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Elliptical affine shape distributions for real normed division algebras

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  • Díaz-García, José A.
  • Caro-Lopera, Francisco J.

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.

Suggested Citation

  • Díaz-García, José A. & Caro-Lopera, Francisco J., 2016. "Elliptical affine shape distributions for real normed division algebras," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 139-149.
    • Handle: RePEc:eee:jmvana:v:144:y:2016:i:c:p:139-149
    DOI: 10.1016/j.jmva.2015.11.003
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    References listed on IDEAS

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    1. D. Kabe, 1984. "Classical statistical analysis based on a certain hypercomplex multivariate normal distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 31(1), pages 63-76, December.
    2. Chih-Chien Yang & Chih-Chiang Yang, 2007. "Separating Latent Classes by Information Criteria," Journal of Classification, Springer;The Classification Society, vol. 24(2), pages 183-203, September.
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