Summary statistics for inhomogeneous marked point processes

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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.
Original languageUndefined
Pages (from-to)905-928
Number of pages24
JournalAnnals of the Institute of Statistical Mathematics
Volume68
Issue number4
DOIs
Publication statusPublished - Aug 2016

Keywords

  • EWI-26224
  • MSC-60D05
  • MSC-60G55
  • Marked point process
  • Nearest neighbour distance distribution function
  • Generating functional
  • Multivariate point process
  • Intensity-reweighted moment stationarity
  • Reduced Palm measure
  • METIS-318440
  • IR-100959
  • $J$-function
  • $n$-point correlation function

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