The Pólya information divergence

  • Authors:
  • Marian Grendá/r;Robert K. Niven

  • Affiliations:
  • Department of Mathematics, FPV UMB, 974 01, Banská/ Bystrica, Slovakia/ Institute of Mathematics and Computer Science of the Slovak Academy of Sciences (SAS), Banská/ Bystrica, Slovakia/ a ...;School of Engineering and Information Technology, The University of New South Wales at ADFA, Canberra, ACT 2600, Australia

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2010

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Abstract

Extensions of Sanov's Theorem and the Conditional Limit Theorem (CoLT) are established for a multicolor Polya-Eggenberger (PE) urn sampling scheme, giving the Polya information divergence and a Polya extension to the Maximum Relative Entropy (MaxEnt) method. Polya MaxEnt includes the standard MaxEnt, as well as its variants used in Bose-Einstein, Fermi-Dirac and intermediate (Acharya-Swamy) statistics, as special cases. In the PE setting, standard MaxEnt is, in general, asymptotically inconsistent.