A K-function for inhomogeneous random measures with geometric features
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A K-function for inhomogeneous random measures with geometric features. / Svane, Anne Marie; Stephensen, Hans Jacob Teglbjærg; Waagepetersen, Rasmus.
In: Spatial Statistics, Vol. 51, 100656, 2022, p. 1-30.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - A K-function for inhomogeneous random measures with geometric features
AU - Svane, Anne Marie
AU - Stephensen, Hans Jacob Teglbjærg
AU - Waagepetersen, Rasmus
N1 - Publisher Copyright: © 2022 Elsevier B.V.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Fiber process
KW - Inhomogeneous
KW - K-function
KW - Marked point process
KW - Random measure
KW - Tangent directions
U2 - 10.1016/j.spasta.2022.100656
DO - 10.1016/j.spasta.2022.100656
M3 - Journal article
AN - SCOPUS:85127921508
VL - 51
SP - 1
EP - 30
JO - Spatial Statistics
JF - Spatial Statistics
SN - 2211-6753
M1 - 100656
ER -
ID: 307743477