MATHEMATICA BOHEMICA, Vol. 122, No. 1, pp. 21-36, 1997

Boolean cluster models: mean cluster dilations and spherical contact distances

Jan Rataj, Ivan Saxl

Jan Rataj, Mathematical Institute of the Charles University, Sokolovska 83, 180 00 Praha 8, Czech Republic; Ivan Saxl, Mathematical Institute of the Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Praha 1, Czech Republic

Abstract: Boolean cluster point processes with various cluster distributions are examined by means of their spherical contact distribution function. Special attention is paid to clusters with strong independence properties (Poisson clusters) and regular clusters.

Keywords: Poisson process, cluster process, Boolean model, Matern model, spherical contact distribution function

Classification (MSC 1991): 60D05, 60G55, 62M30

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