Pure and Applied Geophysics

, Volume 171, Issue 7, pp 1251–1281 | Cite as

Impact of Three-Parameter Weibull Models in Probabilistic Assessment of Earthquake Hazards

  • Sumanta Pasari
  • Onkar Dikshit


This paper investigates the suitability of a three-parameter (scale, shape, and location) Weibull distribution in probabilistic assessment of earthquake hazards. The performance is also compared with two other popular models from same Weibull family, namely the two-parameter Weibull model and the inverse Weibull model. A complete and homogeneous earthquake catalog (Yadav et al. in Pure Appl Geophys 167:1331–1342, 2010) of 20 events (M ≥ 7.0), spanning the period 1846 to 1995 from north–east India and its surrounding region (20°–32°N and 87°–100°E), is used to perform this study. The model parameters are initially estimated from graphical plots and later confirmed from statistical estimations such as maximum likelihood estimation (MLE) and method of moments (MoM). The asymptotic variance–covariance matrix for the MLE estimated parameters is further calculated on the basis of the Fisher information matrix (FIM). The model suitability is appraised using different statistical goodness-of-fit tests. For the study area, the estimated conditional probability for an earthquake within a decade comes out to be very high (≥0.90) for an elapsed time of 18 years (i.e., 2013). The study also reveals that the use of location parameter provides more flexibility to the three-parameter Weibull model in comparison to the two-parameter Weibull model. Therefore, it is suggested that three-parameter Weibull model has high importance in empirical modeling of earthquake recurrence and seismic hazard assessment.


North–east India recurrence interval Weibull models conditional probability Fisher information matrix 



The authors are grateful to Dr. Debasis Kundu, Professor and Head of Department of Mathematics and Statistics, Indian Institute of Technology Kanpur for his generous guidance and thorough review of the manuscript. The authors would also like to thank the two anonymous reviewers for their critical comments and technical inputs. The first author [S.P.] thankfully acknowledges the financial support from the Council of Scientific and Industrial Research (CSIR), New Delhi, India.


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Authors and Affiliations

  1. 1.Department of Civil EngineeringIndian Institute of Technology KanpurKanpurIndia

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