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Stochastic earthquake interevent time modeling from exponentiated Weibull distributions

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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.

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Modified after Yadav et al. (2010) and Pasari and Dikshit (2014)

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Acknowledgements

The generic mapping tool (GMT) system (Wessel and Smith 1995) and the MATLAB software (MATLAB 2010) were used for plotting and numerical computation purposes. Constructive comments and important suggestions of two anonymous reviewers are duly acknowledged. This study was partially supported by two grants received from RIG and ACRG of BITS Pilani.

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Authors and Affiliations

  1. Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani, 333031, India

    Sumanta Pasari

  2. Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    Onkar Dikshit

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  1. Sumanta Pasari
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  2. Onkar Dikshit
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Correspondence to Sumanta Pasari.

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Pasari, S., Dikshit, O. Stochastic earthquake interevent time modeling from exponentiated Weibull distributions. Nat Hazards 90, 823–842 (2018). https://doi.org/10.1007/s11069-017-3074-1

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