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An Entropic Pathway to Multivariate Gaussian Density

H.J. Haubold, A.M. Mathai and S. Thomas

A general principle called ”conservation of the ellipsoid of concentration” is introduced and a generalized entropic form of order α is optimized under this principle. It is shown that this can produce a density which can act as a pathway to multivariate Gaussian density. The resulting entropic pathway contains as special cases the Boltzmann-Gibbs (Shannon) and Tsallis (Havrda-Charv´at) entropic forms.