Probability distributions for discrete one-dimensional coverage processes

Recursive decomposition of fundamental events in the directional, one-dimensional, discrete, stationary Boolean model has resulted in analytic representation of the event probabilities and the recursive representation of clump-length and gap-length densities. This paper applies the methodology to find analytic expressions for distributions of a number of random variables, including the number of grains covering a point. It extends the methodology, including clumpand gap-length analysis, to more general coverage processes where marking probabilities and grain-length distributions are point-dependent, and to the case where there can be multiple grains commencing at a marked point. ( 1998 Elsevier Science B.V. All rights reserved.