IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v167y2023ics096007792201236x.html
   My bibliography  Save this article

Normal distribution based on maximum Deng entropy

Author

Listed:
  • Li, Siran
  • Xiao, Fuyuan

Abstract

We define the distribution of uncertainty based on Deng entropy and proved that the limiting form of the distribution is the normal distribution by the characteristic function. We conduct some discussion on the distribution, and we further analyze the error of its normal approximation and give the conditions that should be satisfied for the requirement of given error. Finally, we reveal the relationship between the distribution and the binomial distribution and the advantages of taking it as a prior distribution in evidence theory.

Suggested Citation

  • Li, Siran & Xiao, Fuyuan, 2023. "Normal distribution based on maximum Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:chsofr:v:167:y:2023:i:c:s096007792201236x
    DOI: 10.1016/j.chaos.2022.113057
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792201236X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.113057?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. Cui, Huizi & Zhou, Lingge & Li, Yan & Kang, Bingyi, 2022. "Belief entropy-of-entropy and its application in the cardiac interbeat interval time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Chenhui Qiang & Yong Deng & Kang Hao Cheong, 2022. "Information Fractal Dimension Of Mass Function," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(06), pages 1-12, September.
    3. Wang, Hongping & Fang, Yi-Ping & Zio, Enrico, 2022. "Resilience-oriented optimal post-disruption reconfiguration for coupled traffic-power systems," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    4. Ni, Lei & Chen, Yu-wang & de Brujin, Oscar, 2021. "Towards understanding socially influenced vaccination decision making: An integrated model of multiple criteria belief modelling and social network analysis," European Journal of Operational Research, Elsevier, vol. 293(1), pages 276-289.
    5. Xingyuan Chen & Yong Deng, 2022. "An Evidential Software Risk Evaluation Model," Mathematics, MDPI, vol. 10(13), pages 1-19, July.
    6. Balakrishnan, Narayanaswamy & Buono, Francesco & Longobardi, Maria, 2022. "On Tsallis extropy with an application to pattern recognition," Statistics & Probability Letters, Elsevier, vol. 180(C).
    7. Lei, Mingli, 2022. "Information dimension based on Deng entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    8. Beynon, Malcolm & Curry, Bruce & Morgan, Peter, 2000. "The Dempster-Shafer theory of evidence: an alternative approach to multicriteria decision modelling," Omega, Elsevier, vol. 28(1), pages 37-50, February.
    9. 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).
    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. Zhao, Tong & Li, Zhen & Deng, Yong, 2024. "Linearity in Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

    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. Yu, Zihan & Deng, Yong, 2022. "Derive power law distribution with maximum Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Lei, Mingli, 2022. "Information dimension based on Deng entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    3. Zeng, Ziyue & Xiao, Fuyuan, 2023. "A new complex belief entropy of χ2 divergence with its application in cardiac interbeat interval time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    4. Zhao, Tong & Li, Zhen & Deng, Yong, 2024. "Linearity in Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    5. Xingyuan Chen & Yong Deng, 2022. "An Evidential Software Risk Evaluation Model," Mathematics, MDPI, vol. 10(13), pages 1-19, July.
    6. Zhao, Tong & Li, Zhen & Deng, Yong, 2023. "Information fractal dimension of Random Permutation Set," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    7. Ortiz-Vilchis, Pilar & Lei, Mingli & Ramirez-Arellano, Aldo, 2024. "Reformulation of Deng information dimension of complex networks based on a sigmoid asymptote," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    8. Tang, Daogui & Fang, Yi-Ping & Zio, Enrico, 2023. "Vulnerability analysis of demand-response with renewable energy integration in smart grids to cyber attacks and online detection methods," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    9. Zhou, Qianli & Deng, Yong, 2023. "Generating Sierpinski gasket from matrix calculus in Dempster–Shafer theory," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    10. Wang, Ying-Ming & Yang, Jian-Bo & Xu, Dong-Ling & Chin, Kwai-Sang, 2006. "The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees," European Journal of Operational Research, Elsevier, vol. 175(1), pages 35-66, November.
    11. Sonal, & Ghosh, Debomita, 2022. "Impact of situational awareness attributes for resilience assessment of active distribution networks using hybrid dynamic Bayesian multi criteria decision-making approach," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    12. Kangas, Annika S. & Kangas, Jyrki, 2004. "Probability, possibility and evidence: approaches to consider risk and uncertainty in forestry decision analysis," Forest Policy and Economics, Elsevier, vol. 6(2), pages 169-188, March.
    13. Yan, Lisen & Peng, Jun & Gao, Dianzhu & Wu, Yue & Liu, Yongjie & Li, Heng & Liu, Weirong & Huang, Zhiwu, 2022. "A hybrid method with cascaded structure for early-stage remaining useful life prediction of lithium-ion battery," Energy, Elsevier, vol. 243(C).
    14. Fescioglu-Unver, Nilgun & Yıldız Aktaş, Melike, 2023. "Electric vehicle charging service operations: A review of machine learning applications for infrastructure planning, control, pricing and routing," Renewable and Sustainable Energy Reviews, Elsevier, vol. 188(C).
    15. Yang, J.B. & Wang, Y.M. & Xu, D.L. & Chin, K.S., 2006. "The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties," European Journal of Operational Research, Elsevier, vol. 171(1), pages 309-343, May.
    16. Justin Moskolaï Ngossaha & Raymond Houé Ngouna & Bernard Archimède & Mihaela-Hermina Negulescu & Alexandru-Ionut Petrişor, 2024. "Toward Sustainable Urban Mobility: A Multidimensional Ontology-Based Framework for Assessment and Consensus Decision-Making Using DS-AHP," Sustainability, MDPI, vol. 16(11), pages 1-22, May.
    17. Emanuele Salerno, 2020. "Identifying Value-Increasing Actions for Cultural Heritage Assets through Sensitivity Analysis of Multicriteria Evaluation Results," Sustainability, MDPI, vol. 12(21), pages 1-13, November.
    18. S. Nodoust & A. Mirzazadeh & G.-W. Weber, 2020. "An evidential reasoning approach for production modeling with deteriorating and ameliorating items," Operational Research, Springer, vol. 20(1), pages 1-19, March.
    19. Zhang, Yifan & Shu, Gang & Li, Ya, 2017. "Strategy-updating depending on local environment enhances cooperation in prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 224-232.
    20. Hao, Yucheng & Jia, Limin & Zio, Enrico & Wang, Yanhui & He, Zhichao, 2024. "A network-based approach to improving robustness of a high-speed train by structure adjustment," Reliability Engineering and System Safety, Elsevier, vol. 243(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:eee:chsofr:v:167:y:2023:i:c:s096007792201236x. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.