Shape theory via affine transformation: Some generalisations

Details Shape theory via affine transformation: Some generalisations Shape theory via affine transformation: Some generalisations

2010-12-29

arxiv.org/abs/1012.5856v1

Mathematics

Statistics Theory

13 pages

Scientific paper

This work sets the statistical affine shape theory 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.

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