Open Access
April, 1986 Clump Counts in a Mosaic
Peter Hall
Ann. Probab. 14(2): 424-458 (April, 1986). DOI: 10.1214/aop/1176992525


A mosaic process is formed by centering independent and identically distributed random shapes at the points of a Poisson process in $k$-dimensional space. Clusters of overlapping shapes are called clumps. This paper provides approximations to the distribution of the number of clumps of a specified order within a large region. The approximations cover two different situations--"moderate-intensity" mosaics, in which the covered proportion of the region is neither very large nor very small; and "sparse" mosaics, in which the covered proportion is quite small. Both these mosaic types can be used to model observed phenomena, such as counts of bacterial colonies in a petri dish or dust particles on a membrane filter.


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Peter Hall. "Clump Counts in a Mosaic." Ann. Probab. 14 (2) 424 - 458, April, 1986.


Published: April, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0606.60017
MathSciNet: MR832018
Digital Object Identifier: 10.1214/aop/1176992525

Primary: 60D05
Secondary: 60G55

Keywords: Clump , geometric probability , mosaic , Normal approximation , Poisson approximation , random set

Rights: Copyright © 1986 Institute of Mathematical Statistics

Vol.14 • No. 2 • April, 1986
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