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| Titel |
Extremum statistics: a framework for data analysis |
| VerfasserIn |
S. C. Chapman, G. Rowlands, N. W. Watkins |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 9, no. 5/6 ; Nr. 9, no. 5/6, S.409-418 |
| Datensatznummer |
250006555
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| Publikation (Nr.) |
 copernicus.org/npg-9-409-2002.pdf |
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| Zusammenfassung |
| 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. |
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