Clump counts in a mosaic
type: Item
instance of: scholarly article
title: Clump counts in a mosaic
zbMATH Open document ID: 0606.60017
published in: The Annals of Probability
publication date: 1986-01-01T00:00:00Z
review text: Asymptotic expressions are derived for the mean and variance of the number of isolated grains of a Boolean model within a bounded sampling region as the grain volume tends to zero while the proportion of volume covered by the process tends to a positive constant. When the volume fraction tends to zero, the number of clumps of any specified order n within the sampling region is shown to be asymptotically Poisson distributed. For \(n\geq 2\), an integral expression is given for the mean number of clumps of order n, which involves the probability that n independent realisations of a grain placed at n specified positions form a connected set.
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 3980120
zbMATH Keywords: Boolean model
zbMATH Keywords: asymptotic distribution
zbMATH Keywords: clump size
zbMATH Keywords: number of clumps
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992525
OpenAlex ID: W2023833834
DOI: 10.1214/AOP/1176992525
author: Peter Hall
description: scientific article; zbMATH DE number 3980120