Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions

Caro-Lopera F.J.; Leiva V.; Balakrishnan N.

doi:10.1016/j.jmva.2011.07.004

dc.creator	Caro-Lopera F.J.	spa
dc.creator	Leiva V.	spa
dc.creator	Balakrishnan N.	spa
dc.date.accessioned	2015-10-09T13:17:52Z
dc.date.available	2015-10-09T13:17:52Z
dc.date.created	2012
dc.identifier.issn	0047259X
dc.identifier.uri	http://hdl.handle.net/11407/1363
dc.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.	eng
dc.language.iso	eng
dc.relation.isversionof	http://www.sciencedirect.com/science/article/pii/S0047259X11001461	spa
dc.source	Scopus	spa
dc.title	Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions	eng
dc.type	Article	eng
dc.rights.accessrights	info:eu-repo/semantics/restrictedAccess
dc.rights.accessrights	info:eu-repo/semantics/restrictedAccess
dc.contributor.affiliation	Departamento de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia	spa
dc.contributor.affiliation	Departamento de Estadística, Universidad de Valparaíso, Valparaíso, Chile	spa
dc.contributor.affiliation	Dept. of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada	spa
dc.contributor.affiliation	King Saud University, Faculty of Science, Riyadh, Saudi Arabia	spa
dc.identifier.doi	10.1016/j.jmva.2011.07.004
dc.subject.keyword	Generalized birnbaum-saunders distribution	eng
dc.subject.keyword	Kronecker product	eng
dc.subject.keyword	Multivariate analysis	eng
dc.subject.keyword	Schur or entry-wise product	eng
dc.subject.keyword	Shape theory	eng
dc.relation.ispartofen	Journal of Multivariate Analysis, febrero de 2012, volume 104, issue 1, pp 126-139	eng
dc.type.driver	info:eu-repo/semantics/article

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