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

• Activity Number: 403
• Type: Contributed
• Date/Time: Wednesday, August 10, 2005 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Alejandro Veen*+ and Frederic Paik Schoenberg
• Companies: University of California, Los Angeles and University of California, Los Angeles
• Keywords: weighted K-function ; inhomogeneous K-function ; K function ; point processes ; seismology ; earthquakes

Abstract

We investigate the properties of a weighted analogue of Ripley's K-function, 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 the mean of K-functions computed on a repeatedly thinned point pattern 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.