© 2015 Taylor & Francis. 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.
Caro-Lopera, F. J., & Díaz-García, J. A. (2016). Diagonalization matrix and its application in distribution theory. Statistics, 50(N/A), 870-880. https://doi.org/10.1080/02331888.2015.1104312, https://doi.org/10.1080/02331888.2015.1104312