On $f$-divergences between Cauchy distributions

Frank Nielsen, Kazuki Okamura

We prove that the $f$-divergences between univariate Cauchy distributions are always symmetric and can be expressed as functions of the chi-squared divergence. We show that this property does not hold anymore for multivariate Cauchy distributions. We then present several metrizations of $f$-divergences between univariate Cauchy distributions.

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