IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i3p280-d490354.html
   My bibliography  Save this article

Ordering Awad–Varma Entropy and Applications to Some Stochastic Models

Author

Listed:
  • Răzvan-Cornel Sfetcu

    (Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 010014 Bucharest, Romania
    These authors contributed equally to this work.)

  • Sorina-Cezarina Sfetcu

    (Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 010014 Bucharest, Romania
    These authors contributed equally to this work.)

  • 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, 050711 Bucharest, Romania
    “Costin C. Kiriţescu” National Institute of Economic Research, Calea 13 Septembrie, 050711 Bucharest, Romania
    These authors contributed equally to this work.)

Abstract

We consider a generalization of Awad–Shannon entropy, namely Awad–Varma entropy, introduce a stochastic order on Awad–Varma residual entropy and study some properties of this order, like closure, reversed closure and preservation in some stochastic models (the proportional hazard rate model, the proportional reversed hazard rate model, the proportional odds model and the record values model).

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:280-:d:490354
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/3/280/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/3/280/
    Download Restriction: no
    ---><---

    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. Kumar, Vikas & Taneja, H.C., 2011. "Some characterization results on generalized cumulative residual entropy measure," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1072-1077, August.
    3. Malhotra, Gifty & Srivastava, R. & Taneja, H.C., 2019. "Calibration of the risk-neutral density function by maximization of a two-parameter entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 45-54.
    4. Di Crescenzo, Antonio & Longobardi, Maria, 2004. "A measure of discrimination between past lifetime distributions," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 173-182, April.
    5. Preda, Vasile & Dedu, Silvia & Gheorghe, Carmen, 2015. "New classes of Lorenz curves by maximizing Tsallis entropy under mean and Gini equality and inequality constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 925-932.
    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. Sunoj, S.M. & Sankaran, P.G., 2012. "Quantile based entropy function," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1049-1053.
    8. Nader Ebrahimi & S. Kirmani, 1996. "A measure of discrimination between two residual life-time distributions and its applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(2), pages 257-265, June.
    9. Oikonomou, Th. & Provata, A. & Tirnakli, U., 2008. "Nonextensive statistical approach to non-coding human DNA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2653-2659.
    10. Darooneh, Amir H. & Dadashinia, Cyruse, 2008. "Analysis of the spatial and temporal distributions between successive earthquakes: Nonextensive statistical mechanics viewpoint," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3647-3654.
    11. Preda, Vasile & Dedu, Silvia & Sheraz, Muhammad, 2014. "New measure selection for Hunt–Devolder semi-Markov regime switching interest rate models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 350-359.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Răzvan-Cornel Sfetcu & Vasile Preda, 2024. "Order Properties Concerning Tsallis Residual Entropy," Mathematics, MDPI, vol. 12(3), pages 1-16, January.
    2. Cristina-Liliana Pripoae & Iulia-Elena Hirica & Gabriel-Teodor Pripoae & Vasile Preda, 2022. "Fisher-like Metrics Associated with ϕ -Deformed (Naudts) Entropies," Mathematics, MDPI, vol. 10(22), pages 1-26, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. da Silva, Sérgio Luiz Eduardo Ferreira, 2021. "Newton’s cooling law in generalised statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    2. Chanchal Kundu, 2015. "Generalized measures of information for truncated random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(4), pages 415-435, May.
    3. Martins, Francisco Leonardo Bezerra & do Nascimento, José Cláudio, 2022. "Power law dynamics in genealogical graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    4. Abbasnejad, M. & Arghami, N.R. & Morgenthaler, S. & Mohtashami Borzadaran, G.R., 2010. "On the dynamic survival entropy," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1962-1971, December.
    5. Sankaran, P.G. & Sunoj, S.M. & Nair, N. Unnikrishnan, 2016. "Kullback–Leibler divergence: A quantile approach," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 72-79.
    6. Răzvan-Cornel Sfetcu & Vasile Preda, 2023. "Fractal Divergences of Generalized Jacobi Polynomials," Mathematics, MDPI, vol. 11(16), pages 1-12, August.
    7. Gzyl, Henryk & Mayoral, Silvia, 2016. "Determination of zero-coupon and spot rates from treasury data by maximum entropy methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 38-50.
    8. Florentin ŞERBAN & Anca-Teodora ŞERBAN-OPRESCU & George-Laurenţiu ŞERBAN-OPRESCU, 2017. "Appraisal of Scientific Research in European Countries. An Entropy-Based Analysis," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(1), pages 103-116.
    9. Moretto, Enrico & Pasquali, Sara & Trivellato, Barbara, 2016. "Option pricing under deformed Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 246-263.
    10. Sunoj, S.M. & Krishnan, Aswathy S. & Sankaran, P.G., 2018. "A quantile-based study of cumulative residual Tsallis entropy measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 410-421.
    11. Răzvan-Cornel Sfetcu & Vasile Preda, 2024. "Order Properties Concerning Tsallis Residual Entropy," Mathematics, MDPI, vol. 12(3), pages 1-16, January.
    12. Sfetcu, Răzvan-Cornel, 2016. "Tsallis and Rényi divergences of generalized Jacobi polynomials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 131-138.
    13. Asadi, Majid & Ebrahimi, Nader & Soofi, Ehsan S., 2005. "Dynamic generalized information measures," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 85-98, January.
    14. N. Unnikrishnan Nair & S. M. Sunoj & Rajesh G., 2023. "Relation between Relative Hazard Rates and Residual Divergence with some Applications to Reliability Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 784-802, February.
    15. Ren, Fei & Gu, Gao-Feng & Zhou, Wei-Xing, 2009. "Scaling and memory in the return intervals of realized volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(22), pages 4787-4796.
    16. Ferreira, D.S.R. & Ribeiro, J. & Oliveira, P.S.L. & Pimenta, A.R. & Freitas, R.P. & Dutra, R.S. & Papa, A.R.R. & Mendes, J.F.F., 2022. "Spatiotemporal analysis of earthquake occurrence in synthetic and worldwide data," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    17. Nanda, Asok K. & Sankaran, P.G. & Sunoj, S.M., 2014. "Rényi’s residual entropy: A quantile approach," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 114-121.
    18. K. Nair & P. Sankaran & S. Smitha, 2011. "Chernoff distance for truncated distributions," Statistical Papers, Springer, vol. 52(4), pages 893-909, November.
    19. Kumar, Vikas & Rekha,, 2018. "A quantile approach of Tsallis entropy for order statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 916-928.
    20. Martins, Adriel M.F. & Fernandes, Leonardo H.S. & Nascimento, Abraão D.C., 2023. "Scientific progress in information theory quantifiers," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:280-:d:490354. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.