Probability distributions for discrete one-dimensional coverage processes

doi:10.1016/S0165-1684(98)00101-7

Probability distributions for discrete one-dimensional coverage processes

1998-09-01

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DOI：10.1016/S0165-1684(98)00101-7

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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. Et extends the methodology, including clump- and 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. (C) 1998 Elsevier Science B.V. All rights reserved.

Keyword:

germ-grain model

nonstationary random set

directional Boolean model

infinite-server queue

Probability distributions for discrete one-dimensional coverage processes

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