A statistical method for analyzing the relative location of points in a bounded region

This paper develops a statistical method for analyzing the relative location of points in a bounded region. The location of points in relation to the center of the region in which they are located is discussed. Four spatial objects called reference objects are defined to represent the relative location: (1) the boundary, (2) skeleton, (3) nucleus, and (4) global center: The distribution of distance between points and a reference object yields a cumulative distribution function, (CDF). Comparison of CDFs for a reference object allows us to analyze whether the points tend to be located close to the reference object or, for instance, whether the points are clustered around the center of the region. The significance of the CDF is statistically tested by Monte Carlo simulation. The method proposed is applied to the distribution of restaurants in retail clusters.