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Stochastic earthquake interevent time modeling from exponentiated Weibull distributions

Author

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  • Sumanta Pasari

    (Birla Institute of Technology and Science Pilani)

  • Onkar Dikshit

    (Indian Institute of Technology Kanpur)

Abstract

In view of the growing importance of stochastic earthquake modeling in disaster preparation, the present study introduces a new family of exponentiated Weibull distribution and examines its performance in earthquake interevent time analysis in a stationary point process. This three-parameter (one scale and two shapes) distribution not only covers the Weibull distribution, exponentiated exponential distribution, Burr-type X distribution, Rayleigh distribution, and exponential distribution as special sub-families, but also offers monotone and non-monotone hazard shapes. Here we first describe some of the exponentiated Weibull distribution properties, such as the survival rate, mode, median, and hazard rate. We then provide statistical inference and goodness-of-fit measures to examine the suitability of exponentiated Weibull model in comparison with other popular models, like exponential, gamma, lognormal, Weibull, and exponentiated exponential. Finally, we conduct real data analysis to assess the usefulness and flexibility of exponentiated Weibull distribution in the context of seismic interevent time modeling and associated applications. Results suggest that the exponentiated Weibull distribution has a comparable performance with other popular distributions of its nature. However, further investigations are necessary to confirm the importance and flexibility of exponentiated Weibull distribution in statistical seismology.

Suggested Citation

  • Sumanta Pasari & Onkar Dikshit, 2018. "Stochastic earthquake interevent time modeling from exponentiated Weibull distributions," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 90(2), pages 823-842, January.
    • Handle: RePEc:spr:nathaz:v:90:y:2018:i:2:d:10.1007_s11069-017-3074-1
    DOI: 10.1007/s11069-017-3074-1
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    References listed on IDEAS

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    1. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    2. Manisha & M. MASOOM ALI & JUNGSOO WOO, 2006. "Exponentiated Weibull distribution," Statistica, Department of Statistics, University of Bologna, vol. 66(2), pages 139-147.
    3. Chi-Hsuan Chen & Jui-Pin Wang & Yih-Min Wu & Chung-Han Chan & Chien-Hsin Chang, 2013. "A study of earthquake inter-occurrence times distribution models in Taiwan," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 69(3), pages 1335-1350, December.
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    Cited by:

    1. Weijin Xu & Jian Wu & Mengtan Gao, 2023. "Temporal distribution model and occurrence probability of M ≥ 6.5 earthquakes in North China Seismic Zone," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 119(1), pages 125-141, October.
    2. Sumanta Pasari & Andrean V. H. Simanjuntak & Anand Mehta & Neha & Yogendra Sharma, 2021. "A synoptic view of the natural time distribution and contemporary earthquake hazards in Sumatra, Indonesia," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 108(1), pages 309-321, August.

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