Basic inequalities for weighted entropies

Yuri Suhov, Izabella Stuhl, Salimeh Yasaei Sekeh, Mark Kelbert

Research output: Contribution to journalArticle

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Abstract

The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. In this paper, we establish a number of simple inequalities for the weighted entropies (general as well as specific), mirroring similar bounds on standard (Shannon) entropies and related quantities. The required assumptions are written in terms of various expectations of weight functions. Examples are weighted Ky Fan and weighted Hadamard inequalities involving determinants of positive-definite matrices, and weighted Cramér-Rao inequalities involving the weighted Fisher information matrix.

Original languageEnglish (US)
Pages (from-to)817-848
Number of pages32
JournalAequationes Mathematicae
Volume90
Issue number4
DOIs
StatePublished - Aug 1 2016

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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