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The Maximal Extension of the Strict Concavity Region on the Parameter Space for Sharma-Mittal Entropy Measures: II

In: Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics

Author

Listed:
  • R. P. Mondaini

    (Federal University of Rio de Janeiro, COPPE, Centre of Technology)

  • S. C. de Albuquerque Neto

    (Federal University of Rio de Janeiro, COPPE, Centre of Technology)

Abstract

The two-dimensional (s, r)-parameter space ⊂ℝ++ of Sharma-Mittal class of entropy measures has as its region of strict concavity the epigraph of the curve r = s. This is the region corresponding to the Havrda-Charvat entropy measure. In the present contribution, we rigorously show that we can extend this region by deriving a family of epigraph regions based on the negative definiteness criterion of the quadratic form associated with the Hessian matrix of the Sharma-Mittal entropies. A maximally extended region is obtained as the greatest lower bound of these families of epigraph regions. These results motivate the further consideration of fully synergetic entropy measure distributions, which is the fundamental aim of this research line.

Suggested Citation

  • R. P. Mondaini & S. C. de Albuquerque Neto, 2023. "The Maximal Extension of the Strict Concavity Region on the Parameter Space for Sharma-Mittal Entropy Measures: II," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics, pages 181-196, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-33050-6_11
    DOI: 10.1007/978-3-031-33050-6_11
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