IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v99y2015icp149-155.html
   My bibliography  Save this article

Central limit theorems under special relativity

Author

Listed:
  • McKeague, Ian W.

Abstract

Several relativistic extensions of the Maxwell–Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.

Suggested Citation

  • McKeague, Ian W., 2015. "Central limit theorems under special relativity," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 149-155.
    • Handle: RePEc:eee:stapro:v:99:y:2015:i:c:p:149-155
    DOI: 10.1016/j.spl.2014.12.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715215000061
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2014.12.028?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. M. C. Jones & Arthur Pewsey, 2009. "Sinh-arcsinh distributions," Biometrika, Biometrika Trust, vol. 96(4), pages 761-780.
    2. Kaniadakis, G., 2006. "Towards a relativistic statistical theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 17-23.
    3. G. Kaniadakis, 2009. "Maximum entropy principle and power-law tailed distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 70(1), pages 3-13, July.
    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. Eck, Daniel J. & McKeague, Ian W., 2016. "Central Limit Theorems under additive deformations," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 156-162.
    2. Arthur Pewsey, 2018. "Parametric bootstrap edf-based goodness-of-fit testing for sinh–arcsinh distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 147-172, March.

    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. Kaiwei Liu & Xingcheng Wang & Zhihui Qu, 2019. "Train Operation Strategy Optimization Based on a Double-Population Genetic Particle Swarm Optimization Algorithm," Energies, MDPI, vol. 12(13), pages 1-26, June.
    2. Christophe Ley, 2014. "Flexible Modelling in Statistics: Past, present and Future," Working Papers ECARES ECARES 2014-42, ULB -- Universite Libre de Bruxelles.
    3. da Silva, Sérgio Luiz Eduardo Ferreira, 2021. "Newton’s cooling law in generalised statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    4. Magne Mogstad & Joseph P Romano & Azeem M Shaikh & Daniel Wilhelm, 2024. "Inference for Ranks with Applications to Mobility across Neighbourhoods and Academic Achievement across Countries," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(1), pages 476-518.
    5. de Lima, M.M.F. & Costa, M.O. & Silva, R. & Fulco, U.L. & Oliveira, J.I.N. & Vasconcelos, M.S. & Anselmo, D.H.A.L., 2024. "Viral proteins length distributions: A comparative analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    6. Daniel Hadley & Harry Joe & Natalia Nolde, 2021. "On the Selection of Loss Severity Distributions to Model Operational Risk," Papers 2107.03979, arXiv.org.
    7. J. Hambuckers & C. Heuchenne, 2017. "A robust statistical approach to select adequate error distributions for financial returns," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(1), pages 137-161, January.
    8. Sladana Babic & Laetitia Gelbgras & Marc Hallin & Christophe Ley, 2019. "Optimal tests for elliptical symmetry: specified and unspecified location," Working Papers ECARES 2019-26, ULB -- Universite Libre de Bruxelles.
    9. Lee, Sharon X. & McLachlan, Geoffrey J., 2022. "An overview of skew distributions in model-based clustering," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    10. Francisco J. Rubio & Yili Hong, 2016. "Survival and lifetime data analysis with a flexible class of distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(10), pages 1794-1813, August.
    11. Mondal, Sagnik & Genton, Marc G., 2024. "A multivariate skew-normal-Tukey-h distribution," Journal of Multivariate Analysis, Elsevier, vol. 200(C).
    12. Yuanhua Feng & Wolfgang Karl Härdle, 2021. "Uni- and multivariate extensions of the sinh-arcsinh normal distribution applied to distributional regression," Working Papers CIE 142, Paderborn University, CIE Center for International Economics.
    13. Ley, Christophe & Paindaveine, Davy, 2010. "Multivariate skewing mechanisms: A unified perspective based on the transformation approach," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1685-1694, December.
    14. Christopher Partlett & Prakash Patil, 2017. "Measuring asymmetry and testing symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 429-460, April.
    15. Fabio CLEMENTI & Mauro GALLEGATI, 2017. "NEW ECONOMIC WINDOWS ON INCOME AND WEALTH: THE k-GENERALIZED FAMILY OF DISTRIBUTIONS," Journal of Social and Economic Statistics, Bucharest University of Economic Studies, vol. 6(1), pages 1-15, JULY.
    16. Djennad, Abdelmajid & Rigby, Robert & Stasinopoulos, Dimitrios & Voudouris, Vlasios & Eilers, Paul, 2015. "Beyond location and dispersion models: The Generalized Structural Time Series Model with Applications," MPRA Paper 62807, University Library of Munich, Germany.
    17. Stella, Massimo & Brede, Markus, 2014. "A κ-deformed model of growing complex networks with fitness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 360-368.
    18. Tsai, Arthur C. & Liou, Michelle & Simak, Maria & Cheng, Philip E., 2017. "On hyperbolic transformations to normality," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 250-266.
    19. Qin, Xianan & Song, Congwei, 2021. "Towards understanding the non-Gaussian pore size distributions of nonwoven fabrics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    20. Manuel Ammann & Alexander Feser, 2019. "Robust Estimation of Risk-Neutral Moments," Working Papers on Finance 1902, University of St. Gallen, School of Finance.

    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:stapro:v:99:y:2015:i:c:p:149-155. 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.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.