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Summary statistics for inhomogeneous marked point processes
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2016 (English)In: Annals of the Institute of Statistical Mathematics, ISSN 0020-3157, E-ISSN 1572-9052, Vol. 68, no 4, p. 905-928Article in journal (Refereed) Published
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Abstract [en]

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 -point correlation functions and reduce to cross - and -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.

Place, publisher, year, edition, pages
2016. Vol. 68, no 4, p. 905-928
Keywords [en]
Generating functional, Intensity-reweighted moment stationarity, J-function, Marked point process, ltivariate point process, Nearest neighbour distance distribution function, n-point correlation nction, Reduced Palm measure
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-124314DOI: 10.1007/s10463-015-0515-zISI: 000379513000009OAI: oai:DiVA.org:umu-124314DiVA, id: diva2:958144
Available from: 2016-09-06 Created: 2016-08-04 Last updated: 2018-06-07Bibliographically approved

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Cronie, Ottmar

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