A new look at q-exponential distributions via excess statistics

J.-F. Bercher and C. Vignat

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 22, 5422-5432

Abstract: Q-exponential distributions play an important role in nonextensive statistics. They appear as the canonical distributions, i.e. the maximum generalized q-entropy distributions under mean constraint. Their relevance is also independently justified by their appearance in the theory of superstatistics introduced by Beck and Cohen. In this paper, we provide a third and independent rationale for these distributions. We indicate that q-exponentials are stable by a statistical normalization operation, and that Pickands’ extreme values theorem plays the role of a CLT-like theorem in this context. This suggests that q-exponentials can arise in many contexts if the system at hand or the measurement device introduces some threshold. Moreover we give an asymptotic connection between excess distributions and maximum q-entropy. We also highlight the role of Generalized Pareto Distributions in many applications and present several methods for the practical estimation of q-exponential parameters.

Keywords: q-exponentials; Generalized Pareto Distributions; Excess distributions; Maximum entropy principle; Nonextensive statistics (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:22:p:5422-5432

DOI: 10.1016/j.physa.2008.05.038

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