A new look at q-exponential distributions via excess statistics

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 superstatistic...

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Bibliographic Details
Published in:Physica A 2008-09, Vol.387 (22), p.5422-5432
Main Authors: Bercher, J.-F., Vignat, C.
Format: Article
Language:English
Subjects:
[formula omitted]-exponentials
Computation and Language
Computer Science
Excess distributions
Generalized Pareto Distributions
Maximum entropy principle
Nonextensive statistics
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Summary: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.
ISSN:0378-4371
1873-2119
0378-4371
DOI:10.1016/j.physa.2008.05.038