The Cauchy Distribution in Information Theory

Abstract

The Gaussian law reigns supreme in the information theory of analog random variables. This paper showcases a number of information theoretic results which find elegant counterparts for Cauchy distributions. New concepts such as that of equivalent pairs of probability measures and the strength of real-valued random variables are introduced here and shown to be of particular relevance to Cauchy distributions.

Keywords

• information measures
• Cauchy distribution
• relative entropy
• Kullback–Leibler divergence
• differential entropy
• Fisher’s information