Central Limit Theorems under additive deformations

Daniel J. Eck; Ian W. McKeague

doi:10.1016/j.spl.2016.06.010

Central Limit Theorems under additive deformations

Daniel J. Eck^*
, Ian W. McKeague

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

1 Citation (Scopus)

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 Classical central limit theory is then no longer applicable, even when standard independence assumptions are preserved.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

Original language	English
Pages (from-to)	156-162
Journal	Statistics and Probability Letters
Volume	118
DOIs	https://doi.org/10.1016/j.spl.2016.06.010
Publication status	Published - 1 Nov 2016
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

Kaniadakis addition
Probability on Lie groups
Tsallis entropy

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10.1016/j.spl.2016.06.010

https://www.sciencedirect.com/science/article/am/pii/S016771521630092X

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title = "Central Limit Theorems under additive deformations",

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 Classical central limit theory is then no longer applicable, even when standard independence assumptions are preserved.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

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AU - Eck, Daniel J.

AU - McKeague, Ian W.

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N2 - 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.

AB - 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.

KW - Kaniadakis addition

KW - Probability on Lie groups

KW - Tsallis entropy

UR - https://www.scopus.com/pages/publications/84978711987

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84978711987&origin=recordpage

U2 - 10.1016/j.spl.2016.06.010

DO - 10.1016/j.spl.2016.06.010

M3 - RGC 21 - Publication in refereed journal

C2 - 27499566

SN - 0167-7152

VL - 118

SP - 156

EP - 162

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

Central Limit Theorems under additive deformations

Abstract

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Research Keywords

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