Abstract
This paper investigates a problem which arises when we wish to determine a region whose density is not less than a pre-determined density. It is observed that the area of the region varies according to the size of spatial data units although the density is fixed. To avoid this variation, we propose a 'variational' density which guarantees that the expected area of the region is invariant regardless of the size of spatial data units. As a simple example, the invariant density is explicitly obtained in the case of the Poisson point process.
