### 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

*Nonlinear Processes in Geophysics*,

*20*(4), 549-561. https://doi.org/10.5194/npg-20-549-2013

**On the identification of dragon kings among extreme-valued outliers.** / Riva, M.; Neuman, Shlomo P; Guadagnini, A.

Research output: Contribution to journal › Article

*Nonlinear Processes in Geophysics*, vol. 20, no. 4, pp. 549-561. https://doi.org/10.5194/npg-20-549-2013

}

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.

UR - http://www.scopus.com/inward/record.url?scp=84984408670&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84984408670&partnerID=8YFLogxK

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 -