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Some properties of line segment processes

Published online by Cambridge University Press:  14 July 2016

Philip Parker  and
Richard Cowan
Philip Parker
Affiliation:
Flinders University of South Australia
Richard Cowan
Affiliation:
Flinders University of South Australia
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Abstract

This paper formulates the random process of line-segments in the Euclidean plane. Under conditions more general than Poisson, expressions are obtained, for Borel A ⊂ R2, for the first moments of M(A), the number of segment mid-points in A; N(A), the number of segments which intersect with convex A; S(A), the total length within A of segments crossing A; and C(A) the number of segment-segment crossings within A. In the case of Poisson mid-points, the distribution of the rth nearest line-segment to a given point is found.

Keywords

GEOMETRICAL PROBABILITYRANDOM LINE-SEGMENTS IN A PLANEPOINT PROCESSMEAN STATIONARITYISOTROPYPOISSON PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 96 - 107
Copyright
Copyright © Applied Probability Trust 1976 

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