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An alternative one-parameter measure of divergence is proposed, quantifying the discrepancy among general probability densities. Its main mathematical properties include (i) comparison among an arbitrary number of functions, (ii) the possibility of assigning different weights to each function according to its relevance on the comparative procedure, and (iii) ability to modify the relative contribution of different regions within the domain. Applications to the study of atomic density functions, in both conjugated spaces, show the versatility and universality of this divergence.

Geometric Rényi divergence: A comparative measure with applications to atomic densities