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- Volume 12 (1993)
- Number 2 - Proceedings of the sixth European congr...
- Properties of the Voronoi tessellation corresponding to the generalized planar Gauss-Poisson process
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Properties of the Voronoi tessellation corresponding to the generalized planar Gauss-Poisson process
Abstract
The Voronoi mosaics corresponding to the planar Neyman—Scott process of point pairs and regular quadruples (vertices of a square) are investigated. The mean values of cell parameters are those of a Poisson—Voronoi tessellation (PVT) of the same intensity of generating points. If the inter—daughter distances are comparable with or smaller than the mean nearest neighbour distance of the parent process, then higher moments of cell area and perimeter distributions differ considerably from the PVT values. If, moreover, the orientation of clusters is fixed, then also a pronounced anisotropy of cell boundaries is observed. The results are compared with those of standard statistical quadrat testing methods and a good agreement is found.