Discrete Manhattan and Chebyshev pair correlation functions in k dimensions

摘要: Pair correlation functions provide a summary statistic which quantifies the amount of spatial between objects in domain. While pair are commonly used to quantify continuous-space point processes, on-lattice discrete case is less studied. Recent work has brought attention case, wherein formed by normalizing empirical distances against probability distribution random lattice with Manhattan and Chebyshev metrics. These distance distributions typically derived on an ad hoc basis as required for specific applications. Here we present generalized approach deriving metrics, extending lattices k dimensions. We also variability functions, important understanding reliability confidence statistic.