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Entropy 2014, 16(10), 5523-5536; doi:10.3390/e16105523

Extreme Value Laws for Superstatistics

School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK
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Received: 11 September 2014 / Revised: 15 October 2014 / Accepted: 15 October 2014 / Published: 20 October 2014
(This article belongs to the Collection Advances in Applied Statistical Mechanics)
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Abstract

We study the extreme value distribution of stochastic processes modeled by superstatistics. Classical extreme value theory asserts that (under mild asymptotic independence assumptions) only three possible limit distributions are possible, namely: Gumbel, Fréchet and Weibull distribution. On the other hand, superstatistics contains three important universality classes, namely χ2-superstatistics, inverse χ2 -superstatistics, and lognormal superstatistics, all maximizing different effective entropy measures. We investigate how the three classes of extreme value theory are related to the three classes of superstatistics. We show that for any superstatistical process whose local equilibrium distribution does not live on a finite support, the Weibull distribution cannot occur. Under the above mild asymptotic independence assumptions, we also show that χ2-superstatistics generally leads an extreme value statistics described by a Fréchet distribution, whereas inverse χ2 -superstatistics, as well as lognormal superstatistics, lead to an extreme value statistics associated with the Gumbel distribution. View Full-Text
Keywords: extreme value statistics; superstatistics; limit laws extreme value statistics; superstatistics; limit laws
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Rabassa, P.; Beck, C. Extreme Value Laws for Superstatistics. Entropy 2014, 16, 5523-5536.

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