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A set of new three-parameter entropies in terms of a generalized incomplete Gamma function

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  • Asgarani, Somayeh

Abstract

In this paper, by considering the first three Khinchin axioms (K1–K3) and neglecting the fourth (K4), a set of new three-parameter entropies will be introduced which are expressed in terms of a generalized incomplete Gamma function as Sd,c1,c2[p]∝∑iΓ(d+1,1−c1lnpi,1−c2lnpi). Also, its asymptotic behavior will be found and it will be shown that, for some special values of parameters, some known entropies like Tsallis, Kaniadakis and Abe entropies are recovered.

Suggested Citation

  • Asgarani, Somayeh, 2013. "A set of new three-parameter entropies in terms of a generalized incomplete Gamma function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 1972-1976.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:9:p:1972-1976
    DOI: 10.1016/j.physa.2012.12.018
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    References listed on IDEAS

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    1. Curado, Evaldo M.F. & Nobre, Fernando D., 2004. "On the stability of analytic entropic forms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 94-106.
    2. Beck, Christian, 2000. "Application of generalized thermostatistics to fully developed turbulence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 277(1), pages 115-123.
    3. G. Kaniadakis, 2009. "Maximum entropy principle and power-law tailed distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 70(1), pages 3-13, July.
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    1. Asgarani, Somayeh & Mirza, Behrouz, 2015. "Two-parameter entropies, Sk,r, and their dualities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 185-192.

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