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Objects arranged randomly in space: an accessible theory

Published online by Cambridge University Press:  01 July 2016

Richard Cowan
Richard Cowan*
Affiliation:
CSIRO Division of Mathematics and Statistics, Lindfield
*
∗ Present address: Department of Statistics, University of Hong Kong, Pokfulam Road, Hong Kong.
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Abstract

This expository paper deals with many problems concerning bounded objects arranged randomly in space. The objects are of rather general shapes and sizes, whilst the random mechanisms for positioning and orienting them are also fairly general. There are no restrictions on the dependence between shapes, sizes, orientations and positions of objects. The only substantive assumption is that the objects are distributed in a ‘statistically uniform' way throughout the whole of the space. We focus on the statistical properties of features seen in an observation window, itself of general size and shape.

Keywords

RANDOM GEOMETRYINTEGRAL GEOMETRYGEOMETRIC STATISTICSRANDOM SETS

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Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 3 , September 1989 , pp. 543 - 569
Copyright
Copyright © Applied Probability Trust 1989 

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