TY - JOUR
T1 - Elliptical affine shape distributions for real normed division algebras
AU - Díaz-García, José A.
AU - Caro-Lopera, Francisco J.
PY - 2016/2/1
Y1 - 2016/2/1
N2 - © 2015 Elsevier Inc. The statistical affine shape theory is set in this work in the context of real normed division algebras. The general densities apply for every field: real, complex, quaternion, octonion, and for any noncentral and non-isotropic elliptical distribution; then the separated published works about real and complex shape distributions can be obtained as corollaries by a suitable selection of the field parameter and univariate integrals involving the generator elliptical function. As a particular case, the complex normal affine density is derived and applied in brain magnetic resonance scans of normal and schizophrenic patients.
AB - © 2015 Elsevier Inc. The statistical affine shape theory is set in this work in the context of real normed division algebras. The general densities apply for every field: real, complex, quaternion, octonion, and for any noncentral and non-isotropic elliptical distribution; then the separated published works about real and complex shape distributions can be obtained as corollaries by a suitable selection of the field parameter and univariate integrals involving the generator elliptical function. As a particular case, the complex normal affine density is derived and applied in brain magnetic resonance scans of normal and schizophrenic patients.
U2 - 10.1016/j.jmva.2015.11.003
DO - 10.1016/j.jmva.2015.11.003
M3 - Article
SP - 139
EP - 149
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
SN - 0047-259X
ER -