On Wishart distribution: Some extensions

On Riesz distribution

“…Finally, we define the measure or volume element (dX) when Díaz-García and Gutiérrez-Jáimez (2011). If X ∈ F m×n then (dX) (the Lebesgue measure in F m×n ) denotes the exterior product of the βmn functionally independent variables Observe, that for the Lebesgue measure (dS) defined thus, it is required that S ∈ P β m , that is, S must be a non singular Hermitian matrix (Hermitian definite positive matrix).…”

“…In the field of spherical functions (Jack polynomials including James' zonal polynomials) we can mention the work of Sawyer (1997). Parallel results on distribution theory based on real normed division algebras have been also developed in statistics and random matrix theory, see Forrester (2009), Díaz-García andGutiérrez-Jáimez (2011), Díaz-García and Gutiérrez-Jáimez (2012a), among others. A detailed study of functions with matrix arguments on symmetric cones, such as Jack and Davis' invariants polynomials and hypergeometric types series, among others, appear in Gross and Richards (1987), Díaz-García and Gutiérrez-Jáimez (2012b) and Díaz-García and Gutiérrez-Jáimez (2009), for real normed division algebras.…”

Parametrising correlation matrices

“…Proof. Without imposing the constraint that each diagonal entry in R in (1.5) equals unity, but still requiring the diagonal entries of L therein to be positive, the change of variables for the volume forms is specified by [5] (dR) = 2 N N ∏ j=1 l (F),1 jj β(N−j)+1 (dL), (4.21) where β = 1, 2, 4 for (F) = r, c, q and l (r),1 jj…”

Wishart distributions: Advances in theory with Bayesian application

“…Abul-Magd et al [1] proposed a generalization to Wishart-Laguerre ensembles. Adhikari [2] generalized the Wishart distribution for probabilistic structural dynamics, and Díaz-García and Gutiérrez-Jáimez [9] extended the Wishart distribution for real normed division algebras. Munilla and Cantet [22] also formulated a special structure for the Wishart distribution to apply in modeling the maternal animal.…”