Article ID Journal Published Year Pages File Type
977840 Physica A: Statistical Mechanics and its Applications 2008 11 Pages PDF
Abstract

QQ-exponential distributions play an important role in nonextensive statistics. They appear as the canonical distributions, i.e. the maximum generalized qq-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 qq-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 qq-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 qq-entropy. We also highlight the role of Generalized Pareto Distributions in many applications and present several methods for the practical estimation of qq-exponential parameters.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
Authors
, ,