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Characterization of some measures of information theory and the sum form functional equations — Generalized directed divergence — I

  • Pl. Kannappan
Section IV Information Theoretic Approach
Part of the Lecture Notes in Computer Science book series (LNCS, volume 286)

Abstract

Most of the well known measures like the Shannon entropy, the entropy of degree β, the generalized directed divergence (the information improvement), the weighted entropies etc. have many algebraic properties in common, in particular, the sum representation. They also possess some form of ‘additivity’. Characterization of information measures through these and other algebraic properties satisfied by them involve many functional equations, of which the fundamental equation of information theory and the ‘sum form’ play distinct roles. Here the focus is made on the ‘sum form’, illustrating however at least in one instance the interconnection between these two types of functional equations. Also emphasis is made on the generalized directed divergence.

Keywords

Functional Equation Shannon Entropy Information Measure Fundamental Equation Algebraic Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Pl. Kannappan
    • 1
  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada

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