The Annals of Probability

Clump Counts in a Mosaic

Peter Hall

Abstract

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.

Article information

Source
Ann. Probab., Volume 14, Number 2 (1986), 424-458.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176992525

Digital Object Identifier
doi:10.1214/aop/1176992525

Mathematical Reviews number (MathSciNet)
MR832018

Zentralblatt MATH identifier
0606.60017

JSTOR