A statistical method is presented for determining randomness of points spatially distributed in two-dimensional space. The procedure is based on a distance-to-particle (nearest neighbor) model derived from an elementary Poisson process. In a previous derivation of the method, an extension to the model was proposed and used without adequate empirical justification. Herein the test is derived in detail and its performance evaluated with Monte Carlo simulations. Results indicate that the model extension provides adequate representations when the null hypothesis is true.
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