Central Limit Theorems under additive deformations

Daniel J. Eck and Ian W. McKeague

Statistics & Probability Letters, 2016, vol. 118, issue C, 156-162

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 Classical central limit theory is then no longer applicable, even when standard independence assumptions are preserved.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.

Keywords: Probability on Lie groups; Kaniadakis addition; Tsallis entropy (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2016.06.010

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