Show simple item record

dc.creatorDíaz-García J.A.
dc.creatorCaro-Lopera F.J.
dc.descriptionThis paper derives the elliptical matrix variate version of the well known univariate Birnbaum–Saunders distribution of 1969. A generalisation based on a matrix transformation is proposed, instead of the independent element-to-element elliptical extension of the Gaussian univariate case. Some results on Jacobians were needed to derive the new matrix variate distribution. A number of particular distributions are studied and some basic properties are found. Finally, an example based on real data of two populations is given and the maximum likelihood estimates are obtained for the class of Kotz models. A comparison with the Gaussian kernel is also given by using a modified BIC criterion. © 2020 Elsevier B.V.
dc.publisherElsevier B.V.
dc.sourceJournal of Statistical Planning and Inference
dc.subjectBirnbaum–Saunders distributionspa
dc.subjectElliptical distributionsspa
dc.subjectKotz distributionspa
dc.subjectMatrix multivariate distributionsspa
dc.subjectRandom matricesspa
dc.titleMatrix variate Birnbaum–Saunders distribution under elliptical models
dc.publisher.facultyFacultad de Ciencias Básicasspa
dc.affiliationDíaz-García, J.A., Independent Scholar
dc.affiliationCaro-Lopera, F.J., Universidad de Medellín, Faculty of Basic Sciences, Carrera 87 No.30-65, of. 4-216, Medellín, Colombia
dc.relation.referencesBalakrishnan, N., Kundu, D., Birnbaum–Saunders distribution: A review of model, analysis and applications (2019) Appl. Stoch. Models Bus. Ind., 35 (1), pp. 1-151. , with discussion
dc.relation.referencesBirnbaum, Z.W., Saunders, S.C., A new family of life distributions (1969) J. Appl. Probab., 6, pp. 637-652
dc.relation.referencesCadet, A., Polar coordinates in Rnp
dc.relation.referencesapplication to the computation of the Wishart and beta laws (1996) Sankhyā A, 58, pp. 101-113
dc.relation.referencesCaro-Lopera, F.J., Díaz-García, J.A., Diagonalization matrix and its application in distribution theory (2016) Statistics, 50 (4), pp. 870-880
dc.relation.referencesCaro-Lopera, F.J., Leiva, V., Balakrishnan, N., Connection between the hadamard and matrix products with an application to matrix-variate Birnbaum–Saunders distributions (2012) J. Multivariate Anal., 104 (1), pp. 126-139
dc.relation.referencesChen, J.J., Novick, M.R., Bayesian analysis for binomial models with generalized beta prior distributions (1984) J. Educ. Stat., 9, pp. 163-175
dc.relation.referencesDavis, A.W., Invariant polynomials with two matrix arguments, extending the zonal polynomials: Applications to multivariate distribution theory (1979) Ann. Inst. Stat. Math. A, 31, pp. 465-485
dc.relation.referencesDesmond, A., Stochastic models of failure in random enviorments (1985) Canad. J. Stat., 13, pp. 171-183
dc.relation.referencesDíaz-García, J.A., Caro-Lopera, F.J., Pérez Ramírez, F.O., Multivector variate distributions (2019) Sankhyā, , (in press)
dc.relation.referencesDíaz-García, J.A., Domínguez Molina, J.R., Some generalisations of Birnbaum–Saunders and sinh-normal distributions (2006) Int. Math. Forum., 1 (35), pp. 1709-1727
dc.relation.referencesDíaz-García, J.A., Domínguez Molina, J.R., A new family of life distributions for dependent data: Estimation (2007) Comput. Statist. Data Anal., 51 (12), pp. 5927-5939
dc.relation.referencesDíaz-García, J.A., Gutiérrez-Jáimez, R., Functions of singular random matrices and its applications (2005) Test, 14 (2), pp. 475-487
dc.relation.referencesDíaz-García, J.A., Leiva-Sánchez, V., A new family of life distributions based on elliptically contoured distributions (2005) J. Stat. Plan. Inf., 128 (2), pp. 445-457
dc.relation.referencesDíaz-García, J.A., Leiva-Sánchez, V., A new family of life distributions based on the elliptically contoured distributions (2006) J. Statist. Plann. Inference, J. Stat. Plan. Inf., 137 (4), pp. 1512-1513. , Erratum to
dc.relation.referencesFang, K.T., Zhang, Y.T., Generalized Multivariate Analysis (1990), Science Press, Springer-Verlag Beijing
dc.relation.referencesGupta, A.K., Varga, Y., Bodnar, T., Elliptical Contoured Models in Statistics and Portfolio Theory (2013), second ed. Springer New York
dc.relation.referencesHerz, C.S., Bessel functions of matrix argument (1955) Ann. of Math., 61 (3), pp. 474-523
dc.relation.referencesJames, A.T., Normal multivariate analysis and the orthogonal group (1954) Ann. Math. Stat., 25 (1), pp. 40-75
dc.relation.referencesKass, R.E., Raftery, A.E., Bayes factor (1995) J. Am. Stat. Soc., 90, pp. 773-795
dc.relation.referencesKotz, S., Nadarajah, S., Multivariate T Distributions and their Applications (2004), Cambridge University Press United Kingdom
dc.relation.referencesLibby, D.L., Novick, M.R., Multivariate generalized beta distributions with applications to utility assessment (1982) J. Educ. Stat., 7, pp. 271-294
dc.relation.referencesMagnus, J.R., Linear Structures (1988), Charles Griffin & Company Ltd London
dc.relation.referencesMagnus, J.R., Neudecker, H., Matrix Differential Calculus with Application in Statistics and Econometrics (2007), third ed. John Wiley & Sons Chichester
dc.relation.referencesMathai, A.M., Jacobian of Matrix Transformations and Functions of Matrix Argument (1997), World Scinentific Singapore
dc.relation.referencesMuirhead, R.J., Aspects of Multivariate Statistical Theory (2005), John Wiley & Sons New York
dc.relation.referencesNg, H.K.T., Kundu, D., Balakrishnan, N., Modified moment estimation for the two-parameter Birnbaum–Saunders distribution (2003) Comput. Stat. Data Anal., 43 (2003), pp. 283-298
dc.relation.referencesOlkin, I., Rubin, H., Multivariate beta distributions and independence properties of Wishart distribution (1964) Ann. Math. Stat., 35 (1), pp. 261-269. , Correction
dc.relation.referencesRaftery, A.E., Bayesian model selection in social research (1995) Sociol. Methodol., 25, pp. 111-163
dc.relation.referencesRao, C.R., Linear Statistical Inference and Its Applications (2005), second ed. John Wiley & Sons New York
dc.relation.referencesRoy, S.N., Some Aspects of Multivariate Analysis (1957), John Wiley & Sons, Inc. New York
dc.relation.referencesSánchez, L., Leiva, V., Caro-Lopera, F., Cysneiros, F.J., On matrix-variate BirnbaumSaunders distributions and their estimation and application (2015) Braz. J. Probab. Stat., 29 (4), pp. 790-812
dc.relation.referencesSrivastava, M.S., Khatri, C.G., An Introduction To Multivariate Analysis (1979), North-Holland Publ Amsterdam
dc.relation.referencesYang, C.C., Yang, C.C., Separating latent classes by information criteria (2007) J Classification, 24, pp. 183-203

Files in this item


There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record