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Extremum statistics: a framework for data analysis
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Chapman, Sandra C., Rowlands, G. (George) and Watkins, Nicholas W.. (2002) Extremum statistics: a framework for data analysis. Nonlinear Processes in Geophysics, Vol.9 . pp. 409418. ISSN 10235809

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Official URL: http://www.nonlinprocessesgeophys.net/9/409/2002...
Abstract
Recent work has suggested that in highly correlated
systems, such as sandpiles, turbulent fluids, ignited
trees in forest fires and magnetization in a ferromagnet close to a critical point, the probability distribution of a global quantity (i.e. total energy dissipation, magnetization and so forth) that has been normalized to the first two moments follows a specific nonGaussian curve. This curve follows a form suggested by extremum statistics, which is specified by a single parameter a (a = 1 corresponds to the FisherTippett Type I (“Gumbel”) distribution).
Here we present a framework for testing for extremal
statistics in a global observable. In any given system, we
wish to obtain a, in order to distinguish between the different FisherTippett asymptotes, and to compare with the
above work. The normalizations of the extremal curves are
obtained as a function of a. We find that for realistic ranges of data, the various extremal distributions, when normalized to the first two moments, are difficult to distinguish. In addition, the convergence to the limiting extremal distributions for finite data sets is both slow and varies with the asymptote.
However, when the third moment is expressed as a function
of a, this is found to be a more sensitive method.
Item Type:  Journal Article 

Subjects:  G Geography. Anthropology. Recreation > G Geography (General) Q Science > QC Physics 
Divisions:  Faculty of Science > Physics 
Library of Congress Subject Headings (LCSH):  Geophysics  Data processing, Statistics 
Journal or Publication Title:  Nonlinear Processes in Geophysics 
Publisher:  Copernicus GmbH 
ISSN:  10235809 
Official Date:  8 February 2002 
Volume:  Vol.9 
Page Range:  pp. 409418 
Status:  Peer Reviewed 
Access rights to Published version:  Open Access 
References:  Aji, V., and Goldenfeld, N.: Fluctuations in finite critical and turbulent 
URI:  http://wrap.warwick.ac.uk/id/eprint/588 
Data sourced from Thomson Reuters' Web of Knowledge
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