Summary statistics for inhomogeneous marked point processes

2014/07/11 by Ottmar Cronie, Cronie, O., M. N. M. van Lieshout +1 · 1 citation
Mathematics · #Point processes and geometric inequalities #Morphological variations and asymmetry

paper · pdf · doi:10.48550/arxiv.1407.3089

Abstract

We propose new summary statistics for intensity-reweighted moment stationary marked point processes with particular emphasis on discrete marks. The new statistics are based on the n-point correlation functions and reduce to cross J- and D-functions when stationarity holds. We explore the relationships between the various functions and discuss their explicit forms under specific model assumptions. We derive ratio-unbiased minus sampling estimators for our statistics and illustrate their use on a data set of wildfires.

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• Semi-parametric Markov models for multi-type point patterns

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