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A J–function for inhomogeneous point processes
Authors:M. N. M. van Lieshout
Affiliation:CWI & Eindhoven University of Technology, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
Abstract:We propose new summary statistics for intensity‐reweighted moment stationary point processes, that is, point processes with translation invariant n‐point correlation functions for all inline image, that generalise the well known J‐, empty space, and spherical Palm contact distribution functions. We represent these statistics in terms of generating functionals and relate the inhomogeneous J‐function to the inhomogeneous reduced second moment function. Extensions to space time and marked point processes are briefly discussed.
Keywords:conditional intensity  empty space function  generating functional  J‐function  inhomogeneity  intensity‐reweighted moment stationarity  marked point process  minus sampling estimator  product density  reduced second moment measure  spatial interaction  spherical Palm contact distribution function
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