Diagonalization matrix and its application in distribution theory |
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Authors: | Francisco J. Caro-Lopera |
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Affiliation: | Department of Basic Sciences, Universidad de Medellín, Carrera 87 No.30-65, of. 5-103, Medellín, Colombia |
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Abstract: | Some matrix representations of diverse diagonal arrays are studied in this work; the results allow new definitions of classes of elliptical distributions indexed by kernels mixing Hadamard and usual products. A number of applications are derived in the setting of prior densities from the Bayesian multivariate regression model and families of non-elliptical distributions, such as the matrix multivariate generalized Birnbaum–Saunders density. The philosophy of the research about matrix representations of quadratic and inverse quadratic forms can be extended as a methodology for exploring possible new applications in non-standard distributions, matrix transformations and inference. |
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Keywords: | Hadamard matrix product Kronecker matrix product permutations matrix multivariate elliptical distributions matrix multivariate generalized Birnbaum–Saunders distributions prior distribution |
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