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The distribution of the distance between random points

Published online by Cambridge University Press:  14 July 2016

Vangalur S. Alagar
Vangalur S. Alagar*
Affiliation:
Concordia University, Montreal
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Abstract

This paper considers the distribution of distance between random points and shows how the distribution can be found when the points are chosen uniformly and independently in a hypersphere or in two adjacent unit squares. The value of a powerful extension of the classical Crofton technique is illustrated here for solving such geometric probability problems. This method is quite different from those employed by Hammersley and Oser.

Keywords

DISTRIBUTION OF DISTANCEHYPERSPHEREADJACENT SQUARESTRANSPORTATION MODELSPATTERN RECOGNITIONGEOMETRIC PROBABILITY

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 3 , September 1976 , pp. 558 - 566
Copyright
Copyright © Applied Probability Trust 1976 

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References

[1] Hammersley, J.M. (1950) The distribution of the distance in a hypersphere. Ann. Math. Statist. 21, 447–452.Google Scholar
[2] Kendall, M.G. and Moran, P.A.P. (1962) Geometric Probability. Griffin Statistical Monographs, Griffin, London.Google Scholar
[3] Lord, R.D. (1954) The distribution of distance in a hypersphere. Ann. Math. Statist. 24, 794–798.Google Scholar
[4] Moore, D.J.H. and Parker, D.J. (1974) Analysis of global pattern features. Pattern Recognition 6, 149–164.CrossRefGoogle Scholar
[5] Moran, P.A.P. (1966) A note on recent research in geometrical probability. J. Appl. Prob. 3, 453–463.CrossRefGoogle Scholar
[6] Moran, P.A.P. (1969) A second note on recent research in geometrical probability. Adv. Appl. Prob. 1, 73–89.CrossRefGoogle Scholar
[7] Oser, H.J. (1975) The average distance of two points in adjacent unit squares. Unpublished.CrossRefGoogle Scholar
[8] Wong, E. and Steppe, A.J. (1969) Invariant recognition of geometric spaces. In Methodologies of Pattern Recognition. Academic Press, New York and London, 535–546.Google Scholar