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A note on point process analysis of Chinese earthquake data

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Abstract

In the analysis of Chinese earthquake history byLee andBrillinger (1979), the autointensity function of the earthquake sequence is estimated, based on a parametric model for the catalog inclusion probabilities. We show that an estimate of the autointensity function with essentially the same features can be obtained by smoothing the data to yield a nonparametric estimate of the inclusion probabilities. In addition, however, we illustrate that a somewhat less smooth estimate would lead to an autointensity function with little structure. The shape of the estimated autointensity function is hence dependent on the assumed smoothness of the inclusion probabilities. This is an issue which cannot be resolved statistically.

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References

  1. Friedman, J. H., andStuetzle, W. (1982),Smoothing of Scatter Plots. Project ORION Tech. Rep. 003, Dept. of Statistics, Stanford University.

  2. Guttorp, P., andThompson, M. L. (1989),Estimating Second Order Parameters from Partially Observed Stationary Point Processes, submitted to the Journal of the Royal Statistical Society, Ser. B.

  3. Lee, W. H. K., andBrillinger, D. R. (1979),On Chinese Earthquake History — An Attempt to Model an Incomplete Data Set by Point Process Analysis, Pure Appl. Geophys.117, 1229–1257.

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Guttorp, P., Thompson, M.L. A note on point process analysis of Chinese earthquake data. PAGEOPH 133, 541–546 (1990). https://doi.org/10.1007/BF00878004

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Key words

  • Incomplete catalog
  • autointensity
  • smoothing