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Central Limit Theorems under additive deformations

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  • Eck, Daniel J.
  • McKeague, Ian W.

Abstract

Additive deformations of statistical systems arise in various areas of physics. Classical central limit theory is then no longer applicable, even when standard independence assumptions are preserved. This paper investigates ways in which deformed algebraic operations lead to distinctive central limit theory. We establish some general central limit results that are applicable to a range of examples arising in nonextensive statistical mechanics, including the addition of momenta and velocities via Kaniadakis addition, and Tsallis addition. We also investigate extensions to random additive deformations, and find evidence (based on simulation studies) for a universal limit specific to each statistical system.

Suggested Citation

  • Eck, Daniel J. & McKeague, Ian W., 2016. "Central Limit Theorems under additive deformations," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 156-162.
    • Handle: RePEc:eee:stapro:v:118:y:2016:i:c:p:156-162
    DOI: 10.1016/j.spl.2016.06.010
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    References listed on IDEAS

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    1. Potirakis, S.M. & Minadakis, G. & Eftaxias, K., 2012. "Analysis of electromagnetic pre-seismic emissions using Fisher information and Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 300-306.
    2. Kaniadakis, G., 2006. "Towards a relativistic statistical theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 17-23.
    3. Singh, Vijay P. & Cui, Huijuan, 2015. "Modeling sediment concentration in debris flow by Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 49-58.
    4. McKeague, Ian W., 2015. "Central limit theorems under special relativity," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 149-155.
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    Cited by:

    1. Timothy C. Irwin, 2020. "Accrual Accounting and the Government's Intertemporal Budget Constraint," Public Budgeting & Finance, Wiley Blackwell, vol. 40(4), pages 128-141, December.

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