Some Information Measures Properties of the GOS-Concomitants from the FGM Family

Suter, Florentina; Cernat, Ioana Dănilă; Drăgan, Mihai

doi:10.3390/e24101361

Cited by 5 publications

(3 citation statements)

References 45 publications

(60 reference statements)

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“…Developments may include solving the analogue of Equations ( 15), (18), and (20), for other remarkable families of entropies (Renyi, Sharma-Taneja-Mittal, Naudts, etc). New examples are needed, in addition to the PDF solutions of normal type ( [71][72][73][74]).…”

Section: Discussionmentioning

confidence: 99%

Holonomic and Non-Holonomic Geometric Models Associated to the Gibbs–Helmholtz Equation

Pripoae,

Hirica,

Pripoae

et al. 2023

Mathematics

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By replacing the internal energy with the free energy, as coordinates in a “space of observables”, we slightly modify (the known three) non-holonomic geometrizations from Udriste’s et al. work. The coefficients of the curvature tensor field, of the Ricci tensor field, and of the scalar curvature function still remain rational functions. In addition, we define and study a new holonomic Riemannian geometric model associated, in a canonical way, to the Gibbs–Helmholtz equation from Classical Thermodynamics. Using a specific coordinate system, we define a parameterized hypersurface in R4 as the “graph” of the entropy function. The main geometric invariants of this hypersurface are determined and some of their properties are derived. Using this geometrization, we characterize the equivalence between the Gibbs–Helmholtz entropy and the Boltzmann–Gibbs–Shannon, Tsallis, and Kaniadakis entropies, respectively, by means of three stochastic integral equations. We prove that some specific (infinite) families of normal probability distributions are solutions for these equations. This particular case offers a glimpse of the more general “equivalence problem” between classical entropy and statistical entropy.

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Section: Discussionmentioning

confidence: 99%

Holonomic and Non-Holonomic Geometric Models Associated to the Gibbs–Helmholtz Equation

Pripoae,

Hirica,

Pripoae

et al. 2023

Mathematics

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“…There are several papers in which the authors compare random variables from the point of view of residual entropies: for Shannon residual entropy, see [30][31][32]; for Rényi residual entropy, see [33,34]; for Varma residual entropy, see [35]; and for Awad-Varma residual entropy, see [36]. Other orders between random variables can be found in [37][38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Order Properties Concerning Tsallis Residual Entropy

Sfetcu,

Preda

2024

Mathematics

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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.

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“…The authors also propose a bias correction either by adding a bootstrap-based correction or by adding the number of parameters in the candidate model. In [ 20 ], the authors extend, and compute information measures related to Shannon and Tsallis entropies, for the concomitants of the generalized order statistics from the Farlie–Gumbel–Morgenstern family. In [ 21 ], the evaluation of academic performance by using the statistical K-means (SKM) algorithm to produce clusters is investigated.…”

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confidence: 99%