Forma, Vol. 18 (No. 4), pp. 221-247, 2003
Original Paper

Statistical Distributions of Poisson Voronoi Cells in Two and Three Dimensions

Masaharu Tanemura

The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan
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(Received December 2, 2002; Accepted November 29, 2003)

Keywords: Delaunay Triangles, Generalized Gamma Distribution, Kiang's Conjecture, Maximum Likelihood Estimates, Voronoi Tessellation

Abstract. Statistical distributions of geometrical characteristics concerning the Poisson Voronoi cells, namely, Voronoi cells for the homogeneous Poisson point processes, are numerically obtained in two- and three-dimensional spaces based on the computer experiments. In this paper, ten million and five million independent samples of Voronoi cells in two- and three-dimensional spaces, respectively, are generated. Geometrical characteristics such as the cell volume, cell surface area and so on, are fitted to the generalized gamma distribution. Then, maximum likelihood estimates of parameters of the generalized gamma distribution are given.

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