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The statistical shape theory via QR decomposition and based on Gaussian and isotropic models is extended in this paper to the families of non-isotropic elliptical distributions. The new shape distributions are easily ...
Statistical theory of shape under elliptical models and singular value decompositions
The size-and-shape and shape distributions based on non-central and non-isotropic elliptical distributions are derived in this paper by using the singular value decomposition (SVD). The general densities require the ...
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An extension of the well known matrix Kummer relation of Herz (1955) is proposed in this paper by assuming a general model which admits a Taylor expansion. Under certain conditions of the involved parameters, the addressed ...
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This work finds in terms of zonal polynomials, the non isotropic noncentral elliptical shape distributions via singular value decomposition; it avoids the invariant polynomials and the open problems for their computation. ...
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A case of the matrix Kummer relation of Herz (1955) based on the Pearson VII type matrix model is derived in this paper. As a consequence, the polynomial Pearson VII configuration density is obtained and this sets the ...
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The non isotropic noncentral elliptical shape distributions via pseudo-Wishart distribution are founded. This way, the classical shape theory is extended to non isotropic case and the normality assumption is replaced by ...