IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v578y2021ics037843712100399x.html
   My bibliography  Save this article

The q-exponentials do not maximize the Rényi entropy

Author

Listed:
  • Oikonomou, Thomas
  • Kaloudis, Konstantinos
  • Bagci, G. Baris

Abstract

It is generally assumed that the Rényi entropy is maximized by the q-exponentials and is hence useful to construct a generalized statistical mechanics. However, to the best of our knowledge, this assumption has never been explicitly checked. In this work, we consider the Rényi entropy with the linear and escort mean value constraints and check whether it is indeed maximized by q-exponentials. We show, both theoretically and numerically, that the Rényi entropy yields erroneous inferences concerning the optimum distributions of the q-exponential form and moreover exhibits high estimation errors in the regime of long range correlations. Finally, we note that the Shannon entropy successfully detects the power law distributions when the logarithmic mean value constraint is used.

Suggested Citation

  • Oikonomou, Thomas & Kaloudis, Konstantinos & Bagci, G. Baris, 2021. "The q-exponentials do not maximize the Rényi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    • Handle: RePEc:eee:phsmap:v:578:y:2021:i:c:s037843712100399x
    DOI: 10.1016/j.physa.2021.126126
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843712100399X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2021.126126?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. Stanley, H.E. & Buldyrev, S.V. & Goldberger, A.L. & Goldberger, Z.D. & Havlin, S. & Mantegna, R.N. & Ossadnik, S.M. & Peng, C.-K. & Simons, M., 1994. "Statistical mechanics in biology: how ubiquitous are long-range correlations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 205(1), pages 214-253.
    2. Abe, Sumiyoshi & Suzuki, Norikazu, 2005. "Scale-free statistics of time interval between successive earthquakes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 588-596.
    3. Th. Oikonomou & A. Provata, 2006. "Non-extensive trends in the size distribution of coding and non-coding DNA sequences in the human genome," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 259-264, March.
    4. Barry C. Arnold, 2008. "Pareto and Generalized Pareto Distributions," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 7, pages 119-145, Springer.
    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. Karakatsanis, L.P. & Pavlos, G.P. & Iliopoulos, A.C. & Pavlos, E.G. & Clark, P.M. & Duke, J.L. & Monos, D.S., 2018. "Assessing information content and interactive relationships of subgenomic DNA sequences of the MHC using complexity theory approaches based on the non-extensive statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 77-93.
    2. Silva, R. & Silva, J.R.P. & Anselmo, D.H.A.L. & Alcaniz, J.S. & da Silva, W.J.C. & Costa, M.O., 2020. "An alternative description of power law correlations in DNA sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    3. Yuanyuan Zhang & Saralees Nadarajah, 2017. "Flexible Heavy Tailed Distributions for Big Data," Annals of Data Science, Springer, vol. 4(3), pages 421-432, September.
    4. Foellmi, Reto & Martínez, Isabel Z., 2014. "Volatile Top Income Shares in Switzerland? Reassessing the Evolution Between 1981 and 2009," CEPR Discussion Papers 10006, C.E.P.R. Discussion Papers.
    5. 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).
    6. Vladimir Hlasny & Paolo Verme, 2022. "The Impact of Top Incomes Biases on the Measurement of Inequality in the United States," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(4), pages 749-788, August.
    7. Majda Benzidia & Michel Lubrano, 2016. "A Bayesian Look at American Academic Wages: The Case of Michigan State University," AMSE Working Papers 1628, Aix-Marseille School of Economics, France.
    8. Vladimir Hlasny, 2021. "Parametric representation of the top of income distributions: Options, historical evidence, and model selection," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1217-1256, September.
    9. Alvarez-Ramirez, Jose & Espinosa-Paredes, Gilberto & Vazquez, Alejandro, 2005. "Detrended fluctuation analysis of the neutronic power from a nuclear reactor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 227-240.
    10. Wang, Yuanjun & You, Shibing, 2016. "An alternative method for modeling the size distribution of top wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 443-453.
    11. Antonopoulos, Chris G. & Michas, George & Vallianatos, Filippos & Bountis, Tassos, 2014. "Evidence of q-exponential statistics in Greek seismicity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 71-77.
    12. Liu, Guoliang, 2017. "A new physical model for earthquake time interval distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 62-65.
    13. Omer L. Gebizlioglu & Serap Yörübulut, 2016. "A Pseudo-Pareto Distribution and Concomitants of Its Order Statistics," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1043-1064, December.
    14. Nadav Ben Zeev & Tomer Ifergane, 2022. "Firing Restrictions and Economic Resilience: Protect and Survive?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 43, pages 93-124, January.
    15. Razdan, Ashok, 2013. "Networks in extensive air showers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 982-986.
    16. Rotundo, Giulia, 2014. "Black–Scholes–Schrödinger–Zipf–Mandelbrot model framework for improving a study of the coauthor core score," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 296-301.
    17. Chiarucci, Riccardo & Ruzzenenti, Franco & Loffredo, Maria I., 2014. "Detecting spatial homogeneity in the World Trade Web with Detrended Fluctuation Analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 1-7.
    18. da Silva, Sérgio Luiz E.F., 2021. "κ-generalised Gutenberg–Richter law and the self-similarity of earthquakes," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    19. Enora Belz, 2019. "Estimating Inequality Measures from Quantile Data," Economics Working Paper Archive (University of Rennes & University of Caen) 2019-09, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    20. Luigi-Ionut Catana & Vasile Preda, 2022. "A New Stochastic Order of Multivariate Distributions: Application in the Study of Reliability of Bridges Affected by Earthquakes," Mathematics, MDPI, vol. 11(1), pages 1-14, 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:eee:phsmap:v:578:y:2021:i:c:s037843712100399x. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.