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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 computable and then the inference procedure can be studied with the resulting exact densities. An application in Biology is studied under two Kotz models, the best distribution (non-Gaussian) is selected by using a modified Bayesian information criterion (BIC)*. © 2013 © 2013 Taylor & Francis.
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