A closed-form formula for the Kullback-Leibler divergence between Cauchy distributions

05/27/2019

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by   Frédéric Chyzak, et al.

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We report a closed-form expression for the Kullback-Leibler divergence between Cauchy distributions which involves the calculation of a novel definite integral. The formula shows that the Kullback-Leibler divergence between Cauchy densities is always finite and symmetric.