A K-function for inhomogeneous random measures with geometric features

This paper introduces a K-function for assessing second-order properties of inhomogeneous random measures generated by marked point processes. The marks can be geometric objects like fibers or sets of positive volume, and the presented K-function takes into account geometric features of the marks, s...

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Bibliographic Details
Published inSpatial statistics Vol. 51; p. 100656
Main Authors Svane, Anne Marie, Stephensen, Hans Jacob Teglbjærg, Waagepetersen, Rasmus
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.10.2022
Subjects
[formula omitted]-function
Fiber process
Inhomogeneous
Marked point process
Random measure
Tangent directions
Random measure
K-function
Fiber process
Marked point process
Inhomogeneous
Tangent directions
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Summary:This paper introduces a K-function for assessing second-order properties of inhomogeneous random measures generated by marked point processes. The marks can be geometric objects like fibers or sets of positive volume, and the presented K-function takes into account geometric features of the marks, such as tangent directions of fibers. The K-function requires an estimate of the inhomogeneous density function of the random measure. We introduce parametric estimates for the density function based on parametric models that represent large scale features of the inhomogeneous random measure. The proposed methodology is applied to simulated fiber patterns as well as a three-dimensional dataset of steel fibers in concrete.
ISSN:2211-6753
2211-6753
DOI:10.1016/j.spasta.2022.100656