IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v74y2015icp3-14.html
   My bibliography  Save this article

A pentatonic classification of extreme events

Author

Listed:
  • Eliazar, Iddo
  • Cohen, Morrel H.

Abstract

In this paper we present a classification of the extreme events – very small and very large outcomes – of positive-valued random variables. The classification distinguishes five different categories of randomness, ranging from the very ‘mild’ to the very ‘wild’. In analogy with the common five-tone musical scale we term the classification ‘pentatonic’. The classification is based on the analysis of the inherent Gibbsian ‘forces’ and ‘temperatures’ existing on the logarithmic scale of the random variables under consideration, and provides a statistical-physics insight regarding the nature of these random variables. The practical application of the pentatonic classification is remarkably straightforward, it can be performed by non-experts, and it is demonstrated via an array of examples.

Suggested Citation

  • Eliazar, Iddo & Cohen, Morrel H., 2015. "A pentatonic classification of extreme events," Chaos, Solitons & Fractals, Elsevier, vol. 74(C), pages 3-14.
    • Handle: RePEc:eee:chsofr:v:74:y:2015:i:c:p:3-14
    DOI: 10.1016/j.chaos.2014.07.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007791400126X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2014.07.010?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. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook9401, December.
    2. Alfarano, Simone & Milakovic, Mishael, 2008. "Does classical competition explain the statistical features of firm growth?," Economics Letters, Elsevier, vol. 101(3), pages 272-274, December.
    3. repec:cup:cbooks:9781107013445 is not listed on IDEAS
    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. Makoto Maejima & Gennady Samorodnitsky, 1999. "Certain Probabilistic Aspects of Semistable Laws," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(3), pages 449-462, September.
    2. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
    3. Foad Shokrollahi & Marcin Marcin Magdziarz, 2020. "Equity warrant pricing under subdiffusive fractional Brownian motion of the short rate," Papers 2007.12228, arXiv.org, revised Nov 2020.
    4. Furrer, Hansjorg & Michna, Zbigniew & Weron, Aleksander, 1997. "Stable Lévy motion approximation in collective risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 20(2), pages 97-114, September.
    5. Scharfenaker, Ellis, 2020. "Implications of quantal response statistical equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 119(C).
    6. Michna, Zbigniew, 2008. "Asymptotic behavior of the supremum tail probability for anomalous diffusions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 413-417.
    7. Nolan, John P., 1998. "Parameterizations and modes of stable distributions," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 187-195, June.
    8. Stoyan Stoyanov & Borjana Racheva-Iotova & Svetlozar Rachev & Frank Fabozzi, 2010. "Stochastic models for risk estimation in volatile markets: a survey," Annals of Operations Research, Springer, vol. 176(1), pages 293-309, April.
    9. Eliazar, Iddo, 2017. "Inequality spectra," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 824-847.
    10. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    11. Marcin Magdziarz & Janusz Gajda, 2012. "Anomalous dynamics of Black–Scholes model time-changed by inverse subordinators," HSC Research Reports HSC/12/04, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    12. Weron, Karina & Kotulski, Marcin, 1996. "On the Cole-Cole relaxation function and related Mittag-Leffler distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 232(1), pages 180-188.
    13. Katarzyna Sznajd-Weron & Rafal Weron, 1997. "Evolution in a changing environment," HSC Research Reports HSC/97/01, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    14. John C. Frain, 2007. "Small sample power of tests of normality when the alternative is an alpha-stable distribution," Trinity Economics Papers tep0207, Trinity College Dublin, Department of Economics.
    15. Haruna Okamura & Toshihiro Uemura, 2021. "On Symmetric Stable-Type Processes with Degenerate/Singular Lévy Densities," Journal of Theoretical Probability, Springer, vol. 34(2), pages 809-826, June.
    16. Magdziarz, Marcin, 2009. "Stochastic representation of subdiffusion processes with time-dependent drift," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3238-3252, October.
    17. Mercik, Szymon & Weron, Rafal, 1999. "Scaling in currency exchange: a conditionally exponential decay approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 267(1), pages 239-250.
    18. B. Dybiec, 2009. "Epidemics with short and long-range interactions: role of vector dispersal patterns," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 72(4), pages 685-693, December.
    19. Eliazar, Iddo, 2018. "Universal Poisson-process limits for general random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1160-1174.
    20. Lv, Longjin & Xiao, Jianbin & Fan, Liangzhong & Ren, Fuyao, 2016. "Correlated continuous time random walk and option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 100-107.

    More about this item

    Statistics

    Access and download statistics

    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:74:y:2015:i:c:p:3-14. 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.