IDEAS home Printed from https://ideas.repec.org/a/spr/nathaz/v87y2017i1d10.1007_s11069-017-2750-5.html
   My bibliography  Save this article

Gutenberg–Richter b-value determination and large-magnitudes sampling

Author

Listed:
  • F. A. Nava

    (CICESE)

  • V. H. Márquez-Ramírez

    (UNAM)

  • F. R. Zúñiga

    (UNAM)

  • C. Lomnitz

    (Ciudad Universitaria)

Abstract

Aki’s maximum likelihood method of Gutenberg–Richter b-value estimation is based on the premise that magnitudes above a given threshold are distributed exponentially and presupposes that sampling is adequate for all these magnitudes; clearly, sampling will not be adequate for magnitudes having average recurrence times longer than the observation time. Thus, for any given sample, there is a higher-magnitude completeness threshold. The importance of considering this higher-magnitude threshold is discussed, the effect of incomplete large-magnitude sampling is evaluated, and a method is given for correcting the observations.

Suggested Citation

  • F. A. Nava & V. H. Márquez-Ramírez & F. R. Zúñiga & C. Lomnitz, 2017. "Gutenberg–Richter b-value determination and large-magnitudes sampling," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 87(1), pages 1-11, May.
  • Handle: RePEc:spr:nathaz:v:87:y:2017:i:1:d:10.1007_s11069-017-2750-5
    DOI: 10.1007/s11069-017-2750-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11069-017-2750-5
    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/s11069-017-2750-5?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. Didier SORNETTE, 2009. "Dragon-Kings, Black Swans and the Prediction of Crises," Swiss Finance Institute Research Paper Series 09-36, Swiss Finance Institute.
    2. Danijel Schorlemmer & Stefan Wiemer & Max Wyss, 2005. "Variations in earthquake-size distribution across different stress regimes," Nature, Nature, vol. 437(7058), pages 539-542, September.
    3. D. Sornette, "undated". "Dragon-Kings, Black Swans and the Prediction of Crises," Working Papers CCSS-09-005, ETH Zurich, Chair of Systems Design.
    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. Darrell Jiajie Tay & Chung-I Chou & Sai-Ping Li & Shang You Tee & Siew Ann Cheong, 2016. "Bubbles Are Departures from Equilibrium Housing Markets: Evidence from Singapore and Taiwan," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-13, November.
    2. Wosnitza, Jan Henrik & Leker, Jens, 2014. "Can log-periodic power law structures arise from random fluctuations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 228-250.
    3. Wouter Vermeer & Otto Koppius & Peter Vervest, 2018. "The Radiation-Transmission-Reception (RTR) model of propagation: Implications for the effectiveness of network interventions," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-21, December.
    4. V. Filimonov & G. Demos & D. Sornette, 2017. "Modified profile likelihood inference and interval forecast of the burst of financial bubbles," Quantitative Finance, Taylor & Francis Journals, vol. 17(8), pages 1167-1186, August.
    5. A. Sienkiewicz & T. Gubiec & R. Kutner & Z. R. Struzik, 2013. "Dynamic structural and topological phase transitions on the Warsaw Stock Exchange: A phenomenological approach," Papers 1301.6506, arXiv.org.
    6. J. Lorenz & S. Battiston & F. Schweitzer, 2009. "Systemic risk in a unifying framework for cascading processes on networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 71(4), pages 441-460, October.
    7. Domino, Krzysztof, 2020. "Multivariate cumulants in outlier detection for financial data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    8. Rebecca Westphal & Didier Sornette, 2019. "Market Impact and Performance of Arbitrageurs of Financial Bubbles in An Agent-Based Model," Swiss Finance Institute Research Paper Series 19-29, Swiss Finance Institute.
    9. Kozłowska, M. & Denys, M. & Wiliński, M. & Link, G. & Gubiec, T. & Werner, T.R. & Kutner, R. & Struzik, Z.R., 2016. "Dynamic bifurcations on financial markets," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 126-142.
    10. Rodríguez-Martínez, C.M. & Coronel-Brizio, H.F. & Hernández-Montoya, A.R., 2021. "A multi-scale symmetry analysis of uninterrupted trends returns in daily financial indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    11. Daniel Traian Pele & Miruna Mazurencu-Marinescu & Peter Nijkamp, 2013. "Herding Behaviour, Bubbles and Log Periodic Power Laws in Illiquid Stock Markets. A Case Study on the Bucharest Stock Exchange," Tinbergen Institute Discussion Papers 13-109/VIII, Tinbergen Institute.
    12. Heinrich, Torsten, 2016. "The Narrow and the Broad Approach to Evolutionary Modeling in Economics," MPRA Paper 75797, University Library of Munich, Germany.
    13. Sonntag, Dominik, 2018. "Die Theorie der fairen geometrischen Rendite [The Theory of Fair Geometric Returns]," MPRA Paper 87082, University Library of Munich, Germany.
    14. Glette-Iversen, Ingrid & Aven, Terje, 2021. "On the meaning of and relationship between dragon-kings, black swans and related concepts," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    15. Vladimir Filimonov & Didier Sornette, 2014. "Power law scaling and "Dragon-Kings" in distributions of intraday financial drawdowns," Papers 1407.5037, arXiv.org, revised Apr 2015.
    16. Raphael Douady & Antoine Kornprobst, 2018. "An Empirical Approach To Financial Crisis Indicators Based On Random Matrices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(03), pages 1-22, May.
    17. Haas, Armin & Onischka, Mathias & Fucik, Markus, 2013. "Black swans, dragon kings, and Bayesian risk management," Economics Discussion Papers 2013-11, Kiel Institute for the World Economy (IfW Kiel).
    18. Molina-Muñoz, Jesús & Mora-Valencia, Andrés & Perote, Javier, 2020. "Market-crash forecasting based on the dynamics of the alpha-stable distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    19. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    20. Colman, E.R. & Rodgers, G.J., 2014. "Local rewiring rules for evolving complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 80-89.

    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:nathaz:v:87:y:2017:i:1:d:10.1007_s11069-017-2750-5. 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.