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. 409-418. ISSN 1023-5809

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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 non-Gaussian curve. This curve follows a form suggested by extremum statistics, which is specified by a single parameter a (a = 1 corresponds to the Fisher-Tippett 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 Fisher-Tippett 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:	1023-5809
Date:	8 February 2002
Volume:	Vol.9
Page Range:	pp. 409-418
Status:	Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/588

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