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A random effects epidemic-type aftershock sequence model

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  • Lin, Feng-Chang

Abstract

We consider an extension of the temporal epidemic-type aftershock sequence (ETAS) model with random effects as a special case of a well-known doubly stochastic self-exciting point process. The new model arises from a deterministic function that is randomly scaled by a nonnegative random variable, which is unobservable but assumed to follow either positive stable or one-parameter gamma distribution with unit mean. Both random effects models are of interest although the one-parameter gamma random effects model is more popular when modeling associated survival times. Our estimation is based on the maximum likelihood approach with marginalized intensity. The methods are shown to perform well in simulation experiments. When applied to an earthquake sequence on the east coast of Taiwan, the extended model with positive stable random effects provides a better model fit, compared to the original ETAS model and the extended model with one-parameter gamma random effects.

Suggested Citation

  • Lin, Feng-Chang, 2011. "A random effects epidemic-type aftershock sequence model," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1610-1616, April.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1610-1616
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    References listed on IDEAS

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    1. Veen, Alejandro & Schoenberg, Frederic P., 2008. "Estimation of SpaceTime Branching Process Models in Seismology Using an EMType Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 614-624, June.
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    Cited by:

    1. Li, Zhongping & Cui, Lirong & Chen, Jianhui, 2018. "Traffic accident modelling via self-exciting point processes," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 312-320.

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