Matrix variate Birnbaum–Saunders distribution under elliptical models
This 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 result...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad de Medellín
- Repositorio:
- Repositorio UDEM
- Idioma:
- eng
- OAI Identifier:
- oai:repository.udem.edu.co:11407/5895
- Acceso en línea:
- http://hdl.handle.net/11407/5895
- Palabra clave:
- Birnbaum–Saunders distribution
Elliptical distributions
Kotz distribution
Matrix multivariate distributions
Random matrices
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- License
- http://purl.org/coar/access_right/c_16ec
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| dc.title.none.fl_str_mv |
Matrix variate Birnbaum–Saunders distribution under elliptical models |
| title |
Matrix variate Birnbaum–Saunders distribution under elliptical models |
| spellingShingle |
Matrix variate Birnbaum–Saunders distribution under elliptical models Birnbaum–Saunders distribution Elliptical distributions Kotz distribution Matrix multivariate distributions Random matrices |
| title_short |
Matrix variate Birnbaum–Saunders distribution under elliptical models |
| title_full |
Matrix variate Birnbaum–Saunders distribution under elliptical models |
| title_fullStr |
Matrix variate Birnbaum–Saunders distribution under elliptical models |
| title_full_unstemmed |
Matrix variate Birnbaum–Saunders distribution under elliptical models |
| title_sort |
Matrix variate Birnbaum–Saunders distribution under elliptical models |
| dc.subject.spa.fl_str_mv |
Birnbaum–Saunders distribution Elliptical distributions Kotz distribution Matrix multivariate distributions Random matrices |
| topic |
Birnbaum–Saunders distribution Elliptical distributions Kotz distribution Matrix multivariate distributions Random matrices |
| description |
This 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. |
| publishDate |
2021 |
| dc.date.accessioned.none.fl_str_mv |
2021-02-05T14:57:37Z |
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2021-02-05T14:57:37Z |
| dc.date.none.fl_str_mv |
2021 |
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Article |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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3783758 |
| dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/11407/5895 |
| dc.identifier.doi.none.fl_str_mv |
10.1016/j.jspi.2020.04.012 |
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3783758 10.1016/j.jspi.2020.04.012 |
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http://hdl.handle.net/11407/5895 |
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eng |
| language |
eng |
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https://www.scopus.com/inward/record.uri?eid=2-s2.0-85084979891&doi=10.1016%2fj.jspi.2020.04.012&partnerID=40&md5=6c471639fb8438561cbc46d036870367 |
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210 |
| dc.relation.citationstartpage.none.fl_str_mv |
100 |
| dc.relation.citationendpage.none.fl_str_mv |
113 |
| dc.relation.references.none.fl_str_mv |
Balakrishnan, 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 Birnbaum, Z.W., Saunders, S.C., A new family of life distributions (1969) J. Appl. Probab., 6, pp. 637-652 Cadet, A., Polar coordinates in Rnp application to the computation of the Wishart and beta laws (1996) Sankhyā A, 58, pp. 101-113 Caro-Lopera, F.J., Díaz-García, J.A., Diagonalization matrix and its application in distribution theory (2016) Statistics, 50 (4), pp. 870-880 Caro-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 Chen, J.J., Novick, M.R., Bayesian analysis for binomial models with generalized beta prior distributions (1984) J. Educ. Stat., 9, pp. 163-175 Davis, 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 Desmond, A., Stochastic models of failure in random enviorments (1985) Canad. J. Stat., 13, pp. 171-183 Díaz-García, J.A., Caro-Lopera, F.J., Pérez Ramírez, F.O., Multivector variate distributions (2019) Sankhyā, , (in press) Díaz-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 Díaz-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 Díaz-García, J.A., Gutiérrez-Jáimez, R., Functions of singular random matrices and its applications (2005) Test, 14 (2), pp. 475-487 Díaz-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 Díaz-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 Fang, K.T., Zhang, Y.T., Generalized Multivariate Analysis (1990), Science Press, Springer-Verlag Beijing Gupta, A.K., Varga, Y., Bodnar, T., Elliptical Contoured Models in Statistics and Portfolio Theory (2013), second ed. Springer New York Herz, C.S., Bessel functions of matrix argument (1955) Ann. of Math., 61 (3), pp. 474-523 James, A.T., Normal multivariate analysis and the orthogonal group (1954) Ann. Math. Stat., 25 (1), pp. 40-75 Kass, R.E., Raftery, A.E., Bayes factor (1995) J. Am. Stat. Soc., 90, pp. 773-795 Kotz, S., Nadarajah, S., Multivariate T Distributions and their Applications (2004), Cambridge University Press United Kingdom Libby, D.L., Novick, M.R., Multivariate generalized beta distributions with applications to utility assessment (1982) J. Educ. Stat., 7, pp. 271-294 Magnus, J.R., Linear Structures (1988), Charles Griffin & Company Ltd London Magnus, J.R., Neudecker, H., Matrix Differential Calculus with Application in Statistics and Econometrics (2007), third ed. John Wiley & Sons Chichester Mathai, A.M., Jacobian of Matrix Transformations and Functions of Matrix Argument (1997), World Scinentific Singapore Muirhead, R.J., Aspects of Multivariate Statistical Theory (2005), John Wiley & Sons New York Ng, 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 Olkin, I., Rubin, H., Multivariate beta distributions and independence properties of Wishart distribution (1964) Ann. Math. Stat., 35 (1), pp. 261-269. , Correction Raftery, A.E., Bayesian model selection in social research (1995) Sociol. Methodol., 25, pp. 111-163 Rao, C.R., Linear Statistical Inference and Its Applications (2005), second ed. John Wiley & Sons New York Roy, S.N., Some Aspects of Multivariate Analysis (1957), John Wiley & Sons, Inc. New York Sánchez, 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 Srivastava, M.S., Khatri, C.G., An Introduction To Multivariate Analysis (1979), North-Holland Publ Amsterdam Yang, C.C., Yang, C.C., Separating latent classes by information criteria (2007) J Classification, 24, pp. 183-203 |
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Elsevier B.V. |
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Facultad de Ciencias Básicas |
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Elsevier B.V. |
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Journal of Statistical Planning and Inference |
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Universidad de Medellín |
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Repositorio Institucional Universidad de Medellin |
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repositorio@udem.edu.co |
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20212021-02-05T14:57:37Z2021-02-05T14:57:37Z3783758http://hdl.handle.net/11407/589510.1016/j.jspi.2020.04.012This 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.engElsevier B.V.Facultad de Ciencias Básicashttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85084979891&doi=10.1016%2fj.jspi.2020.04.012&partnerID=40&md5=6c471639fb8438561cbc46d036870367210100113Balakrishnan, 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 discussionBirnbaum, Z.W., Saunders, S.C., A new family of life distributions (1969) J. Appl. Probab., 6, pp. 637-652Cadet, A., Polar coordinates in Rnpapplication to the computation of the Wishart and beta laws (1996) Sankhyā A, 58, pp. 101-113Caro-Lopera, F.J., Díaz-García, J.A., Diagonalization matrix and its application in distribution theory (2016) Statistics, 50 (4), pp. 870-880Caro-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. 126-139Chen, J.J., Novick, M.R., Bayesian analysis for binomial models with generalized beta prior distributions (1984) J. Educ. Stat., 9, pp. 163-175Davis, 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. 465-485Desmond, A., Stochastic models of failure in random enviorments (1985) Canad. J. Stat., 13, pp. 171-183Díaz-García, J.A., Caro-Lopera, F.J., Pérez Ramírez, F.O., Multivector variate distributions (2019) Sankhyā, , (in press)Díaz-García, J.A., Domínguez Molina, J.R., Some generalisations of Birnbaum–Saunders and sinh-normal distributions (2006) Int. Math. Forum., 1 (35), pp. 1709-1727Díaz-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. 5927-5939Díaz-García, J.A., Gutiérrez-Jáimez, R., Functions of singular random matrices and its applications (2005) Test, 14 (2), pp. 475-487Díaz-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. 445-457Díaz-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 toFang, K.T., Zhang, Y.T., Generalized Multivariate Analysis (1990), Science Press, Springer-Verlag BeijingGupta, A.K., Varga, Y., Bodnar, T., Elliptical Contoured Models in Statistics and Portfolio Theory (2013), second ed. Springer New YorkHerz, C.S., Bessel functions of matrix argument (1955) Ann. of Math., 61 (3), pp. 474-523James, A.T., Normal multivariate analysis and the orthogonal group (1954) Ann. Math. Stat., 25 (1), pp. 40-75Kass, R.E., Raftery, A.E., Bayes factor (1995) J. Am. Stat. Soc., 90, pp. 773-795Kotz, S., Nadarajah, S., Multivariate T Distributions and their Applications (2004), Cambridge University Press United KingdomLibby, D.L., Novick, M.R., Multivariate generalized beta distributions with applications to utility assessment (1982) J. Educ. Stat., 7, pp. 271-294Magnus, J.R., Linear Structures (1988), Charles Griffin & Company Ltd LondonMagnus, J.R., Neudecker, H., Matrix Differential Calculus with Application in Statistics and Econometrics (2007), third ed. John Wiley & Sons ChichesterMathai, A.M., Jacobian of Matrix Transformations and Functions of Matrix Argument (1997), World Scinentific SingaporeMuirhead, R.J., Aspects of Multivariate Statistical Theory (2005), John Wiley & Sons New YorkNg, 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. 283-298Olkin, I., Rubin, H., Multivariate beta distributions and independence properties of Wishart distribution (1964) Ann. Math. Stat., 35 (1), pp. 261-269. , CorrectionRaftery, A.E., Bayesian model selection in social research (1995) Sociol. Methodol., 25, pp. 111-163Rao, C.R., Linear Statistical Inference and Its Applications (2005), second ed. John Wiley & Sons New YorkRoy, S.N., Some Aspects of Multivariate Analysis (1957), John Wiley & Sons, Inc. New YorkSánchez, 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. 790-812Srivastava, M.S., Khatri, C.G., An Introduction To Multivariate Analysis (1979), North-Holland Publ AmsterdamYang, C.C., Yang, C.C., Separating latent classes by information criteria (2007) J Classification, 24, pp. 183-203Journal of Statistical Planning and InferenceBirnbaum–Saunders distributionElliptical distributionsKotz distributionMatrix multivariate distributionsRandom matricesMatrix variate Birnbaum–Saunders distribution under elliptical modelsArticleinfo:eu-repo/semantics/articlehttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Díaz-García, J.A., Independent ScholarCaro-Lopera, F.J., Universidad de Medellín, Faculty of Basic Sciences, Carrera 87 No.30-65, of. 4-216, Medellín, Colombiahttp://purl.org/coar/access_right/c_16ecDíaz-García J.A.Caro-Lopera F.J.11407/5895oai:repository.udem.edu.co:11407/58952021-02-05 09:57:37.464Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co |