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A non-parametric measure of spatial interaction in point patterns

Published online by Cambridge University Press:  01 July 2016

M. N. M. Van Lieshout
Affiliation:
University of Warwick
A. J. Baddeley
Affiliation:
Universities of Western Australia and Leiden

Extract

The strength and range of interpoint interactions in a spatial point process can be quantified by the function J = (1 - G)/(1 - F), where G is the nearest-neighbour distance distribution function and F the empty space function of the process. J(r) is identically equal to 1 for a Poisson process; values of J(r) smaller or larger than 1 indicate clustering or regularity, respectively. We show that, for a very large class of point processes, J(r) is constant for distances r greater than the range of spatial interaction. Hence both the range and type of interpoint interaction may be inferred from J without parametric model assumptions. We evaluate J(r) explicitly for a variety of point processes. The J function of the superposition of independent point processes is a weighted mean of the J functions of the individual processes.

Type
Stochastic Geometry and Statistical Applications
Copyright
Copyright © Applied Probability Trust 1996 

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