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van Lieshout, M. N. M.

A \(J\)-function for inhomogeneous point processes. (English) Zbl 07881872

Stat. Neerl. 65, No. 2, 183-201 (2011).
Summary: 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 \(n\in\mathbb{N}\), 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.
© 2011 The Author. Statistica Neerlandica © 2011 VVS

Cited in 12 Documents

MSC:

60Gxx Stochastic processes
62Mxx Inference from stochastic processes
62Hxx Multivariate analysis

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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References:

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