Elliptical affine shape distributions for real normed division algebras

José A. Díaz-García and Francisco J. Caro-Lopera

Journal of Multivariate Analysis, 2016, vol. 144, issue C, 139-149

Abstract: 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.

Keywords: Jacobians; Jack polynomials; Generalised hypergeometric functions; Elliptical distribution; Real, complex, quaternion and octonion random matrices; Affine shape (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.jmva.2015.11.003

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