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Likelihood and nearest-neighbor distance properties of multidimensional Poisson cluster processes

Published online by Cambridge University Press:  14 July 2016

Michel Baudin
Michel Baudin*
Affiliation:
École Nationale Supérieure des Mines de Paris
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Abstract

The probability generating functional representation of a multidimensional Poisson cluster process is utilized to derive a formula for its likelihood function, but the prohibitive complexity of this formula precludes its practical application to statistical inference. In the case of isotropic processes, it is however feasible to compute functions such as the probability Q(r) of finding no point in a disc of radius r and the probability Q(r | 0) of nearest-neighbor distances greater than r, as well as the expected number C(r | 0) of points at a distance less than r from a given point. Explicit formulas and asymptotic developments are derived for these functions in the n-dimensional case. These can effectively be used as tools for statistical analysis.

Keywords

POINT PROCESSESPOISSON CLUSTER PROCESSESPROBABILITY GENERATING FUNCTIONAL
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 4 , December 1981 , pp. 879 - 888
Copyright
Copyright © Applied Probability Trust 1981 

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