The Anisotropic Norm of Random Vectors: Defining via a Symmetric Tsallis Divergence

Abstract

An alternative approach to define the anisotropic norm of random vectors is proposed, based on a symmetric Tsallis divergence measure constructed within the present paper. The consideration is motivated by a definition available in the literature, which is based on Kullback-Leibler divergence and, thus, being non-symmetric, what, at least from a theoretical point of view, stimulates to consider some other possibilities in this field.