Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions
In this paper, we establish a connection between the Hadamard product and the usual matrix multiplication. In addition, we study some new properties of the Hadamard product and explore the inverse problem associated with the established connection, which facilitates diverse applications. Furthermore...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2012
- Institución:
- Universidad de Medellín
- Repositorio:
- Repositorio UDEM
- Idioma:
- eng
- OAI Identifier:
- oai:repository.udem.edu.co:11407/1363
- Acceso en línea:
- http://hdl.handle.net/11407/1363
- Palabra clave:
- Generalized birnbaum-saunders distribution
Kronecker product
Multivariate analysis
Schur or entry-wise product
Shape theory
- Rights
- restrictedAccess
- License
- http://purl.org/coar/access_right/c_16ec
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2015-10-09T13:17:52Z2015-10-09T13:17:52Z20120047259Xhttp://hdl.handle.net/11407/136310.1016/j.jmva.2011.07.004In this paper, we establish a connection between the Hadamard product and the usual matrix multiplication. In addition, we study some new properties of the Hadamard product and explore the inverse problem associated with the established connection, which facilitates diverse applications. Furthermore, we propose a matrix-variate generalized Birnbaum–Saunders (GBS) distribution. Three representations of the matrix-variate GBS density are provided, one of them by using the mentioned connection. The main motivation of this article is based on the fact that the representation of the matrix-variate GBS density based on element-by-element specification does not allow matrix transformations. Consequently, some statistical procedures based on this representation, such as multivariate data analysis and statistical shape theory, cannot be performed. For this reason, the primary goal of this work is to obtain a matrix representation of the matrix-variate GBS density that is useful for some statistical applications. When the GBS density is expressed by means of a matrix representation based on the Hadamard product, such a density is defined in terms of the original matrices, as is common for many matrix-variate distributions, allowing matrix transformations to be handled in a natural way and then suitable statistical procedures to be developed.enghttp://www.sciencedirect.com/science/article/pii/S0047259X11001461Journal of Multivariate Analysis, febrero de 2012, volume 104, issue 1, pp 126-139ScopusConnection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributionsArticleinfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1info:eu-repo/semantics/restrictedAccesshttp://purl.org/coar/access_right/c_16ecDepartamento de Ciencias Básicas, Universidad de Medellín, Medellín, ColombiaDepartamento de Estadística, Universidad de Valparaíso, Valparaíso, ChileDept. of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, CanadaKing Saud University, Faculty of Science, Riyadh, Saudi ArabiaCaro-Lopera F.J.Leiva V.Balakrishnan N.Generalized birnbaum-saunders distributionKronecker productMultivariate analysisSchur or entry-wise productShape theoryTHUMBNAILportada.JPGportada.JPGimage/jpeg15491http://repository.udem.edu.co/bitstream/11407/1363/1/portada.JPG6fa6a0a0325b5f3bcba2919e48722d05MD5111407/1363oai:repository.udem.edu.co:11407/13632020-05-27 17:30:53.916Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co |
dc.title.eng.fl_str_mv |
Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions |
title |
Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions |
spellingShingle |
Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions Generalized birnbaum-saunders distribution Kronecker product Multivariate analysis Schur or entry-wise product Shape theory |
title_short |
Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions |
title_full |
Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions |
title_fullStr |
Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions |
title_full_unstemmed |
Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions |
title_sort |
Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions |
dc.contributor.affiliation.spa.fl_str_mv |
Departamento de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia Departamento de Estadística, Universidad de Valparaíso, Valparaíso, Chile Dept. of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada King Saud University, Faculty of Science, Riyadh, Saudi Arabia |
dc.subject.keyword.eng.fl_str_mv |
Generalized birnbaum-saunders distribution Kronecker product Multivariate analysis Schur or entry-wise product Shape theory |
topic |
Generalized birnbaum-saunders distribution Kronecker product Multivariate analysis Schur or entry-wise product Shape theory |
description |
In this paper, we establish a connection between the Hadamard product and the usual matrix multiplication. In addition, we study some new properties of the Hadamard product and explore the inverse problem associated with the established connection, which facilitates diverse applications. Furthermore, we propose a matrix-variate generalized Birnbaum–Saunders (GBS) distribution. Three representations of the matrix-variate GBS density are provided, one of them by using the mentioned connection. The main motivation of this article is based on the fact that the representation of the matrix-variate GBS density based on element-by-element specification does not allow matrix transformations. Consequently, some statistical procedures based on this representation, such as multivariate data analysis and statistical shape theory, cannot be performed. For this reason, the primary goal of this work is to obtain a matrix representation of the matrix-variate GBS density that is useful for some statistical applications. When the GBS density is expressed by means of a matrix representation based on the Hadamard product, such a density is defined in terms of the original matrices, as is common for many matrix-variate distributions, allowing matrix transformations to be handled in a natural way and then suitable statistical procedures to be developed. |
publishDate |
2012 |
dc.date.created.none.fl_str_mv |
2012 |
dc.date.accessioned.none.fl_str_mv |
2015-10-09T13:17:52Z |
dc.date.available.none.fl_str_mv |
2015-10-09T13:17:52Z |
dc.type.eng.fl_str_mv |
Article |
dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/resource_type/c_2df8fbb1 |
dc.type.driver.none.fl_str_mv |
info:eu-repo/semantics/article |
dc.identifier.issn.none.fl_str_mv |
0047259X |
dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/11407/1363 |
dc.identifier.doi.none.fl_str_mv |
10.1016/j.jmva.2011.07.004 |
identifier_str_mv |
0047259X 10.1016/j.jmva.2011.07.004 |
url |
http://hdl.handle.net/11407/1363 |
dc.language.iso.none.fl_str_mv |
eng |
language |
eng |
dc.relation.isversionof.spa.fl_str_mv |
http://www.sciencedirect.com/science/article/pii/S0047259X11001461 |
dc.relation.ispartofen.eng.fl_str_mv |
Journal of Multivariate Analysis, febrero de 2012, volume 104, issue 1, pp 126-139 |
dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_16ec |
dc.rights.accessrights.none.fl_str_mv |
info:eu-repo/semantics/restrictedAccess |
eu_rights_str_mv |
restrictedAccess |
rights_invalid_str_mv |
http://purl.org/coar/access_right/c_16ec |
dc.source.spa.fl_str_mv |
Scopus |
institution |
Universidad de Medellín |
bitstream.url.fl_str_mv |
http://repository.udem.edu.co/bitstream/11407/1363/1/portada.JPG |
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6fa6a0a0325b5f3bcba2919e48722d05 |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 |
repository.name.fl_str_mv |
Repositorio Institucional Universidad de Medellin |
repository.mail.fl_str_mv |
repositorio@udem.edu.co |
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1814159166869078016 |