Information-theoretic inequalities for contoured probability distributions

Onur G. Guleryuz, Erwin Lutwak, Deane Yang, Gaoyong Zhang

Research output: Contribution to journalLetterpeer-review


We show that for a special class of probability distributions that we call contoured distributions, information-theoretic invariants and inequalities are equivalent to geometric invariants and inequalities of bodies in Euclidean space associated with the distributions. Using this, we obtain characterizations of contoured distributions with extremal Shannon and Renyi entropy. We also obtain a new reverse information-theoretic inequality for contoured distributions.

Original languageEnglish (US)
Pages (from-to)2377-2383
Number of pages7
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - Aug 2002


  • Brunn-Minkowski
  • Convex bodies
  • Elliptically contoured
  • Entropy
  • Fisher information
  • Inequalities
  • Isoperimetric inequalities

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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