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Distance distributions associated with poisson processes of geometric figures

Published online by Cambridge University Press:  14 July 2016

Mark Berman
Mark Berman*
Affiliation:
C. S. I. R. O. Division of Mathematics and Statistics, Newtown, New South Wales
*
*Now at Imperial College London.
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Abstract

Consider a process of identically-shaped (but not necessarily equal-sized) figures (e.g. points, clusters of points, lines, spheres) embedded at random in n-dimensional space. A simple technique is derived for finding the distribution of the distance from a fixed point, chosen independently of the process of figures, to the k th nearest figure. The technique also shows that the distribution is independent of the distribution of the orientations of the figures. It is noted that the distribution obtained above (for equal-sized figures) is identical to the distribution of the distance from a fixed figure to the k th nearest of a random process of points.

Keywords

POISSON PROCESSESNEAREST NEIGHBOURDISTANCE METHODSGEOMETRICAL PROBABILITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 1 , March 1977 , pp. 195 - 199
Copyright
Copyright © Applied Probability Trust 1977 

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References

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