IDEAS home Printed from https://ideas.repec.org/a/spr/nathaz/v90y2018i2d10.1007_s11069-017-3074-1.html
   My bibliography  Save this article

Stochastic earthquake interevent time modeling from exponentiated Weibull distributions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11069-017-3074-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11069-017-3074-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Manisha & M. MASOOM ALI & JUNGSOO WOO, 2006. "Exponentiated Weibull distribution," Statistica, Department of Statistics, University of Bologna, vol. 66(2), pages 139-147.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sutapa Chaudhuri & Arumita Roy Chowdhury & Payel Das, 2018. "Implementation of Sugeno: ANFIS for forecasting the seismic moment of large earthquakes over Indo-Himalayan region," 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(1), pages 391-405, January.
    2. Sumanta Pasari & Onkar Dikshit, 2014. "Three-parameter generalized exponential distribution in earthquake recurrence interval estimation," 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. 73(2), pages 639-656, September.
    3. Boikanyo Makubate & Fastel Chipepa & Broderick Oluyede & Peter O. Peter, 2021. "The Marshall-Olkin Half Logistic-G Family of Distributions With Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(2), pages 120-120, March.
    4. D. Gospodinov & V. Karakostas & E. Papadimitriou, 2015. "Seismicity rate modeling for prospective stochastic forecasting: the case of 2014 Kefalonia, Greece, seismic excitation," 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. 79(2), pages 1039-1058, November.
    5. Huang, Lorick & Khabou, Mahmoud, 2023. "Nonlinear Poisson autoregression and nonlinear Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 201-241.
    6. Steffen Volkenand & Günther Filler & Martin Odening, 2020. "Price Discovery and Market Reflexivity in Agricultural Futures Contracts with Different Maturities," Risks, MDPI, vol. 8(3), pages 1-17, July.
    7. Dewei Wang & Chendi Jiang & Chanseok Park, 2019. "Reliability analysis of load-sharing systems with memory," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(2), pages 341-360, April.
    8. Jamie Olson & Kathleen Carley, 2013. "Exact and approximate EM estimation of mutually exciting hawkes processes," Statistical Inference for Stochastic Processes, Springer, vol. 16(1), pages 63-80, April.
    9. Kuroda, Kaori & Hashiguchi, Hiroki & Fujiwara, Kantaro & Ikeguchi, Tohru, 2014. "Reconstruction of network structures from marked point processes using multi-dimensional scaling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 194-204.
    10. van den Hengel, G. & Franses, Ph.H.B.F., 2018. "Forecasting social conflicts in Africa using an Epidemic Type Aftershock Sequence model," Econometric Institute Research Papers EI2018-31, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Chenlong Li & Zhanjie Song & Wenjun Wang, 2020. "Space–time inhomogeneous background intensity estimators for semi-parametric space–time self-exciting point process models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 945-967, August.
    12. Sebastian Meyer & Johannes Elias & Michael Höhle, 2012. "A Space–Time Conditional Intensity Model for Invasive Meningococcal Disease Occurrence," Biometrics, The International Biometric Society, vol. 68(2), pages 607-616, June.
    13. J. Wang, 2016. "Reviews of seismicity around Taiwan: Weibull distribution," 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. 80(3), pages 1651-1668, February.
    14. Habtemicael, Semere & SenGupta, Indranil, 2014. "Ornstein–Uhlenbeck processes for geophysical data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 399(C), pages 147-156.
    15. Hainaut, Donatien, 2019. "Fractional Hawkes processes," LIDAM Discussion Papers ISBA 2019016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Eric W. Fox & Martin B. Short & Frederic P. Schoenberg & Kathryn D. Coronges & Andrea L. Bertozzi, 2016. "Modeling E-mail Networks and Inferring Leadership Using Self-Exciting Point Processes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 564-584, April.
    17. Lizhen Xu & Jason A. Duan & Andrew Whinston, 2014. "Path to Purchase: A Mutually Exciting Point Process Model for Online Advertising and Conversion," Management Science, INFORMS, vol. 60(6), pages 1392-1412, June.
    18. Francine Gresnigt & Erik Kole & Philip Hans Franses, 2017. "Specification Testing in Hawkes Models," Journal of Financial Econometrics, Oxford University Press, vol. 15(1), pages 139-171.
    19. Møller, Jesper & Torrisi, Giovanni Luca, 2007. "The pair correlation function of spatial Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 995-1003, June.
    20. Francine Gresnigt & Erik Kole & Philip Hans Franses, 2017. "Exploiting Spillovers to Forecast Crashes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(8), pages 936-955, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:nathaz:v:90:y:2018:i:2:d:10.1007_s11069-017-3074-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.