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

R. P. Mondaini () and S. C. de Albuquerque Neto
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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

A chapter in Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics, 2023, pp 181-196 from Springer

Abstract: 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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-33050-6_11

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DOI: 10.1007/978-3-031-33050-6_11

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