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Entropy 2015, 17(3), 1103-1122; doi:10.3390/e17031103

Weakest-Link Scaling and Extreme Events in Finite-Sized Systems

1
School of Mineral Resources Engineering, Technical University of Crete, Chania 73100, Greece
2
Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24,10129 Torino, Italy
*
Author to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Received: 21 January 2015 / Revised: 27 February 2015 / Accepted: 3 March 2015 / Published: 9 March 2015
(This article belongs to the Special Issue Entropic Aspects in Statistical Physics of Complex Systems)
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Abstract

Weakest-link scaling is used in the reliability analysis of complex systems. It is characterized by the extensivity of the hazard function instead of the entropy. The Weibull distribution is the archetypical example of weakest-link scaling, and it describes variables such as the fracture strength of brittle materials, maximal annual rainfall, wind speed and earthquake return times. We investigate two new distributions that exhibit weakest-link scaling, i.e., a Weibull generalization known as the κ-Weibull and a modified gamma probability function that we propose herein. We show that in contrast with the Weibull and the modified gamma, the hazard function of the κ -Weibull is non-extensive, which is a signature of inter-dependence between the links. We also investigate the impact of heterogeneous links, modeled by means of a stochastic Weibull scale parameter, on the observed probability distribution. View Full-Text
Keywords: Weibull; gamma distribution; return intervals; superstatistics; fracture strength; stretched exponential; reliability modeling Weibull; gamma distribution; return intervals; superstatistics; fracture strength; stretched exponential; reliability modeling
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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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MDPI and ACS Style

Hristopulos, D.T.; Petrakis, M.P.; Kaniadakis, G. Weakest-Link Scaling and Extreme Events in Finite-Sized Systems. Entropy 2015, 17, 1103-1122.

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