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.

arXiv comment8 pages

References in corpus (2)

• On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract means
• On the Kullback-Leibler divergence between location-scale densities

Cited by in corpus (4)

• Bahadur efficiency of the maximum likelihood estimator and one-step estimator for quasi-arithmetic means of the Cauchy distribution
• On the Kullback-Leibler divergence between location-scale densities
• An equivalence criterion for infinite products of Cauchy measures
• On Voronoi diagrams and dual Delaunay complexes on the information-geometric Cauchy manifolds