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

Frédéric Chyzak (1) , Frank Nielsen (2)

1 SPECFUN - Symbolic Special Functions : Fast and Certified
2 SONY CSL-Paris - Sony Computer Science Laboratory Paris

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.

Domaines: Calcul formel [cs.SC]

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