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Detection of spatial pattern through independence of thinned processes

Renato M. Assuncao·Pablo A. Ferrari
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Abstract

Let N, N' and N'' be point processes such that N' is obtained from N by homogeneous independent thinning and N''= N- N'. We give a new elementary proof that N' and N'' are independent if and only if N is a Poisson point process. We present some applications of this result to test if a homogeneous point process is a Poisson point process.

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Renato M. Assuncao, Pablo A. Ferrari. 2001-03-16. Detection of spatial pattern through independence of thinned processes. https://doi.org/10.1007/s11749-006-0012-z

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