The Cauchy Distribution in Information Theory
Copyright policy )The Cauchy Distribution in Information Theory
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.
Rényi divergence, Science, Physics, QC1-999, relative entropy, Q, Kullback–Leibler divergence, data transmission, Astrophysics, Article, differential entropy, QB460-466, lossy data compression, <i>f</i>-divergence, Cauchy distribution, Fisher’s information, mutual information, entropy power inequality, information measures
Rényi divergence, Science, Physics, QC1-999, relative entropy, Q, Kullback–Leibler divergence, data transmission, Astrophysics, Article, differential entropy, QB460-466, lossy data compression, <i>f</i>-divergence, Cauchy distribution, Fisher’s information, mutual information, entropy power inequality, information measures
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