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Central limit theorems under special relativity

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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