Distances to a Point of Reference in Spatial Point Patterns

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Motivated by a study of social spider behavior, we discuss the distribution of the distances from all the events in a spatial point pattern to a point of reference that has a known location at a given moment of time. The distribution depends on both the shape of the region and the location of the point of reference. The empirical CDF is used to describe the distribution of the distances and compare it to the CDF derived under complete spatial randomness. Empirical distributions are then compared through time focusing on the case in which the point of reference changes with time.