A note on Onicescu's informational energy and correlation coefficient in exponential families
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The informational energy of Onicescu is a positive quantity that measures the amount of uncertainty of a random variable like Shannon's entropy. In this note, we report closed-form formula for Onicescu's informational energy and correlation coefficient when the densities belong to an exponential family. We also report as a byproduct a closed-form formula for the Cauchy-Schwarz divergence between densities of an exponential family.
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