A third order point process characteristics (Q2711682)

For a stationary point process, the authors consider a function \(T(r)\) which they define as the number of \(r\)-closed pairs in an \(r\)-ball centered at the typical point. This is a third-order characteristic of the process (as the intensity is a first order and Ripley's \(K\)-function is a second order characteristic). It can be used, e.g., to detect deviations from a Poisson model. The authors compute \(T(r)\) for Poisson, cluster-Poisson and Gauss-Poisson processes. They consider some estimators for \(T(r)\) by a sample. Simulation results are presented.