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Rènyi entropies and Fisher informations as measures of nonextensivity in a Tsallis setting

Author

Listed:
  • Pennini, F.
  • Plastino, A.R.
  • Plastino, A.

Abstract

We study nonextensive statistical scenarios à la Tsallis with reference to Fisher’s information and Rènyi’s entropy. A new way of evaluating Tsallis’ generalized expectation values is examined within such a context, and is shown to lead to a much better Cramer–Rao bound than the customary procedure. A connection between the information measures of Fisher’s and Rènyi’s is found. We show that Fisher’s measure for translation families remains additive even in a non-extensive Tsallis setting.

Suggested Citation

  • Pennini, F. & Plastino, A.R. & Plastino, A., 1998. "Rènyi entropies and Fisher informations as measures of nonextensivity in a Tsallis setting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 258(3), pages 446-457.
    • Handle: RePEc:eee:phsmap:v:258:y:1998:i:3:p:446-457
    DOI: 10.1016/S0378-4371(98)00272-6
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    Cited by:

    1. Atenas, Boris & Curilef, Sergio, 2021. "A statistical description for the Quasi-Stationary-States of the dipole-type Hamiltonian Mean Field Model based on a family of Vlasov solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    2. Bercher, J.-F., 2013. "Some properties of generalized Fisher information in the context of nonextensive thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(15), pages 3140-3154.
    3. Bercher, J.-F., 2012. "A simple probabilistic construction yielding generalized entropies and divergences, escort distributions and q-Gaussians," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(19), pages 4460-4469.

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