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Testing the Boolean hypothesis in the non-convex case when a bounded grain can be assumed

Abstract : Spatial independence of objects is a strong hypothesis when using boolean models. Methods to test it have then been developed, but only when the objects are convex.We propose here to replace this assumption by a bound assumption of the objects which can be more easily assumed when modeling spatial patterns in ecology and agricultural science. A test is then proposed, based on the length of the voids of the intersection between transect lines and a dilation of the original process related to the bound value. Its application is shown to several examples, together with its extension to an epidemiological case on orchards, where this problem comes from
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Joël Chadoeuf, Jean-Noël Bacro, Gael Thébaud, Gérard Labonne. Testing the Boolean hypothesis in the non-convex case when a bounded grain can be assumed. Environmetrics, Wiley, 2008, 19 (2), pp.123-136. ⟨10.1002/env.860⟩. ⟨hal-02659993⟩

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