IDEAS home Printed from https://ideas.repec.org/a/spr/indpam/v51y2020i4d10.1007_s13226-020-0503-8.html
   My bibliography  Save this article

On Cumulative Tsallis Entropy and Its Dynamic Past Version

Author

Listed:
  • Mohamed Said Mohamed

    (Ain Shams University)

Abstract

Cumulative Tsallis entropy and its residual have developed by many others, and they proposed alternative (second) forms of them. In this article, we illustrate the differences and the relation between the proposed model and its alternative form. Furthermore, we study some properties and features for the concept of cumulative Tsallis entropy and its residual. In addition, we propose a dynamic past form of cumulative Tsallis entropy and obtain some of its properties.

Suggested Citation

  • Mohamed Said Mohamed, 2020. "On Cumulative Tsallis Entropy and Its Dynamic Past Version," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1903-1917, December.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:4:d:10.1007_s13226-020-0503-8
    DOI: 10.1007/s13226-020-0503-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13226-020-0503-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13226-020-0503-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Calì, Camilla & Longobardi, Maria & Ahmadi, Jafar, 2017. "Some properties of cumulative Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 1012-1021.
    2. J. Navarro & Y. Aguila & J. Ruiz, 2001. "Characterizations through reliability measures from weighted distributions," Statistical Papers, Springer, vol. 42(3), pages 395-402, July.
    3. Vikas Kumar, 2017. "Characterization results based on dynamic Tsallis cumulative residual entropy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(17), pages 8343-8354, September.
    4. V. Zardasht & S. Parsi & M. Mousazadeh, 2015. "On empirical cumulative residual entropy and a goodness-of-fit test for exponentiality," Statistical Papers, Springer, vol. 56(3), pages 677-688, August.
    5. G. Rajesh & S. M. Sunoj, 2019. "Some properties of cumulative Tsallis entropy of order $$\alpha $$ α," Statistical Papers, Springer, vol. 60(3), pages 933-943, June.
    6. Madan Mohan Sati & Nitin Gupta, 2015. "Some Characterization Results on Dynamic Cumulative Residual Tsallis Entropy," Journal of Probability and Statistics, Hindawi, vol. 2015, pages 1-8, October.
    7. Murali Rao, 2005. "More on a New Concept of Entropy and Information," Journal of Theoretical Probability, Springer, vol. 18(4), pages 967-981, October.
    Full references (including those not matched with items on IDEAS)

    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. Jafar Ahmadi, 2021. "Characterization of continuous symmetric distributions using information measures of records," Statistical Papers, Springer, vol. 62(6), pages 2603-2626, December.
    2. Mohamed S. Mohamed & Haroon M. Barakat & Salem A. Alyami & Mohamed A. Abd Elgawad, 2022. "Cumulative Residual Tsallis Entropy-Based Test of Uniformity and Some New Findings," Mathematics, MDPI, vol. 10(5), pages 1-14, February.
    3. G. Rajesh & S. M. Sunoj, 2019. "Some properties of cumulative Tsallis entropy of order $$\alpha $$ α," Statistical Papers, Springer, vol. 60(3), pages 933-943, June.
    4. Balakrishnan, Narayanaswamy & Buono, Francesco & Longobardi, Maria, 2022. "A unified formulation of entropy and its application," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    5. Răzvan-Cornel Sfetcu & Vasile Preda, 2024. "Order Properties Concerning Tsallis Residual Entropy," Mathematics, MDPI, vol. 12(3), pages 1-16, January.
    6. Aswathy S. Krishnan & S. M. Sunoj & P. G. Sankaran, 2019. "Quantile-based reliability aspects of cumulative Tsallis entropy in past lifetime," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 17-38, January.
    7. P. Sankaran & S. Sunoj, 2004. "Identification of models using failure rate and mean residual life of doubly truncated random variables," Statistical Papers, Springer, vol. 45(1), pages 97-109, January.
    8. Klein, Ingo, 2017. "(Generalized) maximum cumulative direct, paired, and residual Φ entropy principle," FAU Discussion Papers in Economics 25/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    9. Asok K. Nanda & Shovan Chowdhury, 2021. "Shannon's Entropy and Its Generalisations Towards Statistical Inference in Last Seven Decades," International Statistical Review, International Statistical Institute, vol. 89(1), pages 167-185, April.
    10. 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.
    11. Mohamed Kayid & Mansour Shrahili, 2023. "Characterization Results on Lifetime Distributions by Scaled Reliability Measures Using Completeness Property in Functional Analysis," Mathematics, MDPI, vol. 11(6), pages 1-15, March.
    12. Marius Giuclea & Costin-Ciprian Popescu, 2022. "On Geometric Mean and Cumulative Residual Entropy for Two Random Variables with Lindley Type Distribution," Mathematics, MDPI, vol. 10(9), pages 1-10, April.
    13. Ahmadi, J. & Fashandi, M., 2019. "Characterization of symmetric distributions based on some information measures properties of order statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 141-152.
    14. Narayanaswamy Balakrishnan & Francesco Buono & Maria Longobardi, 2022. "On Cumulative Entropies in Terms of Moments of Order Statistics," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 345-359, March.
    15. Georgios Psarrakos & Antonio Di Crescenzo, 2018. "A residual inaccuracy measure based on the relevation transform," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(1), pages 37-59, January.
    16. Mao, Xuegeng & Shang, Pengjian & Wang, Jianing & Yin, Yi, 2020. "Fractional cumulative residual Kullback-Leibler information based on Tsallis entropy," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    17. Tahmasebi, S. & Longobardi, M. & Kazemi, M.R. & Alizadeh, M., 2020. "Cumulative Tsallis entropy for maximum ranked set sampling with unequal samples," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    18. Benchong Li & Liya Fu, 2018. "Exact test of goodness of fit for binomial distribution," Statistical Papers, Springer, vol. 59(3), pages 851-860, September.
    19. J. S. Allison & L. Santana & N. Smit & I. J. H. Visagie, 2017. "An ‘apples to apples’ comparison of various tests for exponentiality," Computational Statistics, Springer, vol. 32(4), pages 1241-1283, December.
    20. Nair Rohini S. & Abdul Sathar E. I., 2019. "Bivariate Dynamic Weighted Survival Entropy of Order 𝛼," Stochastics and Quality Control, De Gruyter, vol. 34(2), pages 67-85, December.

    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:spr:indpam:v:51:y:2020:i:4:d:10.1007_s13226-020-0503-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.