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Mathematical Geosciences

, Volume 45, Issue 7, pp 851–872 | Cite as

Robust Estimation for the Weibull Process Applied to Eruption Records

  • Ting Wang
  • Mark Bebbington
Article

Abstract

The Weibull process is a parsimoniously parameterized nonhomogeneous Poisson process with monotonic trend, which has been widely used in reliability applications. It has also been used in volcanology to model the process of eruption onsets for a volcano with waning or waxing activity, and thus produce hazard forecasts. However, particularly in the latter application, problems with missing or spurious data can strongly influence the parameter estimates, which are usually obtained by maximizing the log likelihood function, and hence the future hazard. We show how theory developed for robust estimation of a nonhomogeneous Poisson process can be implemented for the Weibull process. The flank eruptions of Mt. Etna, in Sicily, is one of the most complete and best studied records of volcanism. Nevertheless, a number of different catalogs exist. We show how these can be at least partially reconciled by robust estimation, and how the more dubious regions of the catalogs can be identified.

Keywords

Flank eruptions M-estimator Mt. Etna Nonhomogeneous Poisson process 

Notes

Acknowledgements

This work was carried out while the first author was supported as a Massey University postdoctoral fellow by the Natural Hazards Research Platform and the Earthquake Commission. We thank an anonymous reviewer and the editor for helpful suggestions on the original manuscript.

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Copyright information

© International Association for Mathematical Geosciences 2013

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of OtagoDunedinNew Zealand
  2. 2.Volcanic Risk SolutionsMassey UniversityPalmerston NorthNew Zealand

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