IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i22p4311-d976174.html
   My bibliography  Save this article

Fisher-like Metrics Associated with ϕ -Deformed (Naudts) Entropies

Author

Listed:
  • Cristina-Liliana Pripoae

    (Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana 6, RO-010374 Bucharest, Romania)

  • Iulia-Elena Hirica

    (Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania)

  • Gabriel-Teodor Pripoae

    (Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania)

  • Vasile Preda

    (Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania
    “Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics of Romanian Academy, 2. Calea 13 Septembrie, nr.13, Sect. 5, RO-050711 Bucharest, Romania
    “Costin C. Kiritescu” National Institute of Economic Research of Romanian Academy, 3. Calea 13 Septembrie, nr.13, Sect. 5, RO-050711 Bucharest, Romania)

Abstract

The paper defines and studies new semi-Riemannian generalized Fisher metrics and Fisher-like metrics, associated with entropies and divergences. Examples of seven such families are provided, based on exponential PDFs. The particular case when the basic entropy is a ϕ -deformed one, in the sense of Naudts, is investigated in detail, with emphasis on the variation of the emergent scalar curvatures. Moreover, the paper highlights the impact on these geometries determined by the addition of some group logarithms.

Suggested Citation

  • Cristina-Liliana Pripoae & Iulia-Elena Hirica & Gabriel-Teodor Pripoae & Vasile Preda, 2022. "Fisher-like Metrics Associated with ϕ -Deformed (Naudts) Entropies," Mathematics, MDPI, vol. 10(22), pages 1-26, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4311-:d:976174
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/22/4311/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/22/4311/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Iulia-Elena Hirica & Cristina-Liliana Pripoae & Gabriel-Teodor Pripoae & Vasile Preda, 2022. "Lie Symmetries of the Nonlinear Fokker-Planck Equation Based on Weighted Kaniadakis Entropy," Mathematics, MDPI, vol. 10(15), pages 1-22, August.
    2. Naudts, Jan, 2002. "Deformed exponentials and logarithms in generalized thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 323-334.
    3. T. Wada & A. M. Scarfone, 2009. "Asymptotic solutions of a nonlinear diffusive equation in the framework of κ-generalized statistical mechanics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 70(1), pages 65-71, July.
    4. Irene Wei Kiong Ting & Imen Tebourbi & Wen-Min Lu & Qian Long Kweh, 2021. "The effects of managerial ability on firm performance and the mediating role of capital structure: evidence from Taiwan," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-23, December.
    5. Gomez, Ignacio S. & Portesi, Mariela & Borges, Ernesto P., 2020. "Universality classes for the Fisher metric derived from relative group entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    6. Răzvan-Cornel Sfetcu & Sorina-Cezarina Sfetcu & Vasile Preda, 2021. "Ordering Awad–Varma Entropy and Applications to Some Stochastic Models," Mathematics, MDPI, vol. 9(3), pages 1-15, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Răzvan-Cornel Sfetcu & Vasile Preda, 2024. "Order Properties Concerning Tsallis Residual Entropy," Mathematics, MDPI, vol. 12(3), pages 1-16, January.
    2. Kalimeri, M. & Papadimitriou, C. & Balasis, G. & Eftaxias, K., 2008. "Dynamical complexity detection in pre-seismic emissions using nonadditive Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1161-1172.
    3. Vigelis, Rui F. & de Andrade, Luiza H.F. & Cavalcante, Charles C., 2020. "Conditions for the existence of a generalization of Rényi divergence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    4. Lucia, Umberto, 2010. "Maximum entropy generation and κ-exponential model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4558-4563.
    5. Amari, Shun-ichi & Ohara, Atsumi & Matsuzoe, Hiroshi, 2012. "Geometry of deformed exponential families: Invariant, dually-flat and conformal geometries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(18), pages 4308-4319.
    6. Rodrigues, Ana Flávia P. & Cavalcante, Charles C. & Crisóstomo, Vicente L., 2019. "A projection pricing model for non-Gaussian financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    7. Charlie Tatenda Mukaro & Abraham Deka & Sylvester Rukani, 2023. "The influence of intellectual capital on organizational performance," Future Business Journal, Springer, vol. 9(1), pages 1-14, December.
    8. Naudts, Jan, 2004. "Generalized thermostatistics and mean-field theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 279-300.
    9. Răzvan-Cornel Sfetcu & Vasile Preda, 2023. "Fractal Divergences of Generalized Jacobi Polynomials," Mathematics, MDPI, vol. 11(16), pages 1-12, August.
    10. Lenzi, E.K. & Ribeiro, M.A. & Fuziki, M.E.K. & Lenzi, M.K. & Ribeiro, H.V., 2018. "Nonlinear diffusion equation with reaction terms: Analytical and numerical results," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 254-265.
    11. Iulia-Elena Hirica & Cristina-Liliana Pripoae & Gabriel-Teodor Pripoae & Vasile Preda, 2022. "Lie Symmetries of the Nonlinear Fokker-Planck Equation Based on Weighted Kaniadakis Entropy," Mathematics, MDPI, vol. 10(15), pages 1-22, August.
    12. Naudts, Jan, 2004. "Generalized thermostatistics based on deformed exponential and logarithmic functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 32-40.
    13. 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.
    14. Suyari, Hiroki, 2006. "Mathematical structures derived from the q-multinomial coefficient in Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 63-82.
    15. Amblard, Pierre-Olivier & Vignat, Christophe, 2006. "A note on bounded entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 50-56.
    16. Sadeen Ghafoor & Weidong Huo & Man Wang & Yunjiang Geng & Muhammad Zulfiqar & Muhammad Usman Yousaf, 2024. "Unique types and innovation input of family firm CEOs: moderating role of managerial ability in Chinese listed firms," Palgrave Communications, Palgrave Macmillan, vol. 11(1), pages 1-14, December.
    17. Rosa, Wanderson & Weberszpil, José, 2018. "Dual conformable derivative: Definition, simple properties and perspectives for applications," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 137-141.
    18. Chiara Barchielli & Anne Marie Rafferty & Milena Vainieri, 2022. "Integrating Key Nursing Measures into a Comprehensive Healthcare Performance Management System: A Tuscan Experience," IJERPH, MDPI, vol. 19(3), pages 1-14, January.
    19. Dagmar Markechová, 2018. "Tsallis Entropy of Fuzzy Dynamical Systems," Mathematics, MDPI, vol. 6(11), pages 1-19, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4311-:d:976174. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.