distributions and associated distributions, Metrika, 75, 7, pp. 963-976, (2012)
dc.relation.referencesDiaz-Garcia J. A., Gutierrez-Jaimez R., Spherical ensembles, Linear Algebra Appl, 438, pp. 3174-3201, (2013)
dc.relation.referencesDiaz-Garcia J. A., Caro-Lopera F. J., Multimatricvariate distribution under elliptical models, J. Stat. Plann. Infer, 2016, pp. 109-117, (2022)
dc.relation.referencesDiaz-Garcia J. A., Caro-Lopera F. J., Perez Ramirez F. O., Multivector variate distributions: An application in Finance, Sankhyā, 84-A, pp. 534-555, (2022)
dc.relation.referencesDiaz-Garcia J. A., Caro-Lopera F. J., Multimatrix variate distribution, (2024)
dc.relation.referencesDickey J. M., Matricvariate generalizations of the multivariate t- distribution and the inverted multivariate t-distribution, Ann. Math. Statist, 38, pp. 511-518, (1967)
dc.relation.referencesDumitriu I., Eigenvalue statistics for beta-ensembles, (2002)
dc.relation.referencesDray T., Manogue C. A., The exceptional Jordan eigenvalue problem, Inter. J. Theo. Phys, 38, 11, pp. 2901-2916, (1999)
dc.relation.referencesDryden I. L., Mardia K. V., Statistical Shape Analysis, (1998)
dc.relation.referencesEhlers R., Bimatrix variate distributions of Wishart ratios with application, (2011)
dc.relation.referencesEdelman A., Rao R. R., Random matrix theory, Acta Numer, 14, pp. 233-297, (2005)
dc.relation.referencesFang K. T., Li R., Bayesian Statistical Inference on Elliptical Matrix Distributions, J. Multivarialte Anal, 70, pp. 66-85, (1999)
dc.relation.referencesFang K. T., Zhang Y. T., Generalized Multivariate Analysis, (1990)
dc.relation.referencesFang K. T., Zhang Y. T., Ng K. W., Symmetric Multivariate and realted distributions, (1990)
dc.relation.referencesForrester P. J., Log-gases and random matrices, (2009)
dc.relation.referencesGross K. I., Richards D., ST P., Special functions of matrix argument I: Algebraic induction zonal polynomials and hypergeometric functions, Trans. Amer. Math. Soc, 301, 2, pp. 475-501, (1987)
dc.relation.referencesGoodall C. R., Mardia K. V., Multivariate Aspects of Shape Theory, Ann. Statist, 21, pp. 848-866, (1993)
dc.relation.referencesGupta A. K., Varga T., Bondar T., Elliptically Contoured Models in Statistics and Portfolio Theory, (2013)
dc.relation.referencesKabe D. G., Classical statistical analysis based on a certain hypercomplex multivariate normal distribution, Metrika, 31, pp. 63-76, (1984)
dc.relation.referencesKotz S., Nadarajah S., Multivariate t Distributions and Their Applications, (2004)
dc.relation.referencesLibby D. L., Novick M. R., Multivariate Generalized beta distributions with applications to utility assessment, J. Educational Statist, 7, pp. 271-294, (1982)
dc.relation.referencesLi F., Xue Y., Zonal polynomials and hypergeometric functions of quaternion matrix argument, Comm. Statist. Theory Methods, 38, 8, pp. 1184-1206, (2009)
dc.relation.referencesMuirhead R. J., Aspects of Multivariate Statistical Theory, (2005)
dc.relation.referencesNadarajah S., A bivariate gamma model for drought, Water Resour. Res, 43, (2007)
dc.relation.referencesNadarajah S., A bivariate distribution with gamma and beta marginals with application to drought data, J. App. Statist, 36, 3, pp. 277-301, (2013)
dc.relation.referencesOlkin I., Liu R., A bivariate beta distribution, Statist. Prob. Letters, 62, pp. 407-412, (2003)
dc.relation.referencesOlkin I., Rubin H., Multivariate beta distributions and independence properties of Wishart distribution, Ann. Math. Statist, 35, pp. 261-269, (1964)
dc.relation.referencesSarabia J. M., Prieto F., Jorda V., Bivariate beta-generated distributions with application to well-being data, J. Statist. Distributions Appl, 1, (2014)
dc.rights.accesoRestricted access
dc.rights.accessrightsinfo:eu-repo/semantics/restrictedAccess
dc.sourceJournal of the Iranian Statistical Society
dc.sourceJ. Iran. Stat. Soc.
dc.sourceScopus
dc.subjectMatrix Variate
dc.subjectMatrix Variate Elliptical Distributions
dc.subjectMultimatricvariate
dc.subjectMultimatrix Variate
dc.subjectRandom Matrices
dc.subjectReal Normed Division Algebras
dc.titleMultimatricvariate and Multimatrix Variate Distributions Based on Elliptically Contoured Laws under Real Normed Division Algebras
dc.typeArticle
dc.type.localArtículospa
dc.type.versioninfo:eu-repo/semantics/publishedVersion

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