Approximation Methods in Discrete Spatial Density Analysis for Finite Populations

Abstract

The author's three-parameter square-root model for the measurement of discrete spatial density in human populations was previously derived under the assumption that exact coordinate locations of the density points were available. The model, called the population density index (PDI) model, has been expanded to include a set of routines for calculating two-dimensional spatial density measures based upon in situ geometric approximations of the interobject Euclidean distance measure for any finite sample size. The derivation and specification of the algorithm for the abbreviated calculation routines are presented and exemplified. The author has been able to apply the methods of the PDI model to submarine environments at the U.S. Naval Underwater Systems Center, resulting in several U.S. Patent applications.