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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. 409-418. ISSN 1023-5809

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Official URL: http://www.nonlin-processes-geophys.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 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

Official Date:

8 February 2002

Dates:

Date	Event
8 February 2002	Submitted

Volume:

Vol.9

Page Range:

pp. 409-418

Status:

Peer Reviewed

Access rights to Published version:

Open Access

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