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Order Properties Concerning Tsallis Residual Entropy

Author

Listed:
  • Răzvan-Cornel Sfetcu

    (Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 010014 Bucharest, Romania)

  • Vasile Preda

    (Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 010014 Bucharest, Romania
    “Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics, Calea 13 Septembrie 13, 050711 Bucharest, Romania
    “Costin C. Kiriţescu” National Institute of Economic Research, Calea 13 Septembrie 13, 050711 Bucharest, Romania)

Abstract

With the help of Tsallis residual entropy, we introduce Tsallis quantile entropy order between two random variables. We give necessary and sufficient conditions, study closure and reversed closure properties under parallel and series operations and show that this order is preserved in the proportional hazard rate model, proportional reversed hazard rate model, proportional odds model and record values model.

Suggested Citation

  • Răzvan-Cornel Sfetcu & Vasile Preda, 2024. "Order Properties Concerning Tsallis Residual Entropy," Mathematics, MDPI, vol. 12(3), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:417-:d:1327746
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    References listed on IDEAS

    as
    1. Soares, Abner D. & Moura Jr., Newton J. & Ribeiro, Marcelo B., 2016. "Tsallis statistics in the income distribution of Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 158-171.
    2. Kaizoji, Taisei, 2006. "An interacting-agent model of financial markets from the viewpoint of nonextensive statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 109-113.
    3. 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.
    4. Vikas Kumar, 2017. "Characterization results based on dynamic Tsallis cumulative residual entropy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(17), pages 8343-8354, September.
    5. Athanasios Sachlas & Takis Papaioannou, 2014. "Residual and Past Entropy in Actuarial Science and Survival Models," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 79-99, March.
    6. Jiang, Zhi-Qiang & Chen, Wei & Zhou, Wei-Xing, 2008. "Scaling in the distribution of intertrade durations of Chinese stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5818-5825.
    7. 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.
    8. G. Rajesh & S. M. Sunoj, 2019. "Some properties of cumulative Tsallis entropy of order $$\alpha $$ α," Statistical Papers, Springer, vol. 60(3), pages 933-943, June.
    Full references (including those not matched with items on IDEAS)

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