Weighted entropies

Bruce Ebanks

Open Mathematics (2010)

  • Volume: 8, Issue: 3, page 602-615
  • ISSN: 2391-5455

Abstract

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We present an axiomatic characterization of entropies with properties of branching, continuity, and weighted additivity. We deliberately do not assume that the entropies are symmetric. The resulting entropies are generalizations of the entropies of degree α, including the Shannon entropy as the case α = 1. Such “weighted” entropies have potential applications to the “utility of gambling” problem.

How to cite

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Bruce Ebanks. "Weighted entropies." Open Mathematics 8.3 (2010): 602-615. <http://eudml.org/doc/269619>.

@article{BruceEbanks2010,
abstract = {We present an axiomatic characterization of entropies with properties of branching, continuity, and weighted additivity. We deliberately do not assume that the entropies are symmetric. The resulting entropies are generalizations of the entropies of degree α, including the Shannon entropy as the case α = 1. Such “weighted” entropies have potential applications to the “utility of gambling” problem.},
author = {Bruce Ebanks},
journal = {Open Mathematics},
keywords = {Entropy; Weighted additivity; System of functional equations; Utility of gambling; Weighted utility; Branching; weighted additivity; entropy; system of functional equations; utility of gambling; weighted utility; branching; Shannon entropy},
language = {eng},
number = {3},
pages = {602-615},
title = {Weighted entropies},
url = {http://eudml.org/doc/269619},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Bruce Ebanks
TI - Weighted entropies
JO - Open Mathematics
PY - 2010
VL - 8
IS - 3
SP - 602
EP - 615
AB - We present an axiomatic characterization of entropies with properties of branching, continuity, and weighted additivity. We deliberately do not assume that the entropies are symmetric. The resulting entropies are generalizations of the entropies of degree α, including the Shannon entropy as the case α = 1. Such “weighted” entropies have potential applications to the “utility of gambling” problem.
LA - eng
KW - Entropy; Weighted additivity; System of functional equations; Utility of gambling; Weighted utility; Branching; weighted additivity; entropy; system of functional equations; utility of gambling; weighted utility; branching; Shannon entropy
UR - http://eudml.org/doc/269619
ER -

References

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  13. [13] Ng C.T., Measures of information with the branching property over a graph and their representations, Inform. and Control, 1979, 41, 214–231 http://dx.doi.org/10.1016/S0019-9958(79)90571-0 Zbl0423.94006
  14. [14] Ng C.T., Luce R.D., Marley A.A.J., Utility of gambling when events are valued: An application of inset entropy, Theory and Decision, 2009, 67, 23–63 http://dx.doi.org/10.1007/s11238-007-9065-z Zbl1168.91336
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