Weighted entropy: basic inequalities

  • Kelbert M
  • Stuhl I
  • Suhov Y
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Abstract

This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of the Fisher information inequality and entropy power inequality for the weighted entropy and discuss connections with weighted Lieb's splitting inequality. The concepts of rates of the weighted entropy and information are also discussed. Keywords Weighted entropy, Gibbs inequality, Ky-Fan inequality, Fisher information inequality, entropy power inequality, Lieb's splitting inequality, rates of weighted entropy and information 2010 MSC 94A17

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Kelbert, M., Stuhl, I., & Suhov, Y. (2017). Weighted entropy: basic inequalities. Modern Stochastics: Theory and Applications, 4(3), 233–252. https://doi.org/10.15559/17-vmsta85

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