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| Titel |
On the identification of Dragon Kings among extreme-valued outliers |
| VerfasserIn |
M. Riva, S. P. Neuman, A. Guadagnini |
| 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 ; 20, no. 4 ; Nr. 20, no. 4 (2013-07-26), S.549-561 |
| Datensatznummer |
250018990
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| Publikation (Nr.) |
 copernicus.org/npg-20-549-2013.pdf |
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| Zusammenfassung |
| Extreme values of earth, environmental, ecological, physical, biological,
financial and other variables often form outliers to heavy tails of empirical
frequency distributions. Quite commonly such tails are approximated by
stretched exponential, log-normal or power functions. Recently there has been
an interest in distinguishing between extreme-valued outliers that belong to
the parent population of most data in a sample and those that do not. The
first type, called Gray Swans by Nassim Nicholas Taleb (often confused in the
literature with Taleb's totally unknowable Black Swans), is drawn from a
known distribution of the tails which can thus be extrapolated beyond the
range of sampled values. However, the magnitudes and/or space–time locations
of unsampled Gray Swans cannot be foretold. The second type of extreme-valued
outliers, termed Dragon Kings by Didier Sornette, may in his view be
sometimes predicted based on how other data in the sample behave. This
intriguing prospect has recently motivated some authors to propose
statistical tests capable of identifying Dragon Kings in a given random
sample. Here we apply three such tests to log air permeability data measured
on the faces of a Berea sandstone block and to synthetic data generated in a
manner statistically consistent with these measurements. We interpret the
measurements to be, and generate synthetic data that are, samples from
α-stable sub-Gaussian random fields subordinated to truncated
fractional Gaussian noise (tfGn). All these data have frequency distributions
characterized by power-law tails with extreme-valued outliers about the tail
edges. |
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