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2010 | 8 | 3 | 602-615
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Weighted entropies

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
8
Numer
3
Strony
602-615
Opis fizyczny
Daty
wydano
2010-06-01
online
2010-05-30
Twórcy
autor
Bibliografia
  • [1] Aczél J., personal communication, March 13, 2007
  • [2] de Bruijn N.G., Functions whose differences belong to a given class, Nieuw Arch. Wiskd. (2), 1951, 23, 194–218
  • [3] Ebanks B.R., The branching property in generalized information theory, Adv. in Appl. Probab., 1978, 10, 788–802 http://dx.doi.org/10.2307/1426659
  • [4] Ebanks B.R., Branching and generalized-recursive inset entropies, Proc. Amer. Math. Soc., 1980, 79, 260–267 http://dx.doi.org/10.2307/2043247
  • [5] Ebanks B.R., Functional equations for weighted entropies, Results Math., 2009, 55, 329–357 http://dx.doi.org/10.1007/s00025-009-0435-4
  • [6] Ebanks B.R., Sahoo P.K., Sander W., Characterizations of Information Measures, World Scientific, Singapore/New Jersey/London/Hong Kong, 1998
  • [7] Havrda J., Charvát F., Quantification method of classification processes. Concept of structural α-entropy, Kybernetika (Prague), 1967, 3, 30–35
  • [8] Kemperman J.H.B., A general functional equation, Trans. Amer. Math. Soc., 1957, 86, 28–56 http://dx.doi.org/10.2307/1992864
  • [9] Luce R.D., Marley A.A.J., Ng C.T., Entropy-related measures of the utility of gambling, In: Brams S., Gehrlein W., Roberts F. (Eds.), The Mathematics of Preference, Choice, and Order: Essays in Honor of Peter C. Fishburn, Springer, New York, 2009, 5–25 http://dx.doi.org/10.1007/978-3-540-79128-7_1
  • [10] Luce R.D., Ng C.T., Marley A.A.J., Aczél J., Utility of gambling I: Entropy-modified linear weighted utility, Economic Theory, 2008, 36, 1–33 http://dx.doi.org/10.1007/s00199-007-0260-5
  • [11] Luce R.D., Ng C.T., Marley A.A.J., Aczél J., Utility of gambling II: Risk, paradoxes, and data, Economic Theory, 2008, 36, 165–187 http://dx.doi.org/10.1007/s00199-007-0259-y
  • [12] Marley A.A.J., Luce R.D., Independence properties vis-à-vis several utility representations, Theory and Decision, 2005, 58, 77–143 http://dx.doi.org/10.1007/s11238-005-2460-4
  • [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
  • [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
  • [15] Ng C.T., Luce R.D., Marley A.A.J., Utility of gambling under p-additive joint receipt and segregation or duplex decomposition, J. Math. Psych., 2009, 53, 273–286 http://dx.doi.org/10.1016/j.jmp.2009.04.001
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0026-3
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