Characterizations of sum form information measures on open domains
type: Item
instance of: scholarly article
title: Characterizations of sum form information measures on open domains
zbMATH Open document ID: 0880.39019
DOI: 10.1007/BF02755443
author: Bruce Ebanks
author: Pl. Kannappan
author: Wolfgang Sander
author: Prasanna Sahoo
published in: Aequationes Mathematicae
publication date: 1998-01-08T00:00:00Z
full work available at URL: https://eudml.org/doc/137691
review text: This is a survey of information measures depending on \(k\) complete \(n\)-ary probability distributions (the probabilities being either nonnegative or positive), which are sums of terms depending upon only the first, only the second, \dots, only the \(n\)-th \(k\)-component probability vectors. In most results reported, just measurability or no regularity at all is supposed regarding the functions generating these dependencies. Additivity requires that the (measure of) information obtained from two \(k\)-tuples of probability distributions equals the sum of informations obtained from the individual probability distributions (one \(m\)-ary, the other \(n\)-ary). Generalizations of this property and symmetries are also considered. The authors, who also did much of the original work, report that most problems of determining all such information measures have been solved. Some open problems lead to the functional equation \(f(pq) + f(p(1-q)) + f((1-p)q) +f((1-p)(1-q)) = g(p)h(q)\), \(p,q\in]0,1[^{k}\). An 81-item list of references closes the paper.
reviewed by: János Aczél
Mathematics Subject Classification ID: 39B22
Mathematics Subject Classification ID: 26A24
Mathematics Subject Classification ID: 28A20
Mathematics Subject Classification ID: 39B62
Mathematics Subject Classification ID: 94A17
zbMATH DE Number: 1053596
zbMATH Keywords: sum form information measures
zbMATH Keywords: open domains
zbMATH Keywords: probability distributions
zbMATH Keywords: functional equation
zbMATH Keywords: Information improvement
zbMATH Keywords: Deviation
zbMATH Keywords: inaccuracy
zbMATH Keywords: characterization
zbMATH Keywords: Generating function
zbMATH Keywords: Differentiable
zbMATH Keywords: Derivation
zbMATH Keywords: Additive
zbMATH Keywords: Multiplicative type
zbMATH Keywords: Logarithmic functions
MaRDI profile type: Publication
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Characterizations of sum form information measures on open domains (OpenAlex ID)
OpenAlex ID: W1986975014