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Aggregation patterns are often visually detected in sets of location data.These clusters may be the result of interesting dynamics or the effect of purerandomness. We build an asymptotically Gaussian test for the hypothesis ofrandomness corresponding to a Poisson point process. We first compute the exactfirst and second moment of the Ripley K-statistic under the homogeneous Poissonpoint process model. Then we prove the asymptotic normality of a vector of suchstatistics for different scales and compute its covariance matrix. From theseresults, we derive a test statistic that is chi-square distributed. By aMonte-Carlo study, we check that the test is numerically tractable even forlarge data sets and also correct when only a hundred of points are observed.

Testing randomness of spatial point patterns with the Ripley statistic