Explicit Formulas for an Area Based Edge Effect Correction Method and their Application to Ripley’s K-Function

In statistical point-pattern analysis, the most widely method used to minimize edge correction effects is Ripley's local weighting factor. It approximates the point density outside the study area basing on the ratio between the proportions of its search circle inside and outside this area. Since density is area-related, the question arises, why not use directly the proportions of the inside and outside areas of the search circle? What is the difference in performance and statistical power?
We compare the calculation time needed for both methods and the achieved statistical power using different tests: time processing, simulations with virtual experiments and real data sets.
In addition to the available literature, we present explicit formulas for the area based edge correction method applied to a study area with rectangular geometry and the maximum radius of the search circle restricted to a half of the shorter side of the study area. The comparison between Area's and Ripley's methods shows that Area's method is faster. This provides a higher quantity of tests during a reference period and, therefore, a better statistical power.
As long as the point-pattern process can be applied to a rectangular area, we recommend the use of Area's instead of Ripley's method for reducing edge effects in point-pattern analysis.