Multivariate Generalizations of the q--Central Limit Theorem

2007/03/20 by Sabir Umarov, Constantino Tsallis, Umarov, Sabir +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #Probability and Statistical Research #Statistical Mechanics and Entropy #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/0703533

15 pages

arxiv created 2007/03/20 · arxiv updated 2009/12/01

Abstract

We study multivariate generalizations of the q-central limit theorem, a generalization of the classical central limit theorem consistent with nonextensive statistical mechanics. Two types of generalizations are addressed, more precisely the \it direct and \it sequential q-central limit theorems are proved. Their relevance to the asymptotic scale invariance of some specially correlated systems is studied. A q-analog of the classic weak convergence is introduced and its equivalence to the q-convergence is proved for q>1.

Cited by

• Central limit theorem, deformed exponentials and superstatistics
• On a q-Central Limit Theorem Consistent with Nonextensive Statistical Mechanics

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