DETECTING RANDOMNESS IN SPATIAL POINT PATTERNS: A "STAT-GEOMETRICAL" ALTERNATIVE

Abstract

There are several methods to test the hypothesis of complete spatial randomness of point patterns. This work involves a new geometrical-based strategy to detect spatial arrangements, which takes into account both Euclidean and angular distances, defining a triangle-based network. An asymptotic test based on the Kolmogorov-Smirnov statistic is proposed to accommodate this situation. To assess the usefulness of this method (Stat-Geo), simulations based on Monte Carlo procedures, conducted using SPLUS™, give satisfactory results with a high degree of accuracy. As expected, the new technique proposed in this paper, performs better than traditional ones like distance-based or angle-based, since more information (combining distance and angle) is introduced in the decision-making system. This approach is a very simple way to offer high efficiency results for a low computational cost. Furthermore, this alternative method allows barycentric interpolation of the unsampled points into a two-dimensional simplex (triangular) framework.