An alternate measure of the cumulative residual Sharma-Taneja-Mittal entropy

Sfetcu, Răzvan-Cornel; Robe-Voinea, Elena-Graţiela; Şerban, Florentin

doi:10.2478/auom-2025-0022

Abstract

We define a new alternate measure of the cumulative residual Sharma-Taneja-Mittal entropy. For this measure, there are given upper and lower bounds, is introduced a consistent test based on the uniform distribution and some concrete numerical examples are formulated.

References

S. Abe, A note on the q-deformation-theoretic aspect of the generalized entropies in nonextensive physics, Physics Letters A 224 (1997), 326–330.
Search in Google Scholar Back to article
S. Abe, N. Suzuki, Itineration of the Internet over nonequilibrium stationary states in Tsallis statistics, Physical Review E 67 (2003), 016106.
Search in Google Scholar Back to article
S. Abe, N. Suzuki, Law for the distance between successive earthquakes, J. Geophys. Res. 108 (2003), 2113.
Search in Google Scholar Back to article
V.S. Barbu, A. Karagrigoriou, V. Preda, Entropy, divergence rates and weighted divergence rates for Markov chains. I: The alpha-gamma and beta- gamma case, Proc. Rom. Acad. Ser. A Math. Phys. Tech. Sci. Inf. Sci. 18 (2017), 293–301.
Search in Google Scholar Back to article
V.S. Barbu, A. Karagrigoriou, V. Preda, Entropy and divergence rates for Markov chains. II: The weighted case, Proc. Rom. Acad. Ser. A Math. Phys. Tech. Sci. Inf. Sci. 19 (2018), 3–10.
Search in Google Scholar Back to article
V.S. Barbu, A. Karagrigoriou, V. Preda, Entropy and divergence rates for Markov chains. III: The Cressie and Read case and applications, Proc. Rom. Acad. Ser. A Math. Phys. Tech. Sci. Inf. Sci. 19 (2018), 413–421.
Search in Google Scholar Back to article
C. Beck, E.G.D. Cohen, Superstatistics, Physica A 322 (2003), 267–275.
Search in Google Scholar Back to article
V. Crupi, J.D. Nelson, B. Meder, G. Cevolani, K. Tentori, Generalized information theory meets human cognition: Introducing a unified framework to model uncertainty and information search, Cognitive Science, 42 (2018), 1410–1456.
Search in Google Scholar Back to article
A.H. Darooneh, C. Dadashinia, Analysis of the spatial and temporal distributions between successive earthquakes: Nonextensive statistical mechanics viewpoint, 387 (2008), 3647–3654.
Search in Google Scholar Back to article
T.D. Frank, A. Daffertshofer, Exact time-dependent solutions of the Rényi Fokker-Planck equation and the Fokker-Planck equations related to the entropies proposed by Sharma and Mittal, Physica A, 285 (2000), 351–366.
Search in Google Scholar Back to article
S. Ghaffari, A.H. Ziaie, H. Moradpour, F. Asghariyan, F. Feleppa, M. Tavayef, Black hole thermodynamics in Sharma-Mittal generalized entropy formalism, General Relativity and Gravitation, 51 (2019), 93.
Search in Google Scholar Back to article
T. Hasumi, Hypocenter interval statistics between successive earthquakes in the twodimensional Burridge-Knopo model, Physica A 388 (2009), 477–482.
Search in Google Scholar Back to article
E. Haven, The Blackwell and Dubins theorem and Rényi’s amount of information measure: Some applications, Acta Appl. Math. 109 (2010), 743–757.
Search in Google Scholar Back to article
I.-E. Hirică, C.-L. Pripoae, G.-T. Pripoae, V. Preda, Lie symmetries of the nonlinear Fokker-Planck equation based on weighted Kaniadakis entropy, Mathematics 10 (2022), 2776.
Search in Google Scholar Back to article
G.T. Howard, A generalization of the Glivenko-Cantelli theorem, Ann. Math. Stat. 30 (1959), 828–830.
Search in Google Scholar Back to article
I. Iatan, M. Dragan, S. Dedu, V. Preda, Using probabilistic models for data compression, Mathematics 10 (2022), 3847.
Search in Google Scholar Back to article
Z.Q. Jiang, W. Chen, W.X. Zhou, Scaling in the distribution of intertrade durations of Chinese stocks, Physica A 387 (2008), 5818–5825.
Search in Google Scholar Back to article
T. Kaizoji, An interacting-agent model of financial markets from the viewpoint of nonextensive statistical mechanics, Physica A 370 (2006), 109–113.
Search in Google Scholar Back to article
G. Kaniadakis, Non-linear kinetics underlying generalized statistics, Physica A 296 (2001), 405–425.
Search in Google Scholar Back to article
G. Kaniadakis, M. Lissia, A.M. Scarfone, Deformed logarithms and entropies Physica A 340 (2004), 41–49.
Search in Google Scholar Back to article
S. Koltcov, V. Ignatenko, O. Koltsova, Estimating topic modeling performance with Sharma-Mittal entropy, Entropy 21 (2019), 660.
Search in Google Scholar Back to article
Y. Li, Q. Ding, Fusion entropy and its spatial post-multiscale version: Methodology and application, Chaos, Solitons & Fractals 186 (2024), 115345.
Search in Google Scholar Back to article
J. Lima, R.Jr. Silva, J. Santos, Plasma oscillations and nonextensive statistics, Phys. Rev. E 61 (2000), 3260.
Search in Google Scholar Back to article
D.P. Mittal, On some functional equations concerning entropy, directed divergence and inaccuracy, Metrika 22 (1975), 35–46.
Search in Google Scholar Back to article
M.S. Mohamed, H.M. Barakat, S.A. Alyami, M.A. Abd Elgawad, Fractional entropy-based test of uniformity with power comparisons, J. Math. 2021 (2021), 5331260.
Search in Google Scholar Back to article
M.S. Mohamed, H.M. Barakat, S.A. Alyami, M.A. Abd Elgawad, Cumulative residual Tsallis entropy-based test of uniformity and some new findings, Mathematics 10 (2022), 771.
Search in Google Scholar Back to article
H.A. Noughabi, Cumulative residual entropy applied to testing uniformity, Commun. Stat. Theory Methods 50 (2020), 1811339.
Search in Google Scholar Back to article
N. Oikonomou, A. Provata, U. Tirnakli, Nonextensive statistical approach to non-coding human DNA, Physica A 387 (2008), 2653–2659.
Search in Google Scholar Back to article
J. Paul, P.Y. Thomas, Sharma-Mittal entropy properties on record values, Statistica, 76 (2016), 273–287.
Search in Google Scholar Back to article
V. Preda, S. Dedu, I. Iatan, I. Dănilă Cernat, M. Sheraz, Tsallis entropy for loss models and survival models involving truncated and censored random variables, Entropy 24 (2022), 1654.
Search in Google Scholar Back to article
V. Preda, S. Dedu, M. Sheraz, New measure selection for Hunt-Devolder semi-Markov regime switching interest rate models, Physica A 407 (2014), 350–359.
Search in Google Scholar Back to article
C.-L. Pripoae, I.-E. Hirică, G.-T. Pripoae, V. Preda, Lie symmetries of the nonlinear Fokker-Planck equation based on weighted Tsallis entropy, Carpathian J. Math. 38 (2022), 597–617.
Search in Google Scholar Back to article
G. Rajesh, S.M. Sunoj, Some properties of cumulative Tsallis entropy of order α, Stat. Pap. 60 (2019), 933–943.
Search in Google Scholar Back to article
M. Rao, Y. Chen, B.C. Vemuri, F. Wang, Cumulative residual entropy: A new measure of information, IEEE Trans. Inf. Theory 50 (2004), 1220–1228.
Search in Google Scholar Back to article
A.E. Rastegin, Bounds of the Pinsker and Fannes types on the Tsallis relative entropy, Math. Phys. Anal. Geom. 16 (2013), 213–228.
Search in Google Scholar Back to article
I. Raşa, Convexity properties of some entropies, Result. Math. 73 (2018), 105.
Search in Google Scholar Back to article
I. Raşa, Convexity properties of some entropies. II, Result. Math. 74 (2019), 154.
Search in Google Scholar Back to article
J. Sadeghi, M. Rostami, M.R. Alipour, Investigation of phase transition of BTZ black hole with Sharma-Mittal entropy approaches, International Journal of Modern Physics A, 34 (2019), 1950182.
Search in Google Scholar Back to article
M.M. Sati, N. Gupta, Some characterization results on dynamic cumulative residual Tsallis entropy, J. Probab. Stat. 2015 (2015), 694203.
Search in Google Scholar Back to article
A. Sayahian Jahromi, S.A. Moosavi, H. Moradpour, J.P. Morais Graça, I.P. Lobo, I.G. Salako, A. Jawad, Generalized entropy formalism and a new holographic dark energy model, Physics Letters B, 780 (2018), 21–24.
Search in Google Scholar Back to article
A.M. Scarfone, T. Wada, Thermodynamic equilibrium and its stability for microcanonical systems described by the Sharma-Taneja-Mittal entropy, Phys. Rev. E 72 (2005), 026123.
Search in Google Scholar Back to article
R.-C. Sfetcu, S.-C. Sfetcu, V. Preda, Ordering Awad-Varma entropy and applications to some stochastic models, Mathematics 9 (2021), 280.
Search in Google Scholar Back to article
R.-C. Sfetcu, S.-C. Sfetcu, V. Preda, On Tsallis and Kaniadakis divergences, Math. Phys. Anal. Geom. 25 (2022), 7.
Search in Google Scholar Back to article
R.-C. Sfetcu, S.-C. Sfetcu, V. Preda, Some properties of weighted Tsallis and Kaniadakis divergences, Entropy 24 (2022), 1616.
Search in Google Scholar Back to article
R.-C. Sfetcu, S.-C. Sfetcu, V. Preda, Some generalizations concerning inaccuracy measures, Result. Math. 78 (2023), 195.
Search in Google Scholar Back to article
S.-C. Sfetcu, Varma quantile entropy order, Analele Ştiinţifice Univ. Ovidius Constanţa 29 (2021), 249–264.
Search in Google Scholar Back to article
C. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27 (1948), 379–423.
Search in Google Scholar Back to article
B.D. Sharma, I.J. Taneja, Entropy of type (α, β) and other generalized measures in information theory, Metrika 22 (1975), 205–216.
Search in Google Scholar Back to article
T. Simon, G. Dulac, On cumulative Tsallis entropies, Acta Appl. Math. 188 (2023), 9.
Search in Google Scholar Back to article
A.D. Soares, N.J.Jr. Moura, M.B. Ribeiro, Tsallis statistics in the income distribution of Brazil, Chaos, Solitons & Fractals 88 (2016), 158–171.
Search in Google Scholar Back to article
F. Suter, I. Cernat, M. Dragan, Some information measures properties of the GOS-concomitants from the FGM family, Entropy 24 (2022), 1361.
Search in Google Scholar Back to article
A. Toma, Model selection criteria using divergences, Entropy 16 (2014), 2686–2698.
Search in Google Scholar Back to article
A. Toma, A. Karagrigoriou, P. Trentou, Robust model selection criteria based on pseudodistances, Entropy 22 (2020), 304.
Search in Google Scholar Back to article
G. Toscani, Rényi entropies and nonlinear diffusion equations, Acta Appl. Math. 132 (2014), 595–604.
Search in Google Scholar Back to article
B. Trivellato, The minimal k-entropy martingale measure, Int. J. Theor. Appl. Financ. 15 (2012), 1250038.
Search in Google Scholar Back to article
B. Trivellato, Deformed exponentials and applications to finance, Entropy 15 (2013), 3471–3489.
Search in Google Scholar Back to article
C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys. 52 (1988), 479–487.
Search in Google Scholar Back to article
G.A. Tsekouras, C. Tsallis, Generalized entropy arising from a distribution of q indices, Phys. Rev. E 71 (2005), 046144.
Search in Google Scholar Back to article
X. Wang, Y. Li, Q. Qiao, A. Tavares, Y. Liang, Water quality prediction based on machine learning and comprehensive weighting methods, Entropy 25 (2023), 1186.
Search in Google Scholar Back to article
F. Wang, B.C. Vemuri, Non-rigid multi-model image registration using cross-cumulative residual entropy, Int. J. Comp. Vision 74 (2007), 201–215.
Search in Google Scholar Back to article
M. Xu, P. Shang, S. Zhang, Multiscale Rényi cumulative residual distribution entropy: reliability analysis of financial time series, Chaos, Solitons & Fractals 143 (2021), 110410.
Search in Google Scholar Back to article
H. Yoshioka, Y. Yoshioka, Generalized divergences for statistical evaluation of uncertainty in long-memory processes, Chaos, Solitons & Fractals 182 (2024), 114627.
Search in Google Scholar Back to article
M. Younas, A. Jawad, S. Qummer, H. Moradpour, S. Rani, Cosmological implications of the generalized entropy based holographic dark energy models in dynamical Chern-Simons modified gravity, Advances in High Energy Physics, 2019 (2019), 1287932.
Search in Google Scholar Back to article
T. Zhan, J. Zhou, Z. Li, Y. Deng, Generalized information entropy and generalized information dimension, Chaos, Solitons & Fractals 184 (2024), 114976.
Search in Google Scholar Back to article

An alternate measure of the cumulative residual Sharma-Taneja-Mittal entropy

Abstract

Paradigm

My account