Weighted entropies

• Autorzy: Bruce Ebanks
• 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.

Słowa kluczowe

EN

Entropy; Weighted additivity; System of functional equations; Utility of gambling; Weighted utility; Branching

Kategorie tematyczne

• 94A17: Measures of information, entropy
• 39B22: Equations for real functions
• 91B16: Utility theory
• 39B72: Systems of functional equations and inequalities

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 3
• Strony: 602-615

Daty

wydano

2010-06-01

online

2010-05-30

Twórcy

autor

Bruce Ebanks

• Mississippi State University

Bibliografia

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• [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

Identyfikatory

DOI

10.2478/s11533-010-0026-3