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

Abstract

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.

Dates and versions

hal-02420591 , version 1 (20-12-2019)

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Frédéric Chyzak, Frank Nielsen. A closed-form formula for the Kullback-Leibler divergence between Cauchy distributions. 2019. ⟨hal-02420591⟩
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