Generalized index for spatial data sets as a measure of complete spatial randomness

Abstract

Spatial data sets, generated from a wide range of physical systems can be analyzed by counting the number of objects in a set of bins. Previous work has been limited to equal-sized bins, which are inappropriate for some domains (e.g., circular). We consider a nonequal size bin configuration whereby overlapping or nonoverlapping bins cover the domain. A generalized index, defined in terms of a variance between bin counts, is developed to indicate whether or not a spatial data set, generated from exclusion or nonexclusion processes, is at the complete spatial randomness (CSR) state. Limiting values of the index are determined. Using examples, we investigate trends in the generalized index as a..