Wilks’ Factorization of the Complex Matrix Variate Dirichlet Distributions

ABSTRACT: In this paper, it has been shown that the complex matrix variate Dirichlet type I density factors into the complex matrix variate beta type I densities. Similar result has also been derived for the complex matrix variate Dirichlet type II density. Also, by using certain matrix transformati...

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Autores:
Nagar, Daya Krishna
Cui, Xinping
Gupta, Arjun Kumar
Tipo de recurso:
Article of investigation
Fecha de publicación:
2002
Institución:
Universidad de Antioquia
Repositorio:
Repositorio UdeA
Idioma:
eng
OAI Identifier:
oai:bibliotecadigital.udea.edu.co:10495/30420
Acceso en línea:
https://hdl.handle.net/10495/30420
https://revistas.ucm.es/index.php/REMA/article/view/16673
Palabra clave:
Transformación Celular Neoplásica
Cell Transformation, Neoplastic
beta distribution
Complex random matrix
Dirichlet distribution
Jacobian
Complex multivariate gamma function
Wishart distribution
Rights
openAccess
License
http://creativecommons.org/licenses/by/2.5/co/
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dc.title.spa.fl_str_mv Wilks’ Factorization of the Complex Matrix Variate Dirichlet Distributions
title Wilks’ Factorization of the Complex Matrix Variate Dirichlet Distributions
spellingShingle Wilks’ Factorization of the Complex Matrix Variate Dirichlet Distributions
Transformación Celular Neoplásica
Cell Transformation, Neoplastic
beta distribution
Complex random matrix
Dirichlet distribution
Jacobian
Complex multivariate gamma function
Wishart distribution
title_short Wilks’ Factorization of the Complex Matrix Variate Dirichlet Distributions
title_full Wilks’ Factorization of the Complex Matrix Variate Dirichlet Distributions
title_fullStr Wilks’ Factorization of the Complex Matrix Variate Dirichlet Distributions
title_full_unstemmed Wilks’ Factorization of the Complex Matrix Variate Dirichlet Distributions
title_sort Wilks’ Factorization of the Complex Matrix Variate Dirichlet Distributions
dc.creator.fl_str_mv Nagar, Daya Krishna
Cui, Xinping
Gupta, Arjun Kumar
dc.contributor.author.none.fl_str_mv Nagar, Daya Krishna
Cui, Xinping
Gupta, Arjun Kumar
dc.subject.decs.none.fl_str_mv Transformación Celular Neoplásica
Cell Transformation, Neoplastic
topic Transformación Celular Neoplásica
Cell Transformation, Neoplastic
beta distribution
Complex random matrix
Dirichlet distribution
Jacobian
Complex multivariate gamma function
Wishart distribution
dc.subject.proposal.spa.fl_str_mv beta distribution
Complex random matrix
Dirichlet distribution
Jacobian
Complex multivariate gamma function
Wishart distribution
description ABSTRACT: In this paper, it has been shown that the complex matrix variate Dirichlet type I density factors into the complex matrix variate beta type I densities. Similar result has also been derived for the complex matrix variate Dirichlet type II density. Also, by using certain matrix transformations, the complex matrix variate Dirichlet distributions have been generated from the complex matrix beta distributions. Further, several results on the product of complex Wishart and complex beta matrices with a set of complex Dirichlet type I matrices have been derived.
publishDate 2002
dc.date.issued.none.fl_str_mv 2002
dc.date.accessioned.none.fl_str_mv 2022-09-05T21:10:55Z
dc.date.available.none.fl_str_mv 2022-09-05T21:10:55Z
dc.type.spa.fl_str_mv info:eu-repo/semantics/article
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dc.type.local.spa.fl_str_mv Artículo de investigación
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dc.identifier.citation.spa.fl_str_mv Cui, X., K. Gupta, A., & K. Nagar, D. (2005). Wilks’ Factorization of the Complex Matrix Variate Dirichlet Distributions. Revista Matemática Complutense, 18(2), 315 - 328. https://doi.org/10.5209/rev_REMA.2005.v18.n2.16673
dc.identifier.issn.none.fl_str_mv 1139-1138
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10495/30420
dc.identifier.doi.none.fl_str_mv 10.5209/rev_REMA.2005.v18.n2.16673
dc.identifier.eissn.none.fl_str_mv 1988-2807
dc.identifier.url.spa.fl_str_mv https://revistas.ucm.es/index.php/REMA/article/view/16673
identifier_str_mv Cui, X., K. Gupta, A., & K. Nagar, D. (2005). Wilks’ Factorization of the Complex Matrix Variate Dirichlet Distributions. Revista Matemática Complutense, 18(2), 315 - 328. https://doi.org/10.5209/rev_REMA.2005.v18.n2.16673
1139-1138
10.5209/rev_REMA.2005.v18.n2.16673
1988-2807
url https://hdl.handle.net/10495/30420
https://revistas.ucm.es/index.php/REMA/article/view/16673
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.ispartofjournalabbrev.spa.fl_str_mv Rev. Mat. Complut.
dc.rights.spa.fl_str_mv info:eu-repo/semantics/openAccess
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dc.format.extent.spa.fl_str_mv 14
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Springer
dc.publisher.group.spa.fl_str_mv Análisis Multivariado
dc.publisher.place.spa.fl_str_mv Madrid, España
institution Universidad de Antioquia
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spelling Nagar, Daya KrishnaCui, XinpingGupta, Arjun Kumar2022-09-05T21:10:55Z2022-09-05T21:10:55Z2002Cui, X., K. Gupta, A., & K. Nagar, D. (2005). Wilks’ Factorization of the Complex Matrix Variate Dirichlet Distributions. Revista Matemática Complutense, 18(2), 315 - 328. https://doi.org/10.5209/rev_REMA.2005.v18.n2.166731139-1138https://hdl.handle.net/10495/3042010.5209/rev_REMA.2005.v18.n2.166731988-2807https://revistas.ucm.es/index.php/REMA/article/view/16673ABSTRACT: In this paper, it has been shown that the complex matrix variate Dirichlet type I density factors into the complex matrix variate beta type I densities. Similar result has also been derived for the complex matrix variate Dirichlet type II density. Also, by using certain matrix transformations, the complex matrix variate Dirichlet distributions have been generated from the complex matrix beta distributions. Further, several results on the product of complex Wishart and complex beta matrices with a set of complex Dirichlet type I matrices have been derived.COL000053214application/pdfengSpringerAnálisis MultivariadoMadrid, Españainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARTArtículo de investigaciónhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/co/http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by/4.0/Wilks’ Factorization of the Complex Matrix Variate Dirichlet DistributionsTransformación Celular NeoplásicaCell Transformation, Neoplasticbeta distributionComplex random matrixDirichlet distributionJacobianComplex multivariate gamma functionWishart distributionRev. Mat. Complut.Revista Matemática Complutense315328182CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8927https://bibliotecadigital.udea.edu.co/bitstream/10495/30420/2/license_rdf1646d1f6b96dbbbc38035efc9239ac9cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://bibliotecadigital.udea.edu.co/bitstream/10495/30420/3/license.txt8a4605be74aa9ea9d79846c1fba20a33MD53ORIGINALNagarDaya_2011_PropertiesBivariateConfluent.pdfNagarDaya_2011_PropertiesBivariateConfluent.pdfArtículo de investigaciónapplication/pdf254263https://bibliotecadigital.udea.edu.co/bitstream/10495/30420/4/NagarDaya_2011_PropertiesBivariateConfluent.pdf47b15db129be81127ffe04024a15090bMD5410495/30420oai:bibliotecadigital.udea.edu.co:10495/304202022-12-11 12:09:38.27Repositorio Institucional Universidad de Antioquiaandres.perez@udea.edu.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