Section: New Results

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

In the preliminary work [16], Frédéric Chyzak and Frank Nielsen (LIX, Palaiseau and Sony Computer Science Laboratories, Tokyo, Japan) have reported on a closed-form expression for the Kullback-Leibler divergence between Cauchy distributions which involves the calculation of a parametric definite integral with 6 parameters. The formula shows that the Kullback-Leibler divergence between Cauchy densities is always finite and symmetric. This work also serves as a show-case of several methods in computer algebra to the computation of parametrized integrals.