Analysis of a spatial point pattern in relation to a reference point

This paper develops a new method for analyzing the relationship between a set of points and another single point, the latter of which we call a reference point. This relationship has been discussed in various academic fields, such as geography, criminology, and epidemiology. Analytical methods, however, have not yet been fully developed, which has motivated this paper. Our method reveals how the number of points varies by the distance from a reference point and by direction. It visualizes the spatial pattern of points in relation to a reference point, describes the point pattern using mathematical models, and statistically evaluates the difference between two sets of points. We applied the proposed method to analyze the spatial pattern of the climbers of Mt. Azuma, Japan. The result gave us useful and interesting findings, indicating the method's soundness.