 A simple probability model for spatially homogeneous points is the Poisson process in the plane with constant intensity function.Ripley's "K" and "L" functions  are closely related descriptive statistics for detecting deviations from spatial homogeneity.The "K" function (technically its sample-based estimate) is defined as

where "d""ij" is the Euclidean distance between the "i"th and "j"th points in a data set of "n" points, t is the search radius, λ is the average density of points (generally estimated as "n"/"A", where "A" is the area of the region containing all points) and "I" is the indicator function (1 if its operand is true, 0 otherwise).