The K-function for nearly regular point processes.

Abstract

We propose modeling a nearly regular point pattern by a generalized Neyman-Scott process in which the offspring are Gaussian perturbations from a regular mean configuration. The mean configuration of interest is an equilateral grid, but our results can be used for any stationary regular grid. The case of uniformly distributed points is first studied as a benchmark. By considering the square of the interpoint distances, we can evaluate the first two moments of the K-function. These results can be used for parameter estimation, and simulations are used to both verify the theory and to assess the accuracy of the estimators. The methodology is applied to an investigation of regularity in plumes observed from swimming microorganisms.