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

2019/05/27 by Frédéric Chyzak, Frank Nielsen, Chyzak, Frédéric +1 · 1 citation
Physics and Astronomy · Mathematics · Decision Sciences · #Statistical Mechanics and Entropy #Statistical Distribution Estimation and Applications #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.1905.10965

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.

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