IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v177y2023ics0960077923011736.html
   My bibliography  Save this article

Belief Fisher–Shannon information plane: Properties, extensions, and applications to time series analysis

Author

Listed:
  • Contreras-Reyes, Javier E.
  • Kharazmi, Omid

Abstract

This paper introduce the belief Fisher–Shannon (BFS) information plane based on basic probability assignment concept. Moreover, upper and lower bounds of BFS information are also presented. In addition, BFS information plane is extended to belief Fisher–Rényi and fractional belief Fisher–Shannon ones, whose are based on Generalized Rényi and fractional Deng entropies, respectively. This study is exemplified by a simulation study of Logistic, Chebyshev, and Hénon chaotic map time series; and two applications related to fish condition factor and ozone pollutant time series. Time series were discretized using Freedman–Diaconis rule as a histogram estimator. Results indicate that proposed information planes based on histogram estimator provides a more efficient method with respect to parametric and non-parametric methods, such as one based on kernel density function. Therefore, our findings suggest that proposed information planes could be an appropriate tool to better investigate the complex dynamics of these signals.

Suggested Citation

  • Contreras-Reyes, Javier E. & Kharazmi, Omid, 2023. "Belief Fisher–Shannon information plane: Properties, extensions, and applications to time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011736
    DOI: 10.1016/j.chaos.2023.114271
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923011736
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.114271?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. Kharazmi, Omid & Contreras-Reyes, Javier E., 2023. "Deng–Fisher information measure and its extensions: Application to Conway’s Game of Life," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Telesca, Luciano & Lovallo, Michele & Hsu, Han-Lun & Chen, Chien-Chih, 2011. "Analysis of dynamics in magnetotelluric data by using the Fisher–Shannon method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(7), pages 1350-1355.
    3. Wang, Xingyuan & Du, Xiaohui, 2022. "Pixel-level and bit-level image encryption method based on Logistic-Chebyshev dynamic coupled map lattices," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Contreras-Reyes, Javier E., 2015. "Rényi entropy and complexity measure for skew-gaussian distributions and related families," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 84-91.
    5. Reinaldo B. Arellano-Valle & Javier E. Contreras-Reyes & Marc G. Genton, 2013. "Shannon Entropy and Mutual Information for Multivariate Skew-Elliptical Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 42-62, March.
    6. Spichak, David & Aragoneses, Andrés, 2022. "Exploiting the impact of ordering patterns in the Fisher-Shannon complexity plane," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    7. Ran Yu & Yong Deng, 2023. "A generalization of Rényi entropy for basic probability assignment," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(19), pages 6991-7008, October.
    8. Spichak, David & Kupetsky, Audrey & Aragoneses, Andrés, 2021. "Characterizing complexity of non-invertible chaotic maps in the Shannon–Fisher information plane with ordinal patterns," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    9. Contreras-Reyes, Javier E., 2022. "Rényi entropy and divergence for VARFIMA processes based on characteristic and impulse response functions," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    10. Suchandan Kayal & N. Balakrishnan, 2023. "Weighted fractional generalized cumulative past entropy and its properties," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-23, June.
    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. Zhao, Tong & Li, Zhen & Deng, Yong, 2024. "Linearity in Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Zhao, Tong & Li, Zhen & Deng, Yong, 2023. "Information fractal dimension of Random Permutation Set," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Salah H. Abid & Uday J. Quaez & Javier E. Contreras-Reyes, 2021. "An Information-Theoretic Approach for Multivariate Skew- t Distributions and Applications," Mathematics, MDPI, vol. 9(2), pages 1-13, January.
    4. Christian Caamaño-Carrillo & Javier E. Contreras-Reyes, 2022. "A Generalization of the Bivariate Gamma Distribution Based on Generalized Hypergeometric Functions," Mathematics, MDPI, vol. 10(9), pages 1-17, May.
    5. Stosic, Tatijana & Telesca, Luciano & Stosic, Borko, 2021. "Multiparametric statistical and dynamical analysis of angular high-frequency wind speed time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    6. Telesca, Luciano & Lovallo, Michele & Chamoli, Ashutosh & Dimri, V.P. & Srivastava, K., 2013. "Fisher–Shannon analysis of seismograms of tsunamigenic and non-tsunamigenic earthquakes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(16), pages 3424-3429.
    7. Contreras-Reyes, Javier E., 2021. "Lerch distribution based on maximum nonsymmetric entropy principle: Application to Conway’s game of life cellular automaton," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    8. Riquelme, Marco & Bolfarine, Heleno & Galea, Manuel, 2015. "Robust linear functional mixed models," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 82-98.
    9. Telesca, Luciano & Lovallo, Michele & Mohamed, Abuo El-Ela Amin & ElGabry, Mohamed & El-hady, Sherif & Elenean, Kamal M. Abou & ElBary, Rafaat ElShafey Fat, 2012. "Informational analysis of seismic sequences by applying the Fisher Information Measure and the Shannon entropy: An application to the 2004–2010 seismicity of Aswan area (Egypt)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(9), pages 2889-2897.
    10. Moreno-Torres, Lucia Rebeca & Gomez-Vieyra, Armando & Lovallo, Michele & Ramírez-Rojas, Alejandro & Telesca, Luciano, 2018. "Investigating the interaction between rough surfaces by using the Fisher–Shannon method: Implications on interaction between tectonic plates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 560-565.
    11. Minadakis, G. & Potirakis, S.M. & Stonham, J. & Nomicos, C. & Eftaxias, K., 2012. "The role of propagating stress waves on a geophysical scale: Evidence in terms of nonextensivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5648-5657.
    12. Liu, Xilin & Tong, Xiaojun & Zhang, Miao & Wang, Zhu, 2023. "A highly secure image encryption algorithm based on conservative hyperchaotic system and dynamic biogenetic gene algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    13. Tuli, Rohan & Soneji, Hitesh Narayan & Churi, Prathamesh, 2022. "PixAdapt: A novel approach to adaptive image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    14. Rasheed, T. & Butt, S.I. & Pečarić, Đ. & Pečarić, J., 2022. "Generalized cyclic Jensen and information inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    15. Guignard, Fabian & Lovallo, Michele & Laib, Mohamed & Golay, Jean & Kanevski, Mikhail & Helbig, Nora & Telesca, Luciano, 2019. "Investigating the time dynamics of wind speed in complex terrains by using the Fisher–Shannon method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 611-621.
    16. Javier E. Contreras-Reyes & Mohsen Maleki & Daniel Devia Cortés, 2019. "Skew-Reflected-Gompertz Information Quantifiers with Application to Sea Surface Temperature Records," Mathematics, MDPI, vol. 7(5), pages 1-14, May.
    17. Kharazmi, Omid & Contreras-Reyes, Javier E., 2023. "Deng–Fisher information measure and its extensions: Application to Conway’s Game of Life," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    18. 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).
    19. Mêgnigbêto, Eustache, 2014. "Efficiency, unused capacity and transmission power as indicators of the Triple Helix of university–industry–government relationships," Journal of Informetrics, Elsevier, vol. 8(1), pages 284-294.
    20. Telesca, Luciano & Lovallo, Michele & Alcaz, Vasile & Ilies, Ion, 2015. "Site-dependent organization structure of seismic microtremors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 541-547.

    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:177:y:2023:i:c:s0960077923011736. 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.