Acta Stereologica Acta Stereologica -  Volume 12 (1993)  Number 2 - Proceedings of the sixth European congress for stereology - Part one - Dec. 1993 

Spherical contact distances in Neyman-Scott process of regular clusters

Ivan Saxl
Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic

Abstract

The Neyman—Scott cluster process of regular 2k-tuples — vertices of a k—cube of random edge length in Rd, k=0,…,d is considered. The attention is focused on the properties of the spherical contact distribution function H(l). It is shown that the corresponding probability density function h(l) is in certain sense intermediate between hp(l) of the parent process and hcl(l) of the Poisson point process of the daughter process intensity λcl. Particular cases of point pairs and 2d-tuples of constant size in R1, R2, R3 as well as the effect of the edge length distribution are treated in detail and the results are presented in a graphical form.

Keywords : Neyman—Scott cluster process, regular 2k—tup1es, spherical contact distribution function

To cite this article

Ivan Saxl, «Spherical contact distances in Neyman-Scott process of regular clusters», Acta Stereologica [En ligne], Volume 12 (1993), Number 2 - Proceedings of the sixth European congress for stereology - Part one - Dec. 1993, 115-122 URL : https://popups.ulg.ac.be/0351-580x/index.php?id=1464.