Assessing Spatial Point Process Models Using Weighted K-functions: Analysis of California Earthquakes

  • Alejandro Veen
  • Frederic Paik Schoenberg
Part of the Lecture Notes in Statistics book series (LNS, volume 185)


We investigate the properties of a weighted analogue of Ripley’s Kfunction which was first introduced by Baddeley, Møller, and Waagepetersen. This statistic, called the weighted or inhomogeneous K-function, is useful for assessing the fit of point process models. The advantage of this measure of goodness-of-fit is that it can be used in situations where the null hypothesis is not a stationary Poisson model. We note a correspondence between the weighted K-function and thinned residuals, and derive the asymptotic distribution of the weighted K-function for a spatial inhomogeneous Poisson process. We then present an application of the use of the weighted K-function to assess the goodness-of-fit of a class of point process models for the spatial distribution of earthquakes in Southern California.

Key words

Goodness-of-fit of spatial point process models Inhomogeneity Spatial distribution of earthquakes Weighted Ripley’s K-function 


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Copyright information

© Springer Science+Business Media Inc. 2006

Authors and Affiliations

  • Alejandro Veen
    • 1
  • Frederic Paik Schoenberg
    • 1
  1. 1.UCLA Department of StatisticsLos AngelesUSA

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