A large scale simulation experiment was conducted to study the characteristics of random sets involving more than one Voronoi polygon (with respect to a homogeneous Poisson point process). The sets considered are: a random neighbour of a typical Voronoi polygon, the union of these two polygons and the union of a typical Voronoi polygon with all its neighbours. For each of these sets the first two moments and the laws of the number of sides, the perimeter and the area are considered.The conditional distributions of the perimeter and the area, given the number of sides, are also studied.
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