Identifying directional properties of spatial point patterns an investigation of two methods

Analyses of spatial point patterns tend to focus on deviations from randomness by either clustering or regularity. One assumption of these analyses implies that the point generating process is equal in all directions. However, the association of the location of points with a process biased in one or more directions is widely neglected due to a lack of appropriate statistical procedures. This is surprising, since patterns generated by directional processes are important in Geography. The purpose of this thesis is to investigate the blunt-triangle method and the third moment method for their potential of identifying directionality in spatial point patterns. A point process model is presented that combines the properties of both clustering and directionality. Realizations of this model are used with the objective of evaluating the two spatial analytical procedures. The blunt-triangle method is based on the comparison of blunt angles between triplets of points to theoretical blunt-triangle statistics. The failure of these statistics to find the characteristics given in the model can be explained by the dependence of the blunt-triangle method on assumptions of randomness. The third moment method examines the distributions of distances and angles between points, and is thus expected to be sensitive to a directional bias in spatial point patterns. It is shown that if the parameters of the procedure are chosen properly, different levels of directionality can be identified. The third moment method can thus be recommended for empirical applications in Geography