The SPP Procedure

To compute the edge correction factors that appear in the formulas of the distance functions, the SPP procedure implements border edge correction  (Illian et al. 2008; Ripley 1988; Baddeley 2007). Border edge correction is necessary because the data are given for a bounded observation window W, but the pattern itself is assumed to extend beyond the observation window. However, because you can observe only what is within the window, a disc of radius r around a point x that lies close to the boundary of W might extend outside W. Because the original process X is not observed outside W, the number of points of X in is not observable (Baddeley 2007). Ignoring the fact that the observable quantity is less than or equal to leads to a bias that is caused by edge effects. The border edge corrector is a simple strategy to eliminate the bias that is caused by edge effects. Under the border method, the window W is replaced by a reduced window,

where denotes the minimum distance from X to a point on the boundary. The reduced window contains all the points in W that are at least r units away from the boundary .

Based on the preceding definition, the border edge corrected F, K, and G functions are

where ; is the observed nearest-neighbor distance, , for the ith point ; and is the distance from to the boundary . For more information about these border-edge-corrected functions, see  Baddeley (2007).