Poisson Ensembles in Three Dimensions

Abstract

The authors recently derived a method for assessing stochastic randomness in three dimensional Euclidean space. The method was derived from a nearest neighbor spatial Poisson process. An alternative probability model based on a box-counting method derived from a partial sum of a Poisson series is presented in this paper. The performance of the method is evaluated through Monte Carlo simulations with synthetically constructed random distributions. A comparison between the new discrete distribution method and the initial distance method showed that a greater likelihood of detecting randomness existed among populations with the box-counting method.