### Abstract

By analyzing the Japan Meteorological Agency (JMA) seismic catalog for different tectonic settings, we have found that the probability distributions of time intervals between successive earthquakes-interoccurrence times-can be described by the superposition of the Weibull distribution and the log-Weibull distribution. In particular, the distribution of large earthquakes obeys the Weibull distribution with the exponent α_{1} < 1, indicating the fact that the sequence of large earthquakes is not a Poisson process. It is found that the ratio of the Weibull distribution to the probability distribution of the interoccurrence time gradually increases with increase in the threshold of magnitude. Our results infer that Weibull statistics and log-Weibull statistics coexist in the interoccurrence time statistics, and that the change of the distribution is considered as the change of the dominant distribution. In this case, the dominant distribution changes from the log-Weibull distribution to the Weibull distribution, allowing us to reinforce the view that the interoccurrence time exhibits the transition from the Weibull regime to the log-Weibull regime.

Original language | English |
---|---|

Pages (from-to) | 491-498 |

Number of pages | 8 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 388 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2009 Feb 15 |

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### Keywords

- Interoccurrence time
- Log-Weibull distribution
- Seismicity
- Weibull distribution
- Weibull-log Weibull transition

### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistics and Probability

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

*388*(4), 491-498. https://doi.org/10.1016/j.physa.2008.10.023

**The Weibull-log Weibull distribution for interoccurrence times of earthquakes.** / Hasumi, Tomohiro; Akimoto, Takuma; Aizawa, Yoji.

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 388, no. 4, pp. 491-498. https://doi.org/10.1016/j.physa.2008.10.023

}

TY - JOUR

T1 - The Weibull-log Weibull distribution for interoccurrence times of earthquakes

AU - Hasumi, Tomohiro

AU - Akimoto, Takuma

AU - Aizawa, Yoji

PY - 2009/2/15

Y1 - 2009/2/15

N2 - By analyzing the Japan Meteorological Agency (JMA) seismic catalog for different tectonic settings, we have found that the probability distributions of time intervals between successive earthquakes-interoccurrence times-can be described by the superposition of the Weibull distribution and the log-Weibull distribution. In particular, the distribution of large earthquakes obeys the Weibull distribution with the exponent α1 < 1, indicating the fact that the sequence of large earthquakes is not a Poisson process. It is found that the ratio of the Weibull distribution to the probability distribution of the interoccurrence time gradually increases with increase in the threshold of magnitude. Our results infer that Weibull statistics and log-Weibull statistics coexist in the interoccurrence time statistics, and that the change of the distribution is considered as the change of the dominant distribution. In this case, the dominant distribution changes from the log-Weibull distribution to the Weibull distribution, allowing us to reinforce the view that the interoccurrence time exhibits the transition from the Weibull regime to the log-Weibull regime.

AB - By analyzing the Japan Meteorological Agency (JMA) seismic catalog for different tectonic settings, we have found that the probability distributions of time intervals between successive earthquakes-interoccurrence times-can be described by the superposition of the Weibull distribution and the log-Weibull distribution. In particular, the distribution of large earthquakes obeys the Weibull distribution with the exponent α1 < 1, indicating the fact that the sequence of large earthquakes is not a Poisson process. It is found that the ratio of the Weibull distribution to the probability distribution of the interoccurrence time gradually increases with increase in the threshold of magnitude. Our results infer that Weibull statistics and log-Weibull statistics coexist in the interoccurrence time statistics, and that the change of the distribution is considered as the change of the dominant distribution. In this case, the dominant distribution changes from the log-Weibull distribution to the Weibull distribution, allowing us to reinforce the view that the interoccurrence time exhibits the transition from the Weibull regime to the log-Weibull regime.

KW - Interoccurrence time

KW - Log-Weibull distribution

KW - Seismicity

KW - Weibull distribution

KW - Weibull-log Weibull transition

UR - http://www.scopus.com/inward/record.url?scp=57349148711&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57349148711&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2008.10.023

DO - 10.1016/j.physa.2008.10.023

M3 - Article

AN - SCOPUS:57349148711

VL - 388

SP - 491

EP - 498

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 4

ER -