Abstract
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 a-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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 549-561 |
| Number of pages | 13 |
| Journal | Nonlinear Processes in Geophysics |
| Volume | 20 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2013 |
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ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Geophysics
- Geochemistry and Petrology
Cite this
On the identification of dragon kings among extreme-valued outliers. / Riva, M.; Neuman, Shlomo P; Guadagnini, A.
In: Nonlinear Processes in Geophysics, Vol. 20, No. 4, 2013, p. 549-561.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On the identification of dragon kings among extreme-valued outliers
AU - Riva, M.
AU - Neuman, Shlomo P
AU - Guadagnini, A.
PY - 2013
Y1 - 2013
N2 - 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 a-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.
AB - 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 a-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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U2 - 10.5194/npg-20-549-2013
DO - 10.5194/npg-20-549-2013
M3 - Article
AN - SCOPUS:84984408670
VL - 20
SP - 549
EP - 561
JO - Nonlinear Processes in Geophysics
JF - Nonlinear Processes in Geophysics
SN - 1023-5809
IS - 4
ER -